a positioning system with no line-of-sight restrictions for cluttered environments

7/23/2019 A Positioning System With No Line-of-sight Restrictions For Cluttered Environments

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A POSITIONING SYSTEM

WITH NO LINE-OF-SIGHT RESTRICTIONS

FOR CLUTTERED ENVIRONMENTS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF AERONAUTICS A ND ASTRONAUTICS

A ND THE COMMITTEE O N GRADUATE STUDIES

OF STANFORD U NIVERSITY

I N PARTIAL FULFILLMENT OF THE R EQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Eric A. Prigge

August, 2004



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I certify that I have read this dissertation and that, in my opinion, it is fully adequate inscope and quality as a dissertation for the degree of Doctor of Philosophy.

____________________________________Jonathan P. How, Principal AdviserDepartment of Aeronautics and Astronautics

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in

scope and quality as a dissertation for the degree of Doctor of Philosophy.

____________________________________

Stephen M. Rock

Department of Aeronautics and Astronautics

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in

scope and quality as a dissertation for the degree of Doctor of Philosophy.

____________________________________

Robert H. Cannon, Jr.Department of Aeronautics and Astronautics

Approved for the University Committee on Graduate Studies:

____________________________________



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Abstract

Accurate sensing of vehicle position and attitude is a fundamental requirement in

many mobile robot applications, but is a very challenging problem in the cluttered and

unstructured environment of the real world. Many existing indoor positioning systems

are limited in workspace and robustness because they require clear lines-of-sight or do

not provide absolute, drift-free measurements. Examples include overhead vision sys-

tems, where an unobstructed view must be maintained between robot and camera, and

inertial systems, where the measurements drift over time.

The research presented in this dissertation provides a new position and attitude

sensing system designed specifically to meet the challenges of operation in a realistic,

cluttered indoor environment, such as that of an office building or warehouse. The sys-

tem is not limited by line-of-sight restrictions and produces drift-free measurements

throughout an operating area that can span a large building. Accuracy of several

centimeters and a few degrees is delivered at 10 Hz, even when completely surrounded

by obstacles that would defeat existing approaches. Any number of the small sensor

units can be in operation, all providing estimates in a common reference frame.

This positioning system is based on extremely low frequency magnetic fields,

which have excellent characteristics for penetrating line-of-sight obstructions. Beacons



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located throughout the workspace create the low-level fields. A sensor unit on the mobile

robot samples the amplitude of the local magnetic field and processes the measurements

to determine its position and attitude.

This research overcomes limitations in existing magnetic-based systems. The de-

sign of the signal structure, based on pseudorandom codes, enables the use of multiple,

distributed beacons and greatly expands coverage volume. The development of real-time

identification and correction methods mitigates the impact of distortions caused by mate-

rials in the environment. A novel solution algorithm combats both challenges, providing

increased coverage volume and reduced sensitivity to materials. A prototype system was

built to demonstrate these new techniques.

This dissertation first examines the concept for the system and the challenges in

its development. The innovations that enable the system are then detailed, along with the

design of the prototype and results from experimental demonstrations. The positioning

system developed through this research provides an effective solution not only for mobile

robots navigating cluttered environments, but has application in other areas such as object

and personnel tracking, augmented reality, and construction.



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To my family,

Julie, Caleb, Rachel, Roger, Sherry, and Gretchen

Thank you for all the love, support, and joy.



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Table of Contents

1 Introduction

1.1 Uses for Positioning Systems

1.2 Positioning System Technologies

1.3 Research Goals

1.4 The Distributed Magnetic Local Positioning System

1.5 Research Solutions

1.6 Contributions

1.7 Thesis Roadmap

1.8 Summary

2 System Concept and Challenges

2.1 Magnetic Fields

2.1.1 Background

2.1.2 Dipole Magnetic Field

2.1.3 Interaction with Matter

2.1.4 Limitations in the Model

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2.2 Challenge: Sensitivity to Materials

2.2.1 Eddy Field Noise

2.2.2 Iron Noise

2.3 Challenge: Range

2.3.1 Numerous Beacons Distributed throughout Building

2.3.2 Further Issues Created by Numerous Beacons

2.4 DMLP System Concept

2.4.1 Beacon System

2.4.2 Sensor Unit

2.5 Summary

3 Signal Architecture

3.1 Signal Architectures Used in Existing Systems

3.2 New Signal Architecture Using Pseudorandom Codes

3.3 Comparison of Signal Structures

3.4 Distinguishing Beacon Fields with the New Signal Structure

3.5 Initialization

3.6 Optimality of the Signal Architecture

3.7 Summary

4 Eddy Field Noise Mitigation

4.1 Eddy Field Model

4.2 Detection and Mitigation Algorithm

4.3 Experimental Results

4.4 Summary

5 Solving for Position and Attitude

5.1 Survey of Solution Methods

5.2 New Solution Algorithm

5.2.1 Problem Statement

5.2.2 Position Estimation

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5.2.3 Attitude Estimation

5.3 Advantages of the New Solution Algorithm

5.4 Summary

6 Iron Noise Mitigation

6.1 Background

6.2 Introduction to the Approach

6.3 Iron Noise Model



6.6 Summary

7 The Prototype System

7.1 Overview

7.2 Beacons

7.3 Beacon Network

7.4 Sensor Box

7.5 Processor

7.6 Summary

8 Experimental Demonstrations

8.1 Test Results in an Uncluttered Environment

8.2 Test Results with Occlusions

8.3 Summary

9 Conclusions

9.1 Research Overview

9.2 Strengths and Limitations of the DMLP System

9.3 Future Investigation

9.4 Summary

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Appendix A – Examination of an Alternate Signal Architecture

A.1 Alternate Signal Architecture

A.2 Analysis

A.3 Results

A.4 Summary

Bibliography

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List of Tables

Table 2.1. Relative permeability of various materials (from [55]).

Table 7.1. Pseudorandom codes (written in octal notation) used in the pro-

totype system.

Table A.1. For various values of N and U , the average number of duplica-

tions in the simulated system is shown. Ten runs were made at each test

point, and the standard deviation of the number of duplications is given in

parentheses. The “*” designates that at least one of the ten simulations

encountered zero duplications.

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List of Figures

Figure 1.1. In this positioning system, the sensor unit (inset picture) de-

termines its location and attitude to guide the mobile robot throughout the

building.

Figure 1.2. A mobile robot delivering cargo.

Figure 1.3. Sony’s Aibo mobile robot for home entertainment.

Figure 1.4. A mobile robot in the Aerospace Robotics Lab at Stanford

surveys the landscape with an on-board camera.

Figure 1.5. Cye personal robot, from Probotics, uses odometry to navi-

gate. Note the wheels designed for minimal slipping.

Figure 1.6. A mobile robot uses the research positioning system to navi-

gate an “obstacle course” in a cluttered office environment. The inset pic-

ture shows real-time position estimates.

Figure 1.7. The DMLP system uses a network of beacons to permeate a

building with low frequency magnetic fields.

Figure 1.8. Four research innovations are motivated by the two

fundamental challenges.

Figure 2.1. Dipole magnetic field.

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Figure 2.2. The magnetic field vector measured at location P is the same

with (a) or without (b) the obstacle (for most materials).

Figure 2.3. An object in a beacon’s magnetic field creates a small mag-

netic field of its own. The vector sum of the two fields is measured at lo-

cation P.

Figure 2.4. Two examples of a sensor and a conductor in a changing bea-

con magnetic field. In (a), the eddy field causes the sensor to overestimate

the beacon field, while in (b) the eddy field causes the sensor to underes-

timate the beacon field.

Figure 2.5. Two examples of a sensor and an iron object in a beacon

magnetic field. In (a), the iron object’s field causes the sensor to underes-

timate the beacon field, while in (b) the iron object’s field causes the sen-

sor to overestimate the beacon field.

Figure 2.6. Two approaches to building-wide coverage. In (a), a small

number (only one is shown) of powerful beacons; in (b) a large number of

weaker beacons. Several factors dictate that the DMLP system must use

(b), numerous beacons.

Figure 2.7. Block diagram of the DMLP sensor signal processing chain.

Figure 3.1. Position error (m) versus number of beacons, considering

eddy noise. The TDMA and FDMA signal structures used in existing sys-

tems do not extend well to a large number of beacons.

Figure 3.2. Example magnetic field versus time, created by a beacon us-

ing the pseudorandom code signal structure.


eddy noise. The CDMA structure performs well even with a large number

of beacons.

Figure 3.4. Example “neighborhoods” of beacons.

Figure 3.5. A plot of “Quality Factor” versus beacon neighborhood is im-

portant in the initialization process to determine the correct neighborhood.

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eddy noise. The CDMA structure performs nearly as well as a hypotheti-

cal “optimal” structure.

Figure 4.1. Creation of eddy fields in the DMLP system. A beacon gen-

erates a time-varying magnetic field (a), creating potential differences in

the environment. This induced voltage (b) stimulates current flow (c) in

conductors, which in turn produces eddy fields (d).

Figure 4.2. Experiment used to verify the eddy field detection and mitiga-

tion technique.

Figure 4.3. Experimental results demonstrating the effectiveness of the

eddy field noise mitigation technique. When a metallic plate is placed

near the sensor (at 30 s), the Chapter 3 estimator reports an estimate of the

beacon field (B1z) that is 50% in error, while the Chapter 4 estimator is

only 11% in error. The binary, dimensionless signal “eddy indication” is

superimposed on the graph to indicate the transition from the Chapter 3 to

the Chapter 4 estimator.

Figure 4.4. Comparison of estimator performance with a metallic plate in

various positions and orientations. The Chapter 4 estimator performs bet-

ter than the Chapter 3 estimator, mitigating eddy field noise by approxi-

mately 74%.

Figure 5.1. In the DMLP system, the sensor measures the magnetic field

of each nearby beacon. Given these measurements, plus the known bea-

con locations and parameters, the solution algorithm produces an estimate

of the sensor position and attitude.

Figure 5.2. Comparison of existing and new solution methods.

Figure 5.3. The coverage volume of one coil is shown in (a). In (b), a

cross section of the coverage volume of three coils is depicted. Volume I

is covered by all three coils, while volume U is covered by one or more

coils.

Figure 5.4. Example placement of beacons in a building.

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Figure 5.5. A cross section view of the coverage volume of four triple-

coil beacons is shown. In (a), existing solution methods may be used. In

(b), the new solution may be used. The new solution algorithm allows the

beacons to be spaced further apart for the same power consumption, while

still providing continuous coverage.

Figure 5.6. The placement of beacons is shown for three different cases:

(a) triple-coil beacons and existing solution method A, (b) triple-coil bea-

cons and new solution method B, and (c) single-coil beacons and new so-

lution method B. Case (c) allows 21% more coverage volume (for the

same power consumption) than case (a) while requiring only 1/3 of the

frequency content (lowering eddy noise).

Figure 6.1. In this one-dimensional example, the sensor measures the

fields produced by two beacons.

Figure 6.2. An iron mass is placed next to the sensor in the one-

dimensional example. The iron, stimulated by the beacon fields, creates a

field of its own and causes the sensor to overestimate the size of the bea-

con signals. This iron noise causes error in the position estimate, but its

presence can be detected in the residuals.

Figure 6.3. The field produced by the iron in response to beacon i is mod-

eled as a dipole directed along vector Bic.

Figure 6.4. The magnitudes of two residual vectors rise measurably as a

ferromagnetic mass is placed near the sensor, triggering an indication that

iron noise is present.

Figure 6.5. Once iron is indicated, the effects of iron noise on each vector

component of each beacon signal are estimated.

Figure 6.6. An iron mass is placed next to the sensor (at approximately 17

s), causing a 28% error in the estimate of B1x. With the mitigation algo-

rithm, the estimate of B1x is only 7.2% in error.

Figure 6.7. The iron mass causes a 30% error in the estimate of B2x. The

mitigation algorithm reduces the error to 13%.

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Figure 7.1. A prototype beacon. In the DMLP system, beacons generate

low frequency magnetic field signals that permeate a building.

Figure 7.2. Prototype beacons consist of a coil, power amplifier, and a

beacon electronics box (containing the functionality inside the dashed

line).

Figure 7.3. Relationship between the command signal, amplifier drive

voltage, and coil current in a prototype beacon.

Figure 7.4. The beacon network is used to synchronize and monitor the

beacons.

Figure 7.5. The “Sync” signal, carried by the beacon network to all bea-

cons.

Figure 7.6. The prototype sensor box takes vector magnetic field meas-

urements and reports them to the processor. The sensor semiconductors

are located under the circle.

Figure 7.7. Block diagram showing the functionality inside the sensor

box.

Figure 7.8. Implementation of the signal processing chain inside the

processor.

Figure 8.1. The prototype DMLP system and experiment area.

Figure 8.2. A typical experiment. The sensor box (mounted on the tripod)

takes measurements of the magnetic field vector while the laptop com-

puter processes the data to determine position and attitude. The results

can be compared to the grid truth system.

Figure 8.3. Graph of position estimates (in the horizontal plane) generated

by the DMLP sensor in nine separate locations.

Figure 8.4. The sensor is pulled along a track.

Figure 8.5. Sensor X-Y position estimates as it is travels along the grid

lines x=2 m and y=2 m.

Figure 8.6. Wider view of the prototype DMLP experiment area, showing

the non-ideal environment.

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Figure 8.7. The sensor accurately estimates its position and attitude even

though surrounded by over 100 kg of wood and concrete.

Figure 8.8. The sensor accurately estimates its position and attitude even

though it is inside two steel bowls (one above and one directly below).

Figure 8.9. The sensor maintains accurate position and attitude estimates

even though a substantial cast iron object is placed only centimeters away.

Figure 8.10. The sensor generates accurate position and attitude estimates

even inside a steel can.

Figure 8.11. The sensor slides along a track through a steel duct.

Figure 8.12. Experimental results (X-Y position estimates) while sliding

the sensor along the track shown in Figure 8.10, with and without the steel

duct occlusion. The rectangle represents the location of the occlusion.

Figure 8.13. The sensor is moved around on a grid, and various objects

are placed over it, while the estimate of position and attitude is displayed

in real time.

Figure 8.14. The DMLP system is used to navigate a robot through a clut-

tered office environment. The laptop screen (inset picture) displays the

position estimates.

Figure 9.1. The DMLP system provides position and attitude sensing even

in cluttered environments.

Figure 9.2. Numerous beacons distributed throughout a building create

low frequency magnetic fields.

Figure 9.3. The signal architecture presented in Chapter 3 reduces eddy

noise in a system with many beacons.

Figure 9.4. Chapter 4 presents an algorithm to detect and further mitigate

eddy field noise.

Figure 9.5. Chapter 5 presents an algorithm to estimate the sensor position

and attitude.

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Figure 9.6. An algorithm to detect and mitigate the effects of ferromag-

netic materials is presented in Chapter 6.

Figure 9.7. Chapter 7 examines the design of a prototype DMLP system.

Figure 9.8. In Chapter 8, experimental results using the prototype DMLP

system demonstrate position and attitude sensing even in cluttered envi-

ronments. In (a), left, the sensor operates normally even though sur-

rounded by construction materials. In (b), right, a mobile robot uses the

system to navigate a cluttered office environment.

Figure 9.9. The DMLP system could be rapidly deployed using emer-

gency vehicles.

Figure 9.10. Concept for “linear” DMLP beacons.

Figure 9.11. Concept for distributed metal detection.

Figure A.1. The beacons in the simulation are arranged in a regular lat-

tice. Each “panel” in this lattice has four beacons at its corners.

Figure A.2. Predicted position error (m) versus number of beacons, con-

sidering eddy noise. The alternate signal structure performs significantly

better than straightforward TDMA and FDMA structures, approaching the

performance of the Chapter 3 CDMA signal architecture.

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1

1 Introduction

This dissertation describes a positioning system, a means of determining the loca-

tion and attitude of an object in three dimensions. Accurate sensing of location and atti-

tude is valuable in a wide variety of applications, from tracking firefighters in a burning

building to guiding a cleaning robot across a living room floor. However, the measure-

ment of position and attitude is a very challenging problem in the cluttered real world

(i.e., outside of a structured laboratory environment). The positioning systems that are

currently used are generally limited in workspace and robustness because they require

clear lines-of-sight. For example, an overhead vision system (a common type of robot

positioning system) requires an unobstructed view to be maintained between robot and

camera. Alternatives, such as odometry or inertial systems, do not provide absolute,

drift-free measurements and thus accumulate errors over time and distance.

The research presented in this dissertation provides a new position and attitude

sensing system designed specifically to meet the challenges of operation in a realistic,

cluttered indoor environment, such as that of an office building or warehouse. The sys-

tem is not limited by line-of-sight restrictions, and produces drift-free measurements

throughout an operating area that can span a large building. Accuracy of several centi-

meters and a few degrees is delivered at 10 Hz, even when completely surrounded by ob-



2

stacles that would defeat existing approaches (such as an overhead vision system). The

system is designed so that any number of the small sensor units can be in operation, all

providing position estimates in a common reference frame.

This positioning system is based on extremely low frequency magnetic fields,

which have excellent characteristics for penetrating line-of-sight obstructions. Inexpen-

sive beacons located throughout the workspace are used to create the low-level magnetic

fields. A sensor unit on the mobile robot samples the local magnetic field vector and

processes the measurements to determine its position and attitude.

This thesis covers the system concept, the challenges in its development, and the

research solutions that make it possible. This introductory chapter first expands on the

motivation behind the research effort. The uses for positioning systems, in applications

from robotics and construction to home automation and augmented reality, are briefly

examined. The strengths and limitations of existing positioning systems are then pre-

sented, which motivates the design goals for a new, “go-anywhere” local positioning sys-

tem. An overview of the system developed through this research, and how it is especially

suited for indoor operation, is then presented. This first chapter only introduces the fun-

damental challenges and the research solutions that enable the system. A roadmap for the

rest of this work is then provided, directing the reader to further information on the vari-

ous aspects of the system.

1.1 Uses for Positioning Systems

A positioning system, in this work, describes a means of determining the location

and orientation of an object. An example is depicted in Figure 1.1, where a small sensor

unit (inset picture) can determine its position and attitude, with respect to the building-

fixed coordinate frame, as it is carried throughout the building by the mobile robot. Posi-

tioning systems are useful, even required, in a broad range of applications. One example,

the application that served as the primary motivation for this research, is mobile robot

navigation. Mobile robots are no longer just the dream of futurists – they can be found

today making significant contributions in a surprising array of tasks. Their use ranges

from the mundane (e.g., automated inspection tasks [1], floor sweepers [2]) to the dan-

gerous (e.g., construction [3], work in hazardous environments [4]). They cut the costs of



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routine operations (e.g., delivery in manufacturing plants, office buildings, or hospitals

[5]) and provide services for the elderly [6]. Automated Guided Vehicles (AGVs), such

as the cargo transport shown in Figure 1.2, are heavily used in industrial applications [7].

Mobile robots are also finding their way into a growing number of homes, providing se-

curity [8], automation [9], and even entertainment (Figure 1.3). In each of these tasks,

some type of positioning system is essential – autonomous mobile robots must have some

means of estimating where they are and which direction they are heading in order to

navigate to their destination.

Demand for position and attitude information is not exclusive to the realm of mo-

bile robots. Knowledge of a person’s location is useful in many applications, such as

tracking firefighters, shoppers, and children [10]. Information about the location of an

inanimate object, for example a cargo pallet, can streamline inventory and enable ware-

house automation. A positioning system tasked with measuring a person’s joint and limb

locations is used for motion capture [11], a staple in the entertainment and medical indus-

tries. In the exciting field of augmented reality [12], where a person’s visual field of

view is overlaid with extra information, positioning systems are used to track head loca-

tion and gaze direction. In the construction industry, where measurements are taken re-

Figure 1.1. In this positioning system, the sensor unit (inset picture) determines

its location and attitude to guide the mobile robot throughout the building.



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peatedly to find the location for every wall, window, pipe, outlet, and fixture, efficiency

can be improved with a device that can immediately pinpoint its coordinates on the con-

struction site.

These examples only touch upon the diverse ways positioning systems are already

in use. Up-to-date information on the latest applications for positioning systems can be

found in publications such as [13-17]. For a concrete example of how a positioning sys-

tem can bring value to a specific application, the reader is referred to Chapter 9 of this

thesis. A brief case study is presented there of the potential benefits of a local positioning

system (specifically, the positioning system developed in this research) applied to the In-

ternational Space Station. In this one example alone, a local positioning system could

prove advantageous in several ways, including automated inspection, easier docking, en-

hanced astronaut communication (through augmented reality), and improved robotic arm

performance.

Figure 1.2. A mobile robot delivering cargo.



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1.2 Positioning System Technologies

Although accurate sensing of position and attitude is essential for a broad range of

applications, it is still a very challenging problem in the cluttered and unstructured envi-

ronment of the real world. A variety of technologies have been developed, and used suc-

cessfully, to provide position and attitude information. However, many of these existing

positioning systems are inherently limited in their workspace and robustness. These limi-

tations generally fall into two main categories: line-of-sight restrictions and lack of abso-

lute, drift-free measurements. A brief overview of existing positioning techniques, and

their limitations, is presented in this section to motivate the usefulness of a new position-

ing system – the focus of this research.

As a first example, consider a common positioning method where cameras are

mounted on the ceiling, tracking LEDs or markings on a robot (an overhead positioning

system) [18, 19]. This straightforward approach provides an accurate estimate of robot

position and orientation as long as an unobstructed view is available. However, when

this technique is taken from a structured laboratory environment into a real office build-

ing, the results can be unsatisfactory – tables, desks, modular walls, and people may ob-

Figure 1.3. Sony’s Aibo mobile robot for home entertainment.



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struct the line-of-sight between camera and robot. Thus, the robot’s workspace may con-

strained by the limitations of the positioning system (e.g., passable areas declared “off-

limits” simply because the camera’s view is blocked). Further, robustness suffers – the

system may lose track unexpectedly simply due to the motion of people or objects in the

environment.

Other common positioning techniques reverse the architecture, but the same line-

of-sight restrictions still apply. Several methods place the camera on the robot, tracking

markings or features of the building (Figure 1.4). This is an exciting area with much ac-

tive research [20, 21], and enjoys success in many environments. Fundamentally, how-

ever, clear lines-of-sight to the targets are still required. For example, when a robotic

vacuum travels under a bed, the targets in the room (e.g., intersections of walls, corners

of doorframes, etc) are obscured. This technique can also be sensitive to lighting condi-

tions and changes in scenery.

Although line-of-sight restrictions obviously apply to vision-based positioning

systems, this limitation also occurs for many other positioning systems. For example,

Figure 1.4. A mobile robot in the Aerospace Robotics Lab at Stanford surveys

the landscape with an on-board camera.



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positioning systems have been developed based on the time-of-flight of ultrasonic pulses

between mobile emitters and receivers fixed to the building [22]. Obstacles, or even air

currents, along the lines-of-sight can cause a delayed signal to be received, or no signal

altogether, distorting the position estimate. Metrology systems based on infrared light

[23] provide incredibly accurate position information. However, again, obstacles block

the beams and limit the system’s utility in a cluttered environment.

Finally, line-of-sight restrictions also affect positioning systems based on radio

waves. The most familiar system of this type is the Global Positioning System (GPS),

which has achieved wide success in outdoor applications from aircraft navigation [24] to

farming [25]. GPS receivers use precise timing measurements of the radio frequency

(RF) signals from several satellites to estimate location. Other RF localization systems

use signals from cellular phones [26], digital television broadcasts [27], LORAN stations

[28], broadcast radio stations [29], military communication links [30], Ultra-Wideband

(UWB) transmitters [31], and wireless Ethernet stations [32]. RF systems enjoy long

ranges and low power consumption, but, fundamentally, electromagnetic waves are

blocked by certain line-of-sight obstructions, particularly metallic ones, and delayed, re-

fracted, and attenuated by many others [33, 34].

The positioning techniques presented so far have been limited, it has been argued,

by line-of-sight restrictions. However, another characteristic shared by many of these

systems poses a secondary drawback. Consider the overhead vision system, described

previously, tracking LEDs on a robot moving along the floor. While one LED on the ro-

bot is sufficient if only the location is needed, two LEDs are required to determine orien-

tation (considering only one rotational degree of freedom). The further apart these mark-

ings are (i.e., the greater the baseline between them), the greater the orientation accuracy.

Similarly, systems based on time of flight measurements (GPS, etc) require multiple an-

tennas, with baselines between them, to produce accurate attitude information. Thus

these systems fundamentally require a certain vehicle size for attitude measurements, no

matter how small the electronics can be made. Therefore, because of this requirement for

a baseline, none of these techniques may be appropriate for determining the attitude of a

small vehicle such as a “micro” air vehicle.



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Of course, other types of existing positioning systems avoid line-of-sight restric-

tions, and baselines, altogether, but these are typically limited because of drift (i.e., errors

in the position estimates accumulate over time and distance). For example, inertial

measurement units integrate acceleration data, and can estimate the position of a vehicle

with no external inputs. However, these position estimates degrade rapidly over time – a

robot using this system cannot return to the same location from one maneuver to the next.

Realistically, the position estimate of low cost units can drift by meters over the course of

just a few minutes [35, 36].

Odometry, keeping track of the wheel revolutions of a robot to estimate its mo-

tion, is perhaps the most common positioning technique among low-cost mobile robots

(Figure 1.5). The advantage of this method is similar to that of inertial systems – the ro-

bot can go anywhere, with no requirements for clear lines-of-sight to any part of the

building. However, the position estimate error typically accumulates rapidly – in prac-

tice, several centimeters of drift can occur after only a few turns, even on a good surface

[37]. Thus, this method is of limited use for a building-wide robotic application.

Figure 1.5. Cye personal robot, from Probotics, uses odometry to navigate. Note

the wheels designed for minimal slipping.



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To conclude this brief survey of positioning systems, a final approach must be

discussed that is very interesting, and, in fact, was the inspiration for this research. Posi-

tioning systems based on extremely low frequency (ELF) magnetic fields [38, 39] offer

an intriguing alternative because they provide position and attitude sensing with no line-

of-sight restrictions and absolute, drift-free measurements. In these systems, beacons

drive current through coils of wire, creating low frequency magnetic fields that have ex-

cellent characteristics for penetrating line-of-sight obstructions. A mobile sensor unit can

sample the local magnetic field, distinguish the fields produced by the individual bea-

cons, and then solve for its position and attitude relative to the beacon-fixed frame. As

explained in Chapter 2, the ELF beacon fields are not affected by most types of objects,

so this approach can be used in an environment (such as an office or warehouse) with

many obstructions.

Existing magnetic systems work well in the applications they were designed for,

such as digitizing body motion as an actor moves on a stage. However, two main chal-

lenges have prevented existing magnetic field systems from achieving widespread use as

mobile robot positioning systems. The first is their short range. The coverage volume of

existing systems is, at most, on the order of a 10 m sphere – “room-sized” rather than

“building-wide”. The second challenge is sensitivity to certain types of materials. The

area of operation in a motion capture performance can be well controlled, kept free of

metallic masses which can introduce distortion. The physics underlying these two chal-

lenges is introduced later in this chapter, and explored in greater detail in Chapter 2.

Further information about a broad variety of positioning systems can be found in

[40-43].

1.3 Research Goals

All of the positioning system techniques mentioned have merit, and have been

used successfully. However, several limitations have been discussed:

• Line-of-sight restrictions (e.g., vision, ultrasound, RF systems)

• Drifting measurements (e.g., inertial, odometry systems)

• Limited range, sensitivity to materials (e.g., existing magnetic field systems)

• Baselines required for attitude information (e.g., overhead vision, GPS)



10

These limitations can be seen as opportunities for improvement. Many applications that

depend on position measurements could benefit from the development of a new position-

ing system technology that alleviates these restrictions.

The goal of this research, then, is to provide a new position and attitude sensing

system designed specifically to meet the challenges of operation in the cluttered, real-

world indoor environment. The system developed through this research, introduced in

the next section and detailed in the rest of this work, has the following characteristics,

which make it especially suited as a practical indoor positioning system:

1. No line-of-sight restrictions. The sensor functions in a cluttered environment

(i.e., even when surrounded by obstacles). Position measurements continue when

an unforeseen obstacle moves into the workspace or the lighting changes. For

automation applications, this means a cleaning robot can travel under a bed or

next to a table. For personnel tracking, the sensor can be conveniently placed in a

pocket, or can track a soldier diving under cover in a military training exercise.

At a construction site, the sensor can be used to find the location to drill a mount-

ing hole, even if it is inside a cabinet.

2. Absolute, drift-free estimates. The position and attitude estimates of all units are

made with respect to the same, building-fixed coordinate frame. Estimates do not

drift over time, enabling a robot to return to the same location after each maneu-

ver.

3. Building-wide coverage. The sensor operates throughout the volume of an entire

apartment complex or office building. The robots are not limited to the “room-

sized” coverage volume of existing magnetic-based systems or constrained to

move only along guide wires [44].

4. Accuracy suitable for robot navigation. The system provides measurements with

accuracy on the order of a few centimeters and degrees at 10 Hz. This makes it

suitable for common mobile robot tasks such as maneuvering through doorways.

The system is sensitive to certain materials, but accuracy of several centimeters is

maintained even when the sensor comes close to a large mass of metallic material.

5. Small, low power sensor. The system makes vector measurements at one point in

space to determine attitude – no baselines are required. The electronics in the



11

mobile component of the system are small and low power. Thus, this system may

be well suited for “micro” air vehicles.6. Potential for no FCC restrictions. The Federal Communications Commission

(FCC) regulates the use of the electromagnetic spectrum in the United States. A

drawback to RF positioning systems is that they may cause interference with other

RF communication or positioning systems (e.g., [45] discusses the potential con-

flict between UWB and GPS). The system developed in this research does not in-

tentionally radiate electromagnetic waves. Small spurious EM emissions are gen-

erated by its operation, but these are at frequencies below where the FCC regu-

lates [46]. Thus, the system may face fewer hurdles in its adoption.

This system, therefore, was designed to be a practical position and attitude sensor

for realistic, cluttered environments. To provide a concrete picture of the type of applica-

tion this system is targeted for, a brief preview of the system in operation is presented in

Figure 1.6. A mobile robot uses the research positioning system to navi-

gate an “obstacle course” in a cluttered office environment. The inset picture

shows real-time position estimates.



12

Figure 1.6. The picture shows a prototype system where a mobile robot is navigating an

“obstacle course” in a mock office environment. The robot maintains centimeter level

knowledge of position (plotted in the inset picture) at 10 Hz as it travels between desks,

under a table, or through an air-conditioning duct. The small sensor unit on the robot is

completely obscured from the building-fixed components of the system (the beacons) for

much of the route, yet continues to provide drift-free estimates of location and attitude.

So have the challenges of indoor position sensing now been completely solved?

Does this thesis detail the final answer? Of course not – like every other positioning sys-

tem technology, this system has its strengths and weaknesses. In the field of positioning

systems, and typically in engineering in general, no single system is best for all situa-

tions. This research provides a solution that can bring value to certain applications, but it

is inappropriate for others. In Chapter 9, after the system has been described in detail,

conclusions are drawn about the pros and cons of the system. Appropriate applications

are described along with scenarios where it is of limited use. Further, several potential

opportunities to improve upon this system are conceived in Chapter 9.

1.4 The Distributed Magnetic Local Positioning System

To meet the research goals and provide positioning service throughout a cluttered

building, a system was developed based on extremely low frequency (ELF) magnetic

fields. Inexpensive beacons located throughout the building create the low-level fields

(smaller than the earth’s magnetic field). The beacons are approximately the size of a

bicycle wheel, and, since the ELF magnetic fields have excellent characteristics for pene-

trating line-of-sight obstructions, can be installed in unobtrusive locations, such as the

crawlspace between the ceiling and the floor of the next level. The graphic in Figure 1.7

depicts the beacons in this distributed magnetic local positioning (DMLP) system in a

warehouse.

Using the information from the beacon magnetic fields, a small, low-power sensor

unit can determine its position and orientation anywhere in the building. The sensor unit

samples the local magnetic field (a vector quantity) and distinguishes the components of

the field produced by individual beacons. Measurement of the fields from several bea-

cons, along with the known beacon locations and field shapes, allow the sensor to solve



13

for its position and attitude. The ELF beacon fields are not significantly affected by most

objects in the environment, allowing the sensor and beacons to be separated by the ob-

structions common in an office or warehouse. The position and attitude estimates are

made with respect to the building-fixed beacons, allowing all sensor units to provide

drift-free position information in a common reference frame.

However, the use of ELF magnetic fields, though vital in obtaining “go-

anywhere” performance, introduces two challenges that must be overcome to make a

practical, building-wide positioning system. These two challenges, a fundamentally short

range and a sensitivity to certain materials, have prevented existing positioning systems

from achieving widespread use as robotic position sensors.

The first challenge is that certain materials in the environment may introduce

noise into the measurements. Eddy field noise is caused by the interaction of the beacon

fields with conductive objects. The time-varying magnetic fields induce electric currents

to flow in conductors in the environment. These currents, in turn, create magnetic fields

(eddy fields) of their own, summing with the beacon fields and introducing errors into the

position estimates. Further, ferromagnetic objects (mainly iron and certain types of steel)

cause an additional type of error. When exposed to a magnetic field, such as a beacon

Figure 1.7. The DMLP system uses a network of beacons to permeate a building

with low frequency magnetic fields.



14

field, microscopic regions known as domains respond by growing or shrinking. The re-

sult is that the object itself produces a net magnetic field, which superimposes with the

beacon fields and introduces error in the position solution. Chapter 2 provides an in-

depth examination of these noise sources.

The second challenge is the fundamentally short range of magnetic field systems

– the signals generated by the beacons diminish rapidly with distance. When several fac-

tors are considered, such as beacon power consumption, dynamic range, and system ac-

curacy, it is apparent that numerous beacons are needed to cover a large building, not just

a few high power beacons. However, neither the signal structure nor the position and at-

titude solution algorithms that are used in existing systems are suitable for a system with

numerous beacons. Chapter 2 examines this challenge as well.

1.5 Research Solutions

Several innovations were developed through this research [47,48] to confront

these challenges and enable a positioning system uniquely suited for indoor operation.

These innovations can be categorized into four areas: the design of an advantageous sig-

nal architecture, the development of a new position and attitude estimation algorithm, and

the identification of two noise correction techniques. The relationship between the fun-

damental challenges and the research effort are shown in Figure 1.8.

The first research innovation, an alternate signal architecture, attacks both primary

challenges by allowing a large number of beacons to operate at lower overall frequencies

than with alternative signal structures. This allows the positioning system to achieve

building-wide coverage volume with greatly reduced eddy field noise.

The second research innovation is the solution algorithm – the nonlinear process

that takes the measurements of the magnetic fields produced by the beacons and returns

an estimate of sensor position and attitude. The new solution algorithm has several ad-

vantages over existing methods, but two are particularly useful: the algorithm allows the

use of numerous beacons, and a single beacon coil may be placed at each location. These

advantages enable a building-wide coverage volume, greater efficiency (in terms of cov-

erage volume per power consumption), and reduced eddy field noise.



15

Although eddy field noise is reduced by both the signal architecture and the solu-

tion algorithm, it is not eliminated entirely. In fact, in certain environments, it can still be

one of the largest error sources. Therefore, an algorithm was developed to detect and

correct for eddy field noise. The technique is based on a model of the eddy fields created

by the pseudorandom beacon signals. Experimentally, the correction proves to be quite

successful, reducing the effects of eddy noise by an average of 74%.

Finally, mitigating the distortion caused by ferromagnetic objects proves to be

quite problematic. The effects of this noise cannot be detected through the signal from

any individual beacon. However, this disturbance can be observed by considering a col-

lection of several beacon signals. An algorithm was developed to detect and mitigate this

noise. Experimentally, the method reliably detects the presence of iron distortion, and

provides an average of 40% mitigation.

Figure 1.8. Four research innovations are motivated by the two fundamental

challenges.

Short range requires many

beacons

Eddy field noise

mitigation (chapter 4)

Iron noise mitigation

(chapter 6)

New signal architecture

(chapter 3)

New solution algorithm

(chapter 5)

ResearchChallenges

Need new signal

architecture

Need new solution

algortihm

Sensitive to certain materials

Eddy field noise

Ferromagneticdistortion



16

1.6 Contributions

As described in the previous section, this research resulted in several contribu-

tions to help further the state-of-the-art in the field of positioning systems. Specifically,

this research has:

1. Pioneered a new type of positioning system especially suited for the cluttered en-

vironment of the real world. This marks the first time all of these useful charac-

teristics have been provided in a single positioning system:

• No line-of-sight restrictions

• Drift-free measurements in a common, absolute frame

• Building-wide coverage volume

• Accuracy of a few centimeters and degrees

Thus, this research provides a sensing system well suited for mobile robot naviga-

tion, and numerous other applications, amid the obstacles that clutter a typical

building.

2. Designed a signal structure that allows a magnetic field positioning system to at-

tain building-wide coverage. This new signal structure, based on pseudorandom

codes, allows the use of numerous beacons while maintaining low eddy field

noise.

3. Developed a new solution algorithm to estimate position and attitude. This new

algorithm enables the use of numerous, distributed beacons, each with only one

coil per beacon. This is shown to significantly increase the coverage volume, in-

crease efficiency (coverage volume per power consumption), and reduce the

amount of eddy field noise.

4. Produced a technique to mitigate eddy field noise. Working within the new signal

structure, this novel algorithm detects the effects of eddy fields and forms a real-

time correction. Thus, this algorithm mitigates one of the dominant noise sources

in magnetic field positioning systems.

5. Developed an algorithm to mitigate distortions due to ferromagnetic materials.

This novel algorithm examines the magnetic field measurements for the signature

of ferromagnetic distortion and, if “iron noise” is detected, characterizes the



17

source and computes a correction. The algorithm reliably detects iron noise and

modestly reduces its effects.

6. Experimentally demonstrated position and attitude sensing in the cluttered real

world. A prototype system verifies the various techniques developed through this

research, and demonstrates a position and attitude sensing system especially

suited for operation in a cluttered environment.

1.7 Thesis Roadmap

The detailed presentation of this research must begin with background informa-

tion on magnetic fields, the fundamental phenomena of nature used in the positioning

system. The questions often arise: “What are magnetic fields?” and “Why use them as

the basis for this positioning system?” Chapter 2 tackles these questions with an introduc-

tion to magnetism. Coverage includes how magnetic fields are created and the character-

istics that make ELF magnetic fields so appropriate for this local positioning system.

With that background on magnetic fields, Chapter 2 then progresses with a de-

tailed analysis of the challenges to the system. Dominant noise sources, such as eddy

field noise and ferromagnetic distortion, are detailed, from the underlying physics to their

specific effects on the accuracy of the positioning system. The chapter also considers the

second challenge, the intrinsically short range of the signals. Finally, the system concept

is examined in greater detail than the brief preview presented in this chapter. This dis-

cussion of the beacon magnetic fields, their characteristics, and the system challenges sets

the stage for, and is fundamental to the understanding of, the rest of the work.

Chapters 3 through 6 then present the research solutions used to overcome the

challenges detailed in Chapter 2. The research innovations are arranged in the order in

which they appear in the signal processing chain inside the sensor unit. First, Chapter 3

confronts the issues involved with selecting the structure of the beacon signals. The ar-

chitecture of these signals proves to be critical, and a new structure is presented that ex-

tends well to large numbers of beacons while maintaining low overall eddy field noise.

The signal processing that goes inside the sensor box to make use of this signal structure

is also detailed. Chapter 4 continues the processing by adjusting the beacon field meas-

urements to further mitigate the effects of eddy field noise. Chapter 5 then describes an



19

2 System Concept and Challenges

The DMLP system is designed for the challenging task of providing position and

attitude measurements in a cluttered indoor environment, such as an office building or

warehouse. The first chapter introduced the concept for the system and briefly previewed

the challenges in its development. This chapter expands on that discussion, examining

both the concept for the system and the challenges in detail. This material is necessary

for understanding the next four chapters, where innovations are presented which address

these challenges and enable the DMLP system.

The positioning system operates by measuring the amplitude of magnetic fields.

The first topic presented, therefore, is background information on this phenomenon of

nature. The basic equations that mathematically model magnetic fields, and the experi-

mental observations from which these models are derived, are introduced. The character-

istics of magnetic fields, such as their interaction with objects in a cluttered environment,

are then discussed. In particular, the “quasi-steady-state” fields that are used in the

DMLP system are examined. These magnetic signals operate in the extremely low fre-

quency (ELF) band and are unaffected by the presence of most materials and objects

found in many buildings, making them well suited for this “go-anywhere” positioning

system.



20

After this background on magnetic fields, the first of two fundamental system

challenges is examined: positioning systems based on magnetic fields are sensitive to cer-

tain materials. Although ELF magnetic fields are unaffected by most materials in the en-

vironment, there are two primary mechanisms by which materials can introduce error into

the position and attitude estimates. The interaction of time-varying magnetic fields with

conductors in the environment leads to eddy field noise. Further, ferromagnetic materials

can distort even a steady state magnetic field. This effect is referred to as iron noise, af-

ter the principle offending material. The physics underlying these noise sources, and

their effects on a positioning system, are explored.

The second challenging factor for the building-wide DMLP system is the inher-

ently short range of the beacon magnetic fields. An analysis is presented to demonstrate

that, because of this short range, numerous beacons are needed to achieve a large cover-

age volume, not simply a few high-powered beacons. However, this raises two further

issues: both the signal structures and the solution methods used in existing systems are

not appropriate for systems with numerous beacons. A new signal architecture and a new

algorithm to solve for position and attitude are required. These issues are introduced

here, then further described in their respective chapters (Chapter 3, Signal Architecture,

and Chapter 5, Solving for Position and Attitude).

With this background – an introduction to magnetic fields and an examination of

the challenges in using them – the system concept can be presented in greater detail than

the brief preview of the first chapter. The beacon system, responsible for creating the

magnetic fields, and the sensor unit, which measures the fields and processes the data, are

described. The signal processing chain is then examined, linking each of the innovations

in the next chapters into its proper place in the system. This serves as a roadmap, clarify-

ing how the research solutions in the next four chapters answer the challenges raised in

this one.



21

2.1 Magnetic Fields

2.1.1 Background

Magnetism, as a phenomenon of nature, has been known since ancient times (an

engaging history of both the events and personalities can be found in [49]). It is interest-

ing to note that one of the first practical applications of magnetism was, in fact, as a posi-

tioning system – the compass and the earth’s magnetic field provided one of man’s earli-

est forms of navigation. Electricity and magnetism were long studied and explained as

two separate phenomena of nature. The breakthrough discovery by Oersted in 1820, that

electrical current creates a magnetic field (and deflects a compass needle), established the

connection between these primal forces and initiated the modern understanding of mag-

netism.

A simple experimental observation forms the foundation for the theory of magne-

tostatics: two parallel wires, each carrying electrical current, exert force on each other.

This observation is of such a fundamental nature that it is used to define basic units such

as the Ampere (current) and Coulomb (charge). To explain and mathematically model

this “action at a distance,” scientists use the concept of a magnetic field. That is, it is un-

derstood that a wire carrying an electrical current creates a magnetic field in space. Other

electrical currents (e.g. the second wire) then interact with the magnetic field at their par-

ticular location in space, and a force may result.

To calculate the magnetic field at a point in space created by a current, the Biot-

Savart law is used:

2

0

4 r

I r dl dB

)×

=π

µ (2.1)

where dl = differential length of current carrying wire

dB = differential contribution to the magnetic field

I = current flowing through dl

µ 0 = a constant known as the permeability of free space ( µ 0 = 4π x 10-3

G m/A)

r = vector from the current carrying wire to the point in space where the field is to

be calculated, with magnitude r and direction r .



22

The interaction of a current carrying element of wire and a magnetic field is

mathematically described using the Ampere force law:

Bdl dF ×= I (2.2)

where dF is the differential contribution of element dl to the resulting force.

The experimentally derived models provided by equations 2.1 and 2.2 have been

verified to an incredible degree – for example, [50] establishes the accuracy of the expo-

nent of r in the denominator of equation 2.1. The basic concepts and mathematical tools

introduced here will be of use in later sections. Further information on magnetism can be

obtained through references such as [51-53].

2.1.2 Dipole Magnetic Field

The Biot-Savart law may be used to compute the magnetic field created by a cir-

cular loop of wire. Consider a steady electrical current flowing through a circular coil of

wire with one or more turns. A constant magnetic field is produced, depicted in Figure

2.1, called a dipole magnetic field. At a particular point, the vector magnetic field is

given by [54]:

) )( θ )( θ ( r π

NIa µθ r B ˆsinˆcos2

4 3

0 += (2.3)

where N = number of turns of wireθ = elevation angle (see Figure 2.1)

r = distance from center of loop to the point where the field is to be calculated

a = area of loop

The derivation of this analytic, closed-form theoretical result requires two as-

sumptions. First, it is assumed that the total cross-sectional area of the wire itself is small

compared to the loop radius. Second, it is assumed that the point of interest is at a dis-

tance of several times the loop radius. However, this second assumption is not a signifi-

cant limitation. For example, at a distance of five radii from the center of the coil, the

magnetic field predicted by equation 2.3 is in error by only a few percent. Of course, ex-

act results may always be obtained through direct numerical integration of the Biot-

Savart law.



23

This particular geometry plays an important role in the DMLP system. Beacons

use circular coils of wire to generate dipole fields described by equation 2.3. Thus, this

result will be used frequently throughout this work.

2.1.3 Interaction with Matter

Steady state magnetic fields are virtually unaffected by the vast majority of mate-

rials and objects found in a typical building. This unique characteristic, the ability to

penetrate obstructions, is the reason magnetic fields were chosen as the foundation for the

DMLP system. Consider the steady state dipole magnetic field shown in Figure 2.2(a).

The vector magnetic field that is measured at some point in space, for example P, can be

accurately predicted using equation 2.3. In Figure 2.2(b), an obstruction is located be-

tween the beacon and the sensor. Remarkably, the magnetic field vector that is measured

at location P, in most cases, remains unchanged . That is, equation 2.3 may be used to

accurately predict the magnetic field at location P, regardless of whether or not obstruc-

tions exist. There are, however, limitations to this broad characterization of magnetic

r

r

θ

coil of wire

B

Figure 2.1. Dipole magnetic field.



24

fields (i.e., mechanisms by which the obstruction does change the magnetic field) dis-

cussed in the next section.

This useful attribute of magnetic fields (their indifference to the presence of most

materials) may be examined in closer detail. In Figure 2.3, an object is placed within the

magnetic field created by a beacon. The beacon magnetic field may interact with the ob-

ject, potentially causing the object to create a magnetic field of its own, as shown in the

figure. The two magnetic fields, one from the beacon and one from the object, superim-

pose. Thus, a sensor at location P would record the vector sum of the two fields:

object beacon B B B P += (2.4)

The extent to which a material interacts with an external magnetic field, creating a mag-

netic field of its own, is described by its permeability. Most materials – aluminum, con-

crete, wood, plastic, stone, some types of steel, and glass, as examples – have a perme-

ability that is nearly identical to that of empty space. Table 2.1 (from [55]) lists the rela-

tive permeability of several common materials (relative permeability is the ratio of the

permeability of an object to that of the permeability of free space). Thus, most materials

interact very weakly with external magnetic fields, such as the beacon fields in the

DMLP system. Any field produced by an object in the environment ( object B ), is generally

Figure 2.2. The magnetic field vector measured at location P is the same with (a)

or without (b) the obstacle (for most materials).

P

(a) (b)

P



25

much weaker than the beacon field ( beacon B ), and contributes little to the field measured

by the sensor ( P

B ).

Why do most materials interact so weakly with an external magnetic field? The

theories of paramagnetism and diamagnetism address this interaction. These concepts

Figure 2.3. An object in a beacon’s magnetic field creates a small magnetic field

of its own. The vector sum of the two fields is measured at location P.

Table 2.1. Relative permeability of various materials (from [55]).

P

Material Relative Permeability

Air 1.00000037

Aluminum 1.000021

Copper 0.9999906

Mercury 0.999968

Silver 0.9999736

Tungsten 1.00008

Water 0.99999



26

can be explained with the help of quantum mechanics [56], but are beyond the scope of

this work. Fortunately, for the purposes of this research, the small interaction of most

materials with magnetic fields can simply be taken as an experimentally verified fact.

Steady state magnetic fields, therefore, show much potential as a basis for an in-

door positioning system. For example, equation 2.3 accurately predicts the field a sensor

would measure even if it were placed inside an aluminum box (a Faraday cage). This

situation would clearly occlude sensing systems that rely on line-of-sight, such as those

based on vision or RF radiation. For example, RF radiation at 100 MHz incident on alu-

minum foil only 0.025 mm thick can be attenuated by 100 dB [57].

Finally, note that a simple experiment can be performed to verify that steady state

magnetic fields have little interaction with matter. Using a compass, take a measurement

of the earth’s steady state magnetic field. Place a block of aluminum within a few centi-

meters of the compass. Although the needle may twitch while the block is being moved

into place (a dynamic effect), the compass needle will settle to the same steady state

value it had previously.

2.1.4 Limitations in the Model

Magnetic fields appear, so far, to be the perfect foundation for a positioning sys-

tem targeted at cluttered environments. Unfortunately, there are several limitations in the

model described by equation 2.3 – circumstances in which the magnetic field calculated

through equation 2.3 does not accurately predict the actual measurement. Since the

DMLP system relies on equation 2.3 to estimate position and attitude (described in detail

in Chapter 5), these circumstances can introduce error into the estimates. There are three

primary limitations in the model, and each is introduced here.

The first limitation is that equation 2.3 does not capture the effects of changing

magnetic fields. Time-varying magnetic fields induce electrical current to flow in nearby

conductors. These eddy currents create magnetic fields of their own, which superimpose

with the beacon fields. Eddy fields, in a metallic environment, can be one of the largest

error sources in the DMLP system. As such, eddy field noise is described in detail in the

next section (Challenge: Sensitivity to Materials).



27

The second issue is that an object composed of ferromagnetic material may distort

even a steady state magnetic field. That is, the field produced by a ferromagnetic object

in response to an external field (Figure 2.3) may be large compared to that external field.

This effect is another significant error source in the DMLP system, and is also detailed in

the next section.

The third limitation is less important than the first two, and mentioned only for

completeness. A perfect conductor (a superconductor) in the environment can also dis-

tort even a steady state magnetic field. This is known as the Meissner effect [58]. A con-

sequence of this effect is famously used to suspend magnets above superconductors. Su-

perconductors, however, are not common in the average office building, and this limita-

tion is not considered further.

2.2 Challenge: Sensitivity to Materials

The first primary challenge to the success of the DMLP system is that the accu-

racy of the position and attitude estimates may deteriorate when the sensor is close to cer-

tain materials. The two principle mechanisms for this sensitivity to materials, eddy field

noise and iron noise, were introduced in the previous section. This sensitivity to materi-

als is now examined in further detail.

2.2.1 Eddy Field Noise

Eddy field noise is caused by interaction between the time-varying beacon mag-

netic fields and conductors in the environment. Several years after Oersted’s investiga-

tions revealed that an electrical current produces a magnetic field, Faraday discovered

that a changing magnetic field could induce an electrical current to flow in a nearby con-

ductor. This foundational principle of electromagnetism is embodied by Faraday’s law

[59]: time-varying magnetic fields create voltage differences, known as induced emf .

These induced voltages, no different than if they had been created with a battery, cause

electric currents to flow in conductors. These currents, in turn, create magnetic fields

(eddy fields) of their own, summing with the beacon fields and introducing errors into the

position estimates.



28

Faraday’s law is expressed:

dt

d V ind

Ψ−= (2.5)

where V ind is the induced voltage and ψ is the magnetic flux. Magnetic flux is defined as

the inner product of the magnetic field vector B and an “area” vector A, which has

magnitude equal to the area of a region and direction normal to the surface:

A B •=Ψ (2.6)

Consider the effects of a time-varying beacon magnetic field interacting with a

typical conductive object. Assume that A is held constant (for example, an aluminum

plate that is not changing in area), and that B and A are parallel. Equation 2.5 can then be

simplified:

dt dB AV ind −= (2.7)

Now consider a sinusoidal magnetic field:

)cos( t B ω = (2.8)

From Faraday’s law, it is apparent that the amplitude of the induced voltage created by

this magnetic field is proportional to the frequency of the field:

)sin( t AV ind ω ω = (2.9)

as can be seen in the underscored coefficient. Thus, an important characteristic of eddyfield noise has been revealed: the higher the frequency content of the beacon fields, the

greater the induced voltages. Greater induced voltages lead to greater electrical currents,

and in turn to greater eddy fields. The corollary to this fact will prove to be of significant

use in this research effort: the lower the frequency content of the beacon fields, the lower

the eddy field noise. In the limit, a steady state magnetic field does not induce eddy fields

at all (recall that A is assumed constant).

The minus sign in Faraday’s law is a consequence of conservation of energy. This

important fact, known as Lenz’s law, indicates that the induced emf, and the current flow,

will always be oriented in such a way as to oppose the change in the magnetic field.

The effects of eddy fields on the measurements taken by a sensor can now be con-

sidered through an example. Figure 2.4(a) depicts a changing beacon magnetic field, a

sensor, and a metallic object. In this example, the beacon is far away compared to the



29

distance between the sensor and the object. Thus, both sensor and object experience ap-

proximately the same beacon field. The beacon magnetic field vector is increasing in

magnitude and is directed along the +z axis. By Lenz’s law, current flows in the conduc-

tor as shown in the figure, in such a way as to create the dipole field shown. The sensor

measures the vector sum of the beacon field and the eddy field. In the situation depicted

in Figure 2.4(a), the eddy field vector and the beacon field vector are aligned at the sen-

sor’s location. Because of this constructive vector addition, the sensor reports a magnetic

field larger than the beacon field alone. The sensor overestimates the size of the beacon

field, and any position and attitude estimates based on this field estimate will be in error.

In Figure 2.4(b), the same sensor and object are considered, but with respect to

the field from a different beacon. In this case, the beacon vector is increasing in magni-

tude along the +x axis. The resulting eddy currents and field are shown in the figure.

The geometry is now such that the beacon field vector and the eddy field vector are in

opposite directions. The sensor reports a measurement smaller than the beacon field

alone, underestimating the beacon field.

Figure 2.4. Two examples of a sensor and a conductor in a changing beacon mag-

netic field. In (a), the eddy field causes the sensor to overestimate the beacon field,

while in (b) the eddy field causes the sensor to underestimate the beacon field.

x

z Beacon magnetic

field grows in +z

conductor sensor

Beacon magnetic

field grows in +x

conductor sensor

(a) (b)



30

The example in Figure 2.4 demonstrates that the same object may cause the sen-

sor to overestimate the fields from some beacons while underestimating the fields from

other beacons. The effects of eddy fields are thus dependent on the bearing between the

conductor and the sensor, and the angle between that bearing vector and the local beacon

field vector.

The size of the eddy field itself is highly dependent on the geometry of the con-

ductor and its orientation with respect to the beacon field. In Figure 2.4(a), the conductor

is depicted as having a relatively large area normal to the beacon field. The eddy currents

encompass a large area, and a large eddy field is produced. In contrast, the same conduc-

tor has a relatively small area normal to the beacon field in Figure 2.4(b). The eddy cur-

rents encompass a smaller area, and the resulting eddy field is smaller. Further, eddy

fields are also a function of the particular material properties of an object, such as the

conductivity.

The specific sizes and effects of eddy fields in the DMLP system are further ex-

amined in Chapter 4. However, it is important to convey a general sense of the magni-

tude of eddy field effects in the DMLP system. In a typical experiment in the prototype

DMLP system, a relatively large aluminum plate, 30 cm square by 0.5 cm thick, is placed

with its edge 3 cm from a sensor. In the worst geometry (plate normal to the beacon field

vector), eddy fields can cause the sensor estimate of the beacon field to be in error by

50%, leading to position errors on the order of 10-20 cm. Smaller metallic objects (e.g.,

hand tools) do not have a significant effect even when placed within a few centimeters of

the sensor. Similarly, the relatively large plate does not have a significant effect if it

“far” from the sensor - for example, 50 cm away. Note that, to obtain these results, the

DMLP system uses magnetic fields at extremely low frequencies (see Chapters 3 and 7

for more information about spectral content).

2.2.2 Iron Noise

A second primary source of error in magnetic field positioning systems results

from the presence of ferromagnetic materials in the environment. Microscopic regions in

a ferromagnetic material, called domains, rotate and expand when an external magnetic

field is applied. The result is that the field produced by a ferromagnetic object in re-

Beacon magnetic

field steady in +z

ironsensor

Beacon magnetic

field steady in +x

ironsensor

x

z

(a) (b)



31

sponse to an external field (Figure 2.3) may be large compared to the external field.

Thus, iron (and some forms of steel), nickel, and cobalt can distort the field lines of even

a steady state magnetic field. Fortunately, within the set of ferromagnetic materials, iron

is typically the only one found in large quantities in many environments. Therefore, the

effects of ferromagnetic materials are referred to, in this work, as iron noise.

Similar to eddy field noise, the effects of iron are dependent on the bearing be-

tween the iron object and the sensor, and the angle between that bearing vector and the

local beacon field vector. Consider Figure 2.5(a), where a constant beacon magnetic

field, a sensor, and an iron object are depicted. The beacon is far away, compared to the

distance between the sensor and the iron object. Thus both sensor and object experience

approximately the same beacon field. In this example the steady beacon field vector is

directed in the +z direction at the location of the object and sensor. The sensor measures

the vector sum of the beacon field and the field generated by the iron object. In the situa-

tion depicted in Figure 2.5(a), the iron field vector and the beacon field vector are in op-

posite directions at the sensor’s location. Thus the sensor reports a magnetic field smaller

than the beacon field alone, underestimating the size of the beacon field. Position and

attitude estimates based on this field estimate will be in error.

In Figure 2.5(b), the same sensor and object are considered, but with respect to

the field from a different beacon. In this case, the beacon field vector is directed along

the +x axis. The geometry is now such that the beacon field vector and the iron field vec-

tor are aligned. The sensor reports a measurement larger than the beacon field alone,

overestimating the beacon field.

The example in Figure 2.5 demonstrates that the same iron object may cause the

sensor to overestimate the fields from some beacons while underestimating the fields

from other beacons. Note that the model used in this example is an extremely simplistic

one. Real ferromagnetic materials can be anisotropic, where the field vector created by

Figure 2.5. Two examples of a sensor and an iron object in a beacon magnetic field.

In (a), the iron object’s field causes the sensor to underestimate the beacon field,

while in (b) the iron object’s field causes the sensor to overestimate the beacon field.



32

the iron is not parallel to the external field, and have hysteresis, where the size of the

iron’s field is dependent on its past history. This simple model, however, is put to use in

Chapter 6, where an algorithm is presented that can detect the presence of iron noise and

form a correction. It is also important to note that, while eddy field noise (Figure 2.4) is

generated by a changing magnetic field, iron noise (Figure 2.5) may be created by even a

steady state field.

The specific sizes and effects of iron noise in the DMLP system are further exam-

ined in Chapter 6. Again, a brief preview of experimental results helps clarify the magni-

tude of this error source. Consider a relatively large “brick” of iron with a mass of 6 kg.

When placed within 4 cm of the sensor, this ferromagnetic object can cause the estimate

of the beacon field to be in error by 30%, leading to position errors on the order of 10 cm.

However, iron noise diminishes rapidly – with the cube of the distance between the iron

object and the sensor. Thus, the error in a beacon field estimate due to a mass of 6 kg

located 4 cm from the sensor is similar to that of 6,000 kg mass at a 40 cm distance.

2.3 Challenge: Range

The second primary challenge to the success of the DMLP system is the short

range of the beacon fields. The beacons in the DMLP system produce dipole magnetic

fields that are described by equation 2.3. Unfortunately, the fields diminish with the cube

of the distance from the beacon. The challenge that results from this inherently short

range is examined in this section. First, it is shown that numerous beacons are required to

cover a large volume, not just a few extremely powerful beacons. However, the need for

numerous beacons generates two further issues, which are then discussed.

Figure 2.6. Two approaches to building-wide coverage. In (a), a small number

(only one is shown) of powerful beacons; in (b) a large number of weaker beacons.

Several factors dictate that the DMLP system must use (b), numerous beacons.

(a) (b)



33

2.3.1 Numerous Beacons Distributed throughout the Building

Two basic approaches can be taken to obtain a “building-sized” coverage volume,

as depicted in Figures 2.6(a) and (b). In Figure 2.6(a), one powerful beacon, perhaps

with 3 orthogonal coils, is used. Figure 2.6(b) shows a system with many overlapping,

but significantly less powerful, beacons. Considering factors such as power consump-

tion, signal dynamic range, and estimate accuracy, the system that uses numerous distrib-

uted beacons (Figure 2.6(b)) has overwhelming advantages.

First, the total power consumption of the system greatly favors the numerous bea-

con case. With a single beacon, power consumption grows with the square of coverage

volume. In the multiple beacon case, power consumption is directly proportional to cov-

erage volume. Thus, for example, if one thousand beacons in Figure 2.6(b) are used to

cover the same volume as one beacon in Figure 2.6(a), then the total power consumption

will be one thousand times less. System efficiency (power consumption for a given cov-

erage volume), therefore, is highest when numerous, low power, closely spaced beacons

are used.

A second factor supporting the use of numerous beacons is the amplitude level of

the magnetic field. In the single beacon case, the field must be extremely large near the

beacon to be even measurable at the edge of the building. For example, the signal one

meter away from the beacon would be one million times larger than the signal 100 m

from the beacon. This places extreme dynamic range requirements on the electronics,

such as the magnetic field sensor, amplifiers, and the A/D converter.

Finally, the previous argument illustrated that the signal strength, sampled at vari-

ous locations around the building, varies by orders of magnitude in the single beacon

case. However, there is no reason that the thermal noise in the electronics (modeled as

additive white gaussian noise) would differ from location to location. Thus, the single

beacon system has a large variation in signal-to-noise ratio (SNR) across its workspace,

resulting in a large variation in position estimate accuracy.

2.3.2 Further Issues Created by Numerous Beacons

In the previous section, the argument was developed that numerous beacons are

required to achieve a building-wide coverage volume. The use of numerous beacons,



34

however, raises two further issues. Both a new signal structure and a new solution

method are required which are suitable for use with numerous beacons. These issues are

introduced here, then further described in their respective chapters (Chapter 3, Signal Ar-

chitecture, and Chapter 5, Solving for Position and Attitude).

In the next chapter, the signal structures used by existing systems are described.

There, considering the characteristics of eddy noise and the large number of beacons,

both discussed previously, it is demonstrated that existing signal architectures do not ex-

tend well to building-wide coverage volumes. Specifically, the accuracy of the position

estimates, considering eddy field noise, degrades unacceptably when existing signal

structures are used with a large number of beacons.

The use of numerous beacons raises a second issue: the need for an appropriate

“solution method”. A solution method is an algorithm that takes measurements of the

beacon fields and produces sensor position and attitude estimates. In Chapter 5, the solu-

tion methods used by existing systems are surveyed. These methods are not designed for

use with a large number of beacons, and are generally unsuited to the DMLP application.

2.4 DMLP System Concept

So far this chapter has presented background information about magnetic fields

and the challenges in using them in a positioning system. The DMLP system concept can

now be explored in greater detail than the brief preview of the first chapter. First, the

beacon system, responsible for creating the magnetic fields, is presented. Then, the sen-

sor unit, which measures and processes the fields, is described, with particular focus on

the internal signal processing. This discussion serves as a roadmap, helping to clarify

how the research solutions in the next four chapters answer the challenges raised in this

one. Further information about the system concept can be found in Chapter 7, where the

design of a prototype DMLP system is presented in detail.

2.4.1 Beacon System

In the DMLP system, numerous beacons are placed throughout a building, each

creating a dipole magnetic field. A typical beacon consists of a coil of wire, a controller

to generate the proper signal, and power amplifier electronics to force current through the



35

coil. A beacon is similar in dimension to a bicycle wheel – a disk with a diameter of one-

half to one meter, only 5-8 cm thick. The building is permeated with these beacon sig-

nals – the dipole fields overlap, and at any point in space the fields from multiple beacons

can be measured by a sensor.

The spacing between beacons is specific to a particular application and environ-

ment, but a general estimate can be formed. As previously demonstrated, a system with

beacons further apart is less efficient (requiring more power per unit of coverage volume)

and requires more sensor dynamic range. However, a system with beacons that are closer

together has a higher installation cost (more beacons) and might require beacons at in-

convenient locations (e.g., in the center of a large room). A spacing of 10 to 20 m be-

tween beacons is a good compromise for a typical office application. The power required

to drive beacons of this strength is on the order of 100 W, similar to standard electrical

appliances (such as fluorescent lights or computers), and can be provided without

changes to the building’s electrical infrastructure. Chapter 5 contains more information

on the specific beacon geometry (placement in the building) and configuration (number

of coils at each location).

Several hundred beacons may be distributed throughout a large building or ware-

house. Beacons are low cost – mass production could lower the unit price to tens of dol-

lars. One likely location for the beacons is the crawlspace between a ceiling and the floor

of the next higher level. This location is out of sight, unobtrusive, and allows easy access

to power and communication infrastructure.

Although the specific signal structure of the beacon fields is discussed later

(Chapter 3, Signal Architecture), it is straightforward to demonstrate that it must be time-

varying. Consider a sensor unit that measures the amplitude of the total magnetic field

vector at its (currently unknown) location. Since magnetic fields obey superposition, this

total measurement would be the vector sum of several superimposed beacon fields. The

measurement of the sum magnetic field vector by itself (3 measured quantities) is not a

sufficient amount of information to compute the sensor position and attitude (6 un-

knowns). However, if the sensor can distinguish the components of the field that are due

to each beacon (i.e., produce an estimate of the vector magnetic field created by each

beacon), then it would be possible to estimate the position of the sensor. Several methods



36

to distinguish the individual beacon fields are described in the next chapter – time divi-

sion, frequency division, and code division multiple access techniques. Unfortunately, all

require the beacons to generate time-varying magnetic fields. Thus, “ideal” steady-state

fields are not used, and eddy field noise is a primary concern of the DMLP system.

2.4.2 Sensor Unit

The DMLP sensor unit is the mobile component of the system. This small, low- power module takes measurements of the superimposed beacon magnetic fields at its lo-

cation. The measurements are processed to determine the sensor’s position and attitude

with respect to a building-fixed reference frame.

The operation of the sensor is depicted in block diagram format in Figure 2.7. In

the first stage of the system, the magnetic field measurements are acquired. Semiconduc-

tor sensors generate a voltage proportional to the magnetic field amplitude along a par-

ticular axis. Three of these sensors are used, oriented in orthogonal directions, to meas-

ure the vector magnetic field. These three analog signals are amplified, filtered, and digi-

tized by an A/D converter.

Several potential misconceptions about the system can be addressed at this point.

First, note that the system is based on amplitude measurements, not time of flight meas-

urements. Second, the magnetic fields created by the beacons are directly measured,

Figure 2.7. Block diagram of the DMLP sensor signal processing chain.

Signal

Acquisition

Detection

and Eddy

Correction

Position and

Attitude

Estimation

Iron

Correction

Raw magnetic field

measurements

Estimate of

individual beacon

magnetic fields

Sensor position

and attitude

Final sensor

position and

attitude



37

digitized, and processed. The magnetic field signals are not modulated onto carrier

waves, and there is no downconversion process in the sensor. Third, the beacons are not

intended to be antennas, which purposefully radiate electromagnetic waves propagating

through space carrying energy and momentum (although some of this radiation does oc-

cur). Rather, the beacons are large inductors, storing their energy in magnetic fields.

These fields permeate the building, rather than being confined to a ferromagnetic core,

such as in a typical power inductor. The semiconductors in the sensor unit are sensitive

to these storage fields. Thus, the system is described in terms of “beacons” and “sensors”

rather than “transmitters” or “receivers”.

Returning the Figure 2.7, the output of the signal acquisition block (three digital

streams of raw magnetic field measurement data) is sent to the detection process. An op-

timal decorrelating detector is implemented to distinguish the fields produced by individ-

ual beacons. The estimate of the vector magnetic field produced by beacon i, as meas-

ured at the sensor’s location, is given the symbol Bi . Chapter 3, in addition to detailing a

signal structure appropriate for a large number of beacons, describes the operation of this

detection stage.

Although the effects of eddy fields are greatly mitigated by the signal structure in

Chapter 3, eddy noise can still be a significant error source. The eddy correction tech-

nique in Chapter 4 modifies the estimates Bi to further counter the effects of eddy fields.

In Chapter 5, a solution algorithm is presented which takes the magnetic field estimates

( Bi ) , along with the known beacon locations and parameters, and produces an estimate of

sensor position and attitude. Finally, both the beacon magnetic field estimates and the

position and attitude estimates are used by the final stage, a correction for the effects of

distortion due to iron in the environment (described in Chapter 6).

Thus the two primary challenges raised in this chapter are addressed by the tech-

niques of the next four chapters. Magnetic field systems are sensitive to certain materials

(the first primary challenge), through the two mechanisms of eddy field noise and iron

noise. However, two correction steps (Chapters 4 and 6) specifically target each of these

error sources. Further, the focus of both the signal architecture (Chapter 3) and solution

method (Chapter 5) is to reduce the overall eddy noise while allowing the system to ex-

tend to a large number of beacons. The short range of magnetic fields (the second pri-



38

mary challenge) requires numerous beacons to be used, and this leads to issues of the

suitability of existing signal structures and solution algorithms. However, the signal ar-

chitecture (Chapter 3) and solution technique (Chapter 5) are both designed specifically

for the DMLP application with its large number of beacons.

2.5 Summary

In the DMLP system, inexpensive beacons located throughout a building create

low frequency magnetic fields. A mobile sensor unit samples the vector magnetic field at

its location, distinguishes the fields produced by individual beacons, and solves for its

position and attitude. The fields have excellent characteristics for penetrating line-of-

sight obstructions, and are unaffected by most objects and materials found in many envi-

ronments.

The use of magnetic field signals, however, subjects the system to two primary

challenges. First, the system is sensitive to certain materials in the environment – con-

ductors in the environment cause eddy field noise (which is highly dependent in the fre-

quency content of the beacon fields) while ferromagnetic materials cause iron noise. The

second challenge is the inherently short range of the beacon fields, requiring numerous

beacons to achieve building-wide coverage. However, this raises further issues, such as

the need for a new signal structure and solution method that are appropriate for a system

with numerous beacons. These two primary challenges are addressed by the research

presented in the next four chapters.



39

∫



40

3 Signal Architecture

In the DMLP system, numerous beacons are used to create magnetic fields that

permeate a building. The architecture of these beacon signals is of critical importance –

the use of an inappropriate signal structure would lead to greatly increased eddy field

noise, resulting in unacceptably large errors in the position and attitude estimates. This

chapter examines the signal structures used in existing magnetic-based systems and then

presents a new signal architecture that is advantageous for the DMLP application.

First, two signal structures that are used in existing magnetic positioning systems

are examined. Analysis shows that, using these signal architectures, the frequency con-

tent of the beacon signals scales with the number of beacons. For a system with a large

number of beacons, the higher frequency magnetic fields result in unacceptably high lev-

els of eddy field noise. Thus, the signal architectures used in existing systems are appro-

priate for the small volume applications in which they are currently employed, but they

cannot be extended to support a large number of beacons.

An alternative signal structure is then presented that is advantageous for the

DMLP application. This architecture allows numerous beacons to be used, enabling the

DMLP system to have building-wide coverage, while maintaining good eddy field per-

formance (the spectral content of the beacon signals scales only with the square root of



41

the number of beacons in the system). The performance of the new and existing signal

structures is compared, considering systems of various sizes, demonstrating the benefits

of the new signal architecture for applications with large coverage volumes.

The following section then demonstrates how to make use of the new signal archi-

tecture. The signal processing that takes place inside the sensor to distinguish the bea-

cons is examined. The initialization of this signal processing stage is then discussed in

further detail.

The pseudorandom signal structure performs better, for a large number of bea-

cons, than the simple structures used in small systems. However, an infinite number of

potential signal architectures exist. Is the proposed structure the “best” for the DMLP

application? The optimality of this new signal architecture is discussed in the final sec-

tion.

3.1 Signal Architectures Used in Existing Systems

Existing magnetic field positioning systems commonly use two multiple access

methods to distinguish the fields produced by individual beacons. In a Time Division

Multiple Access (TDMA) approach [60], each beacon generates a field during its as-

signed time slot. The sensor is synchronized with the beacons, and thus can distinguish

the beacon fields – only one beacon is producing a field at any given time. In a Fre-

quency Division Multiple Access (FDMA) approach [61], each beacon continuously pro-

duces a sinusoidal field at a unique frequency. The sensor uses frequency selective filter-

ing to discriminate among the beacon signals.

This section investigates the performance of systems using these basic signal

structures as the number of beacons in the system is varied. The purpose of this analysis

is to motivate the requirement for a new signal structure for the DMLP application, which

is then presented in the next section. This analysis of performance is straightforward,

consisting of three steps:

1) For each multiple access approach, it is shown that as the number of beacons

grows, the frequency content of the beacon signals increases.

2) Higher frequency beacon signals result in a larger amount of eddy noise – this

was demonstrated in the last chapter (section 2.2.1, Eddy Field Noise).



42

3) An increase in eddy noise reduces the accuracy of the position and attitude es-

timates. A simulation is used to provide a numerical example of how position

estimates degrade, due to eddy noise, when these basic signal structures are

used in systems with large numbers of beacons.

Consider a positioning system with n beacon coils covering a building. As dis-

cussed previously, in order to solve for position and attitude, the fields generated by indi-

vidual coils must be uniquely identifiable. For typical DMLP applications, n may range

from a dozen to a few thousand. In this analysis, sensors are required to produce position

and attitude estimates every Te seconds. A Te value of 0.1 seconds (i.e., an update rate of

10 Hz) is a reasonable requirement for robotic applications.

First, the operation of a TDMA signal structure is examined. Each beacon is as-

signed a unique time slot in which to “broadcast” during each T e interval. For a large

number of beacons, the time slot allotted to each beacon, Ts = Te/n, is very short. Using

straightforward Fourier analysis, the spectral content of the beacon signals moves to

higher frequencies as n increases and the time slots become shorter. That is, using a

TDMA approach, the beacon signal energy scales in frequency with the number of bea-

cons. For example, with Te of 0.1 sec, for a system with 100 beacons the first “lobe” in

the signal spectrum (containing much of the energy) extends to 1 kHz, but with 1000

beacons the first lobe in the spectrum extends to 10 kHz.

The frequency content of beacon signals using an FDMA approach scales in a

similar fashion. Using the FDMA method, each beacon generates a field at a unique fre-

quency. Thus, as each new beacon is added to the system, it must be assigned the next

broadcast frequency. Assume that the sensor signal processing can distinguish beacons

separated by a frequency spacing of s. Thus, the first beacon in the system could be as-

signed frequency s, the second beacon frequency 2 s, and the ith beacon frequency is. Us-

ing this schedule, the average beacon frequency in a system of n beacons is ns/2. Thus,

the average beacon frequency scales linearly with the number of beacons in the system.

For example, with a spacing s of 10 Hz, a system with 100 beacons could have one bea-

con at 10 Hz, one beacon at 1 kHz, and an average beacon frequency of 500 Hz. A sys-

tem with 1000 beacons would have an average beacon frequency of 5 kHz.



43

The second step in the analysis is to demonstrate that the amount of eddy field

noise produced by the system is directly related to the frequency content of the beacon

signals. However, the previous section on Eddy Field Noise has already shown this. As

a specific example, it was previously derived that the eddy fields produced by a sinusoi-

dal magnetic signal are proportional to the frequency of the signal (equation 2.9). Thus,

given the same environment, the eddy noise produced by a 5 kHz beacon signal is 10

times greater than that produced by a 500 Hz beacon signal.

The final step of the analysis is to relate eddy field noise to the amount of error it

causes in the position estimates. The algorithm that takes noisy magnetic field measure-

ments and produces position and attitude estimates is presented in Chapter 5. Since this

is a numerical algorithm, a simulation is used to complete the analysis. Specifically, the

simulation investigates the relationship between the number of beacons in a system and

the performance of the system, as measured by the position accuracy in the presence of

eddy field noise. The simulation steps through a number of cases – each case increases

the value of n (number of beacons in the system), but all other parameters remain the

same. For each case, signal structures of both the TDMA and FDMA approaches are de-

termined, and the beacon signals are simulated. Eddy field noise is calculated and a

simulated sensor produces a position estimate.

The results of the simulation are shown as a plot of the error in the position esti-

mate, due to eddy noise, versus the number of beacons in the system, using the TDMA

and FDMA signal structures (Figure 3.1). The numerical values shown in the plot are

arbitrary – they are the result of the specific simulation parameters (values were chosen

that are representative of a typical application). The importance of the plot is in the trend

that is revealed – using the TDMA and FDMA signal structures, there is a rapid degrada-

tion in position accuracy, due to eddy field noise, as the number of beacons increases.

Thus, existing signal structures are appropriate for the small volume applications

they were designed for, with a limited number of beacon coils. However, this analysis

concludes that they do not extend well to the large number of beacons needed for a build-

ing-wide application. In the next section, a new signal structure for magnetic field posi-

tioning systems is presented. A comparison then follows, showing the performance ad-



44

vantages of the new structure in applications where a large number of beacons are re-

quired.

3.2 New Signal Architecture Using Pseudorandom Codes

A new signal architecture for magnetic field positioning systems, based on pseu-

dorandom codes, is presented. It is designed to maintain low overall beacon frequency

content even in a system with a large number of beacons. In this Code Division Multiple

Access (CDMA) structure, all beacons produce magnetic fields at all times. Each bea-

con, however, changes the polarity of the current through its coil according to a pseudo-

random code, a special sequence of 1’s and -1’s, assigned to each transmitter. Thus, the

magnetic field vector at any point in Figure 2.1 can be aligned in one of two directions,

depending on the direction of the current flow. Figure 3.2 shows an example of the mag-

Figure 3.1. Predicted position error (m) versus number of beacons, considering

eddy noise. The results show that TDMA and FDMA signal structures used in

existing systems do not extend well to a large number of beacons.

TDMA

FDMA

number of beacons

p o s i t i o n e r r o r ( m )

101 102 103 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0



45

netic field, as measured at a particular point in space along a particular direction, created

by a single beacon. Only a portion of a complete pseudorandom sequence is shown.

Each element of the sequence is called a chip in CDMA terms and the number of

chip periods in a second is called the chipping rate. To distinguish the fields produced by

each beacon, as shown in a later section, samples from an entire code sequence are re-

quired. Thus, if position estimates are desired at 10 Hz, for example, the period of the

entire code must be 0.1 sec. For a code of length 63 chips to complete in 0.1 sec, the

chipping rate must be 630 Hz. For a code of length 1023 chips to complete in 0.1 sec, the

chipping rate must be much higher, 10,230 Hz. The spectral content of a pseudorandom

signal is therefore directly related to its chipping rate – higher chipping rate signals con-

tain more energy at higher frequencies.

The beacons are synchronized so that all chip transitions occur at the same time

and the codes maintain their relative alignment. When the last element in a code se-

quence is reached, the code simply repeats. The beacons maintain synchronization

through a communication link, which can be implemented using a cable or by signals

sent over the building’s electrical wiring. The sensor is also synchronized with the bea-

con network so that magnetic field measurements can be made at the end of each chip

period (this allows the most time for any eddy fields to decay). The synchronization be-

tween beacons and sensor can be implemented using a wireless communication link, or

the sensor can derive the information from the fields themselves. Once the sensor has ob-

tained a sample from each chip during an entire code sequence, the data is processed to

estimate the magnetic field produced by each individual beacon.

The pseudorandom codes selected for the DMLP system are called Gold codes

[62]. The length of a code sequence (the number of elements) is designated N . Gold

codes of length N can be grouped into families, or sets, of N +2 separate codes. The codes

Figure 3.2. Example magnetic field versus time, created by a beacon using the

pseudorandom code signal structure.



46

within a family have good orthogonality properties. That is, the peak cross-correlation

value of any two of these special vectors is small (compared to the peak autocorrelation

of either vector). Also, a code has only a very small auto-correlation with a delayed ver-

sion of itself. With the entire system synchronized, beacons in the system can use all of

the codes in a family at all offsets. That is, two beacons in the system can use the same

code sequence, but offset in time by one or more chips. This is a departure from other

CDMA applications, where a code is generally used by only one transmitter in the sys-

tem, and the codes are not synchronized.

The use of all codes at all offsets allows a system to contain a large number of

beacons while using codes with a small number of elements. A code of length N can

support N ( N +2) beacons (or N offsets of N +2 codes). In other words, if n beacons are

employed in a system, code lengths of only approximately n are required. For exam-

ple, codes of only length 31 can support 1023 beacons (33 codes each with 31 offsets),

and codes of only length 63 can support 4095 beacons (65 codes each with 63 offsets).

Using this CDMA structure, the code length (and thus the frequency content) of the bea-

con signals scales approximately as the square root of the number of beacons. This leads

to performance advantages over the TDMA and FDMA approaches, as described in the

next section.

3.3 Comparison of Signal Structures

The simulation described previously to analyze the performance of FDMA and

TDMA systems may now be applied to the CDMA structure. Again, for each case in the

simulation, the number of beacons in the system is increased, but the other parameters

remain the same. At each case, the CDMA signal structure is determined, the frequency

content and eddy noise are calculated, and the position estimate is generated. Figure 3.3

shows the resulting position accuracy versus the number of beacons for all three signal

structures.

The results show that the CDMA signal structure is comparable to other structures

in systems with a small number of beacons, but is advantageous when a large number of

beacons is considered. This is an expected result. In a TDMA system, as the number of

beacons increases, the time slot assigned to each beacon reduces, and the spectral content



47

of the beacon signals moves to higher frequencies. Similarly, in a FDMA system, as each

new beacon is added to the system, it must operate at the next higher frequency, and the

average spectral content moves to higher frequencies. By Faraday’s Law, the eddy field

noise increases in size as the beacons move to higher frequencies. Of course, in the

CDMA system, as the number of beacons increases, the spectral content of the beacon

signals also increases, but at a much slower rate than the TDMA or FDMA systems. An

increase in the amount of eddy noise leads to greater errors in the position estimates, as

shown in the plot. Note that the discontinuity in the CDMA data around 1000 beacons is

due to a required change in code lengths.

To gain further insight into these results, consider a specific data point – a system

with 1000 beacons. With a CDMA signal structure, codes of length 31 are used. A Te of

0.1 seconds results in a chipping rate 310 Hz. Most of the signal energy is contained at

frequencies under 310 Hz. Contrast this result with the TDMA structure, where each

Figure 3.3. Predicted position error (m) versus number of beacons, considering

eddy noise. The CDMA structure performs well even with a large number of

beacons.

TDMA

FDMA

CDMA

number of beacons


101 102 103 0

0 . 2

0 . 4

0 . 6

0

. 8

1 . 0



48

beacon generates a pulse only 0.1 ms wide (30 times shorter than a chip in the CDMA

system). The first lobe in the spectrum (containing much of the signal energy) extends to

10 kHz. In the FDMA system, with 10 Hz spacing between beacon signals, the average

beacon frequency is 5 kHz. Thus, for a system with 1000 beacons, both the TDMA and

FDMA approaches result in beacon frequencies much higher than those obtained with a

CDMA approach.

In summary, the simulations indicate that all three signal structures perform well

when a small number of beacons are used in the system. In systems with a large number

of beacons, however, the CDMA structure performs significantly better than the TDMA

and FDMA structures.

3.4 Distinguishing Beacon Fields with the New Signal Structure

This section describes the signal processing that occurs inside the sensor – the al-

gorithm that takes the magnetic field measurements and produces an estimate of the

magnetic field vector generated by each individual nearby beacon ( Bi ). Once the mag-

netic field vectors from several beacons have been estimated, they can be used to solve

for sensor position and attitude (described in Chapter 5).

Each beacon in the DMLP system generates a unique signal, based on a pseudo-

random code, as described earlier. A mobile sensor unit samples the vector magnetic

field at its location – this measured magnetic field is a mix of superimposed signals from

several beacons. As described in Chapter 2, there is not enough information in one sam-

ple of the sum field (3 component measurements) to solve for position and attitude (6 un-

knowns). However, if the field from each beacon contributing to the sum could be dis-

tinguished (i.e., determine Bi produced by each nearby beacon), then it may be possible

to solve for position and attitude.

In the DMLP system, a sensor samples the vector magnetic field (taking 3 com-

ponent measurements along three orthogonal directions) once during each chip period.

Once data has been taken for an entire code cycle (i.e., N samples), this set of measure-

ments (designated M ) is operated on to distinguish the individual beacons fields. M is

arranged as a ( N x 3) matrix where each row contains a vector sample taken during a dif-

ferent chip period. Consider one vector component of this set of measurements (i.e., a



49

column of M ), designated M v. Assuming n beacons are close enough to contribute to the

sum:

vi

n

i

ivv bC B M += ∑ (3.1)

where M v = magnetic field measurements along axis v ( N x 1)

Biv = v-axis component of magnetic field produced by beacon i (scalar)

C i = pseudorandom code used by beacon i ( N x 1 sequence of 1’s and –1’s)

N = number of elements in Ci (scalar)

n = number of nearby beacons contributing to M v

bv = constant bias along axis v (e.g., earth’s magnetic field)

Equation 3.1 can be expressed in matrix notation:

321

M

4 4 4 4 34 4 4 4 21 MMM

L

L

L

43421 M

v

b

B

B

)( c )( c

)( c )( c

)( c )( c

v

)( m

)( m

)( m

X A M

v

v

v

v

v

v

= 2

1

21

21

21

133

122

111

3

2

1

(3.2)

where mv(j) = jth element of M v

ci(j) = jth element of code C i

As an example, consider a system that uses codes of length 63 and four beacons are close

to the sensor. Vector M is 63 by 1, containing 63 measurements, one from each chip pe-

riod in the code cycle. Matrix A is 63 by 5, with four columns containing the codes of the

four beacons, and the last column containing all 1’s. Vector X , containing the unknown

amplitudes of the individual beacon fields (and the bias term), is 5 by 1.

The field produced by each beacon, Biv, (contained in X v) is distinguished by a

straightforward operation on the measurement vector ( M v):

( ) v

T T

est v M A A A X 1−

= (3.3)

This operation is carried out on each of the three columns of the set of measurements M .

The result is that each vector component of the field produced by each nearby beacon is

estimated (i.e., each Bi has been obtained).

The “least squares fit” signal processing given by equation 3.3, also known as a

decorrelating detector [63], is appropriate for the DMLP application for two reasons.



50

First, it is necessary due to the system’s large dynamic range. Due to the 1/r 3 characteris-

tic of the dipole field (equation 2.3), it is not uncommon for the sensor to receive one

beacon signal that is 1000 times stronger than another beacon signal. As discussed pre-

viously, the beacon signals are not perfectly orthogonal. If a decorrelating detector is not

used, the strong signal can overwhelm the smaller one, even though they use different

codes. This is especially important in the DMLP application, where relatively short code

lengths are used.

A second benefit of this decorrelating detector is its performance in the presence

of Additive White Gaussian Noise (AWGN). The random thermal motion of electrons in

the sensor and amplifier electronics, which can be modeled as AWGN, is an unavoidable

source of noise in the system (see Chapter 8). In a non-metallic environment (with little

eddy field or iron noise) it can be the dominant source of errors in the position and atti-

tude estimates. The least-squares detector is the optimal (best linear unbiased) estimator

in the presence of this noise [64].

After the estimates have been made (using equation 3.3), an important metric can

be calculated to verify the quality of the results. Let the Dv be defined as the difference

between the actual measurement data M v and the least squares fit that was made to that

data:

est vvv AX M D −= (3.4)

The vector Dv has size N x1. A “small” difference (compared in some way to the “size”

of M v) indicates that the set of field measurements M v matches closely with the field that

would be expected from a group of beacons with amplitudes X vest . A “large” difference

indicates an error condition – the sum field produced by several beacons with amplitudes

X vest does not match the measured data well. To specify this concept in a more concrete

manner a “quality factor” metric is introduced:

)(

)(1

v

v

M std

D std qf −= (3.5)

A quality factor near 1 indicates that the estimates obtained by equation 3.3 are reason-

able, and they can be used to form a position and attitude solution. A low quality factor

indicates that the estimates produced by equation 3.3 are suspect, and the positioning de-



51

vice can signal the operator that an error has occurred. This metric is also used in the ini-

tialization process, discussed in the next section.

Thus, an algorithm has been presented that enables a sensor to use the CDMA

signal structure presented in the previous sections. Specifically, a sensor takes a se-

quence of magnetic field samples and, through equation 3.3, obtains an estimate of the

magnetic field vector ( Bi ) generated by each nearby beacon. In the next chapter, an algo-

rithm is presented which improves upon equation 3.3 and further mitigates the effects of

eddy field noise. Then, in Chapter 5, the estimates Bi are used to determine the sensor’s

position and attitude. Further information on CDMA techniques can be found in [65].

3.5 Initialization

For clarity, one important detail was omitted in the previous section. Which Gold

codes should be used in matrix A in equation 3.3? During normal operation, this is not a

problem. The sensor has a database of the beacon locations and codes. From the last po-

sition estimate, the codes from several of the closest beacons can be selected (generally

3-8 beacons are within range of a sensor). But for a “cold start” (e.g., when first powered

up), the sensor does not know its location or which codes should be used in matrix A.

This section presents a procedure to determine, with no a priori knowledge, which bea-

cons are close to the sensor, and thus which codes should be used in matrix A. This ini-

tialization method requires only one code cycle of data, the same amount needed for the

detection (equation 3.3). Thus, this method can be used once at startup or, with enough

computational power, could be applied every time an estimate is made (i.e., it is invisible

to the rest of the signal processing chain).

The initialization procedure is simply a brute force search based on the quality

factor introduced in the previous section. A standard set of measurements M is taken.

Software then iterates through each grouping, or “neighborhood”, of beacons in the sys-

tem (neighborhoods overlap, as shown in Figure 3.4). At each iteration step, the sensor is

assumed to be in that neighborhood, and the closest 3-8 beacon codes are chosen. Esti-

mates are then made (using equation 3.3) and the quality factor is calculated (equation

3.5). The procedure continues throughout the building, recording the quality factor for

each neighborhood. The neighborhood with the highest quality factor is chosen. Thus,



52

this procedure searches for the neighborhood that can best “explain” the measurement

data M .

The initialization algorithm was tested in a simulation of a building with over

4000 beacons. Realistic noise values were used. The results are shown in a plot of qual-

ity factor versus neighborhood (Figure 3.5). The proper neighborhood, and thus the cor-

rect codes to use in equation 3.3, is readily discernable.

Figure 3.5. A plot of “Quality Factor” versus beacon neighborhood is important

in the initialization process to determine the correct neighborhood.

Figure 3.4. Example “neighborhoods” of beacons.

0 1000 2000 3000 4000

0

0 . 2

0 . 4

0

. 6

0 . 8

1 . 0

Neighborhood

Q u a l i t y F a c

t o r

correct

neighborhood



53

3.6 Optimality of the Signal Architecture

This chapter has presented a specific signal architecture that can reduce the eddy

noise in a magnetic field positioning system, especially one with a large number of bea-

cons. However, there are an infinite number of potential signal structures. Is this CDMA

architecture the “best” approach? This final section considers the optimality of the

DMLP signal architecture.

Earlier discussion (section 3.1) concluded that, using the TDMA and FDMA

structures, the frequency content of the beacon signals scales with n. With the CDMA

approach, frequency content scales only with n , resulting in performance advantages.

Now, a hypothetical signal structure, with an even better scaling, is considered. The

structure uses binary signals, similar to the CDMA approach, where a ‘1’ represents one

polarity of the beacon field and a ‘0’ the opposite polarity. Each beacon generates its

signals according to a code that is simply the binary designation of the beacon. For ex-

ample, beacon 6 (binary 000110) uses code sequence [0 0 0 1 1 0], and beacon 8 (binary

001000) uses code sequence [0 0 1 0 0 0]. Thus, this system is optimal – the codes are

the minimum length (in a binary system) needed to give each beacon a unique signal.

For example, in a system with 4000 beacons, codes of length 12 would be used (212

=

4096). In a similar CDMA system, the codes would have length 63. With this hypotheti-

cal scheme, for a system of n beacons, codes of only length log 2(n) would be needed.However this hypothetical structure does not provide a practical multiple access

method. Consider a receiver that measures M =[0 0 1 1 1 0]. Are beacons 6 and 8 being

received with equal amplitudes, or is it beacon 14? Or perhaps beacons 2, 4, and 8 are

each being received.

This hypothetical structure, scaling with log 2(n), cannot actually be used, but it

can be analyzed using the performance simulation described earlier. The results (Figure

3.6) show that the CDMA approach, while it is not optimal, has performance close to this

hypothetical structure, which uses “optimal” binary sequences. Thus, while optimality of

the CDMA structure has not been established, an argument can be made from a “law of

diminishing returns” standpoint. That is, for a system with numerous beacons (e.g., thou-

sands), the performance difference between using CDMA and some optimal structure is



54

small compared to the performance advantage gained by using the CDMA approach in-

stead of a TDMA or FDMA method.

3.7 Summary

In the DMLP system, numerous beacons are used to create magnetic fields that

permeate a building. The architecture of these beacon signals is of critical importance –

high frequency content in the signals leads to increased eddy field noise and reduced po-

sition and attitude estimate accuracy. Analysis of signal architectures used in existing

systems concludes that, while they are appropriate for the small volume applications in

which they are currently employed, they cannot be extended to support a large number of

beacons. An alternative signal structure is therefore presented that allows numerous bea-

cons to be used while maintaining good eddy field performance. The new signal archi-

tecture, based on pseudorandom codes, enables the DMLP system to have building-wide

coverage.

Figure 3.6. Position error (m) versus number of beacons, considering eddy noise.

The CDMA structure performs nearly as well as a hypothetical “optimal” structure.

TDMA

FDMA

CDMA

“optimal”

number of beacons


101 102 103 0

0 . 2

0 . 4

0 . 6

0

. 8

1 . 0



55

∫



56

4 Eddy Field Noise Mitigation

The signal architecture presented in the previous chapter enables the DMLP sys-

tem to provide service throughout a large volume while maintaining low overall beacon

frequency content. However, while eddy field noise is reduced, it is not eliminated en-

tirely. Even with the DMLP signal structure, eddy fields can still be one of the largest

error sources in an environment cluttered with metallic objects. This chapter presents a

method to detect and further mitigate eddy field noise in the DMLP system.

First, a model is developed to describe the eddy fields produced by the pseudo-

random beacon signals. Then, using the model, the estimation process from Chapter 3

(equation 3.3), which extracts individual beacon field estimates from the measurement

data, is modified to take into account the effects of eddy fields. The improved estimator

is quite effective at detecting and mitigating eddy field noise, as demonstrated by experi-

mental results in the final section.

4.1 Eddy Field Model

As described earlier (Chapter 2), time-varying magnetic fields, such as those used

in the DMLP system, create electrical potential differences (induced emf ) throughout the

area of operation. These voltages stimulate the flow of electrical current in conductors in



57

the environment, which in turn creates additional magnetic fields. These eddy fields sum

with the beacon fields, introducing noise into the measurements. The basic physical

principles underlying eddy fields are examined in further detail in Chapter 2. In this sec-

tion, these basic principles are applied to create a specific model of the eddy field noise

generated by the DMLP system.

First, consider the magnetic field created by a beacon using the pseudorandom

signal structure presented in Chapter 3. As an example, one component of the vector

magnetic field created by a beacon, as measured at some point in space, is shown in Fig-

ure 4.1(a). For clarity, a beacon with a code length of only 7 chips is used in the figure

and in the following example. In the figure, the beacon signal is shown as a series of

abrupt changes. An actual beacon takes a finite amount of time to change its field polar-

ity, due to the inductance of the coil. However, the simple model of the beacon field

shown in the figure is adequate for this work, producing an uncomplicated eddy field

model and tractable mitigation technique.

The abrupt changes in magnetic field in Figure 4.1(a), according to Faraday’s

Law (Chapter 2), induce voltage spikes as shown in Figure 4.1(b). These voltage im-

pulses, applied to a conductive material modeled as a simple “RL” (resistor-inductor) cir-

cuit, generate current transients as shown in Figure 4.1(c). Note that this simple “RL”

material model (see [66]) is adequate for this mitigation technique (more complex models

can be found in [67]). The current transients in Figure 4.1(c) are characterized by a time

constant and amplitude that are functions of the material properties (resistance and induc-

tance) and object geometry. The induced current in Figure 4.1(c) creates magnetic eddy

fields as shown in Figure 4.1(d).

The sensor samples the magnetic field at its location, which is the vector sum of

any nearby beacon fields (e.g., Figure 4.1(a)) and any eddy fields (e.g., Figure 4.1(d)).

As described in Chapter 3, this sampling is done at the end of each chip period. This al-

lows the beacon fields to stabilize (they do not change instantaneously) and provides

some time for eddy fields to decay.

To form a mathematical model of the magnetic fields generated by a DMLP sys-

tem, it is useful to define a “delta code” as a sequence representing the changes in a bea-

con’s pseudorandom code. Each code sequence ci has an associated delta code sequence,



58

∆1i, of the same length. When code ci changes from ‘–1’ to ‘+1’, ∆

1i contains ‘+1’. Simi-

larly, when ci changes from ‘+1’ to ‘-1’, ∆1

i contains ‘-1’. The delta code contains the

value zero when code ci remains the same from one chip to the next. Thus, using the ex-

ample code c1 from Figure 4.1(a):

[ ]1111111

1 −−−=c (4.1)

the associated delta code is

[ ]10010111

1 −−=∆ (4.2)

The purpose for the superscript ‘1’ becomes apparent later in this section.

Figure 4.1. Creation of eddy fields in the DMLP system. A beacon generates a

time-varying magnetic field (a), creating potential differences in the environment.

This induced voltage (b) stimulates current flow (c) in conductors, which in turn

produces eddy fields (d).



59

A simple model of the DMLP system, including the effects of eddy fields, can

now be formed. This simple scenario consists of one beacon using code ci, a sensor, and

a conductive object. Considering one arbitrary vector direction (the v-axis component),

the magnetic field measured by the sensor ( M v) can be modeled as the sum of the beacon

field (with amplitude Biv) and an eddy field (with amplitude E iv):

1

iiviivv E C B M ∆+= (4.3)




N = number of elements in Ci (scalar, N = 7 in this example)

E iv = v-axis component of eddy field created by changes in Biv (scalar)

∆1i = delta code associated with the code of beacon i ( N x 1)

The simple model proposed in equation 4.3, however, does not fully represent the

effects of eddy fields. For certain combinations of object geometry and material proper-

ties, the eddy field created by a change in the beacon signal may last for more than one

chip period. To capture this effect, the definition of a delta code is augmented – the su-

perscript variable is now used to denote a delay in the delta code. Specifically, ∆di, is de-

fined as the delta code ∆1

i cyclically shifted by d -1 elements. For example, two delayed

delta codes associated with code c1 (equation 4.1) and delta code ∆11 (equation 4.2) are:

[ ]00101112

1 −−=∆ (4.4)

and

[ ]01011103

1 −−=∆ (4.5)

The simple model in equation 4.3 can now be extended. The measured field con-

sists of the beacon field, the eddy field created by the beacon field changes, and any ef-

fects of the eddy field that are still present two and three chip periods after the beacon

field changes:

332211

iiviiviiviivv E E E C B M ∆+∆+∆+= (4.6)

The variables in equation 4.6 are defined the same way as in equation 4.3, and the new

variables E 2

iv and E 3

iv represent the amplitude of the eddy field created by the changes in

the field of beacon i, after 2 and 3 chip periods, respectively.



60

It is straightforward to extend this model to account for eddy fields with even

longer time constants. Experimentally, however, it was found that generally only two or

three delta codes in equation 4.6 were needed to account for eddy fields – additional

terms were not necessary and provided only marginal benefits.

The full model of the magnetic fields measured in the DMLP system can now be

described. In an actual implementation, many beacon fields and eddy fields are present.

The measured signal is modeled as the sum of several beacon fields, several eddy fields,

a steady state magnetic field bias (e.g., the earth’s field), and noise. Each beacon field

may generate an independent eddy field, and eddy fields of up to three chip periods are

taken into account. Thus, in the DMLP system, the measured signal is modeled as:

( ) noiseb E E E C B M v

i

iiviiviiviivv ++∆+∆+∆+=∑ 332211 (4.7)




E 1

iv = v-axis component of eddy field, after 1 chip period, created by changes in

Biv (scalar)

E 2

iv = v-axis component of eddy field, after 2 chip periods, created by changes in

Biv (scalar)

E 3iv = v-axis component of eddy field, after 3 chip periods, created by changes in

Biv (scalar)

∆1

i, ∆2

i, ∆3

i = delta codes associated with the code of beacon i ( N x 1)

N = number of elements in Ci

i = index of all beacons near the sensor (contributing to the sum)

bv = bias term along axis v

Thus, the model of the measured signal presented in Chapter 3 (equation 3.1) has

been modified. The new model, equation 4.7, takes into account the effects of eddy field

noise.



61


Expressing equation 4.7 in matrix form:

321

M

MMMMMMM

L

L

L

43421

M

4 4 4 4 4 4 34 4 4 4 4 4 21v

b

E

B

E

E

E

B

cc

cc

cc

v

m

m

m

X A M

v

v

v

v

v

v

v

v

v

v

∆∆∆∆

∆∆∆∆

∆∆∆∆

=

1

2

2

3

1

21

1

1

1

1

22

3

1

2

1

1

11

1

22

3

1

2

1

1

11

122

31

21

111

1)3()3()3()3()3()3(

1)2()2()2()2()2()2(

1)1()1()1()1()1()1(

)3(

)2(

)1(

(4.8)

results in the estimator:

( ) v

T T

est v M A A A X 1−

= (4.9)

Thus, the algorithm described by equation 4.9 takes magnetic field measurements ( M v)

and produces estimates of the individual beacon fields ( Biv), corrected for the effects of

eddy noise. Effectively, matrix A from the last chapter (equation 3.2) has been modified

to account for the effects of eddy noise. This operation (equation 4.9) is carried out on

each component of the vector measurements. The resulting estimates of individual bea-

con fields ( Bi ) are the basis for the position and attitude solution in Chapter 5. As de-

scribed in the last chapter (Section 3.4), this estimator is well suited for the DMLP appli-

cation – it decorrelates the beacon fields (reducing multiple access noise) and mitigates

the thermal electronic noise (modeled as AWGN) in the magnetic field sensors and am-

plifiers.

This modified estimator has two effects. It is successful in mitigating eddy field

noise, as detailed in the next section. However, at the same, it exacerbates the random

fluctuations in the Bi estimates caused by thermal noise in the sensor electronics. This

thermal noise is always present, and causes the “scatter” in the position estimates de-scribed in Chapter 8. Therefore, it is desirable to use the estimator in equations 4.8 and

4.9 when eddy field noise is present, but to use the Chapter 3 estimator otherwise.

In the DMLP prototype system, a threshold was used to trigger the appropriate es-

timator. Specifically, the following criteria worked well: if the difference between the

Chapter 3 estimator and Chapter 4 estimator is greater than 1.0 mG, eddy field noise is



62

indicated, and the Chapter 4 estimate is used. This experimentally determined threshold

value is strict enough that the use of the Chapter 4 estimator is not triggered by random

thermal noise, and yet the presence of a nearby eddy field source is reliably detected (see

the results in the next section).

Note that the algorithm also produces estimates of parameters describing the eddy

fields themselves (e.g., E 11v). The eddy indication and these eddy field parameters can be

reported to the user for use at the navigation level. For example, a mobile robot may take

note of a location with large eddy fields, and later choose paths that avoid that area.


An experiment was performed to verify the eddy field noise reduction technique

presented in this chapter. The experimental hardware included one beacon, a sensor, and

one eddy source (an aluminum plate), as shown in Figure 4.2 (additional information

about the experimental hardware can be found in Chapter 7). The beacon was used to

generate a magnetic field signal using the DMLP pseudorandom signal structure. Themetallic plate was placed in various positions and orientations near the sensor, creating

eddy fields. The sensor recorded magnetic field measurements and then estimated the

amplitude of the beacon field using two different algorithms – the estimator from Chapter

3 (which does not incorporate an eddy model) and the estimator from this chapter. The

results can be used to quantify the effectiveness of the improved estimator.

A code with a length of 63 chips was used, with a code period of 0.1 s (resulting

in a chip period of 1.6 ms). This signal structure is used for the rest of the experimental

work, and is representative of a signal that could be used in a system with thousands of

beacons. The metallic plate is composed of aluminum and measures 40 cm x 35 cm x 0.5

cm.

Figure 4.2. Experiment used to verify the eddy field detection and mitigation

technique.

Figure 4.3. Experimental results demonstrating the effectiveness of the eddy field

noise mitigation technique. When a metallic plate is placed near the sensor (at 30

s), the Chapter 3 estimator reports an estimate of the beacon field (B1z) that is 50%

in error, while the Chapter 4 estimator is only 11% in error. The binary, dimen-

sionless signal “eddy indication” is superimposed on the graph to indicate the tran-

sition from the Chapter 3 to the Chapter 4 estimator.

0 10 20 30 40 50 60 0

5

1 0

1 5

2 0

2 5

time (s)

B f i e l d ( m G )

B1 z (chap 3 estimator)


E11 z

E21 z

E31 z

eddy

indication

(binary flag)



63

At the start of the first experiment, the metal plate was “far” (1 m) from the sen-

sor. After approximately 30 seconds, the plate was placed near the sensor (roughly 3 cm

between the sensor and the plate edge) as shown in Figure 4.2. The results are presented

in Figure 4.3 as a plot of the estimated amplitude of the beacon field (B1z), using both es-

timators, versus time. For the first 30 seconds, when the plate is far, eddy field noise is

not indicated. However, as the plate approaches, the eddy field parameters (e.g., E 11z )

grow rapidly, and the eddy field indication is triggered. A large error appears in the

estimate from the Chapter 3 algorithm (the estimate is incorrect by 50%). The estimator

from this chapter rejects much of the eddy field noise, and generates an output that is in

error by only 11%. In this particular experiment, the effects of eddy field noise were

mitigated by 77%.

Similar experiments were performed at various locations and orientations to con-

firm the effectiveness of the noise mitigation technique. The results from a second ex-

Figure 4.4. Comparison of estimator performance with a metallic plate in vari-

ous positions and orientations. The Chapter 4 estimator performs better than the

Chapter 3 estimator, mitigating eddy field noise by approximately 74%.

0 20 40 60 80 100 120 140 160 180

- 5

0

5

1 0

1 5

2 0

2 5

3 0

time (s)

B f i e l d ( m G )



E11 z

E21 z

E31 z

eddy

indication



64

periment are shown in Figure 4.4. Again, the plot contains the estimates of B1z , E 11z , E

21z ,

and E 31z versus time using the improved estimator, along with B1z using the Chapter 3

estimator and the eddy field indication. During this trial, the plate was placed for ap-

proximately 30 seconds in each of six different locations and orientations. For the first

30 seconds, the plate was far from the experiment area. For the remaining five poses, the

plate was located near the sensor (within 10 cm). It is interesting to note that, as ex-

plained in Chapter 2, in some orientations the nearby plate did not produce eddy fields at

all (at least not in the axis that was being measured). In three poses (30-60 s, 90-120 s,

and 150-180 s), however, the Chapter 4 detector mitigated significant eddy fields. Over

several experiments, in the poses where eddy fields were the strongest, the algorithm pre-

sented in this chapter proved quite effective, mitigating eddy field noise by an average of

approximately 74%.

4.4 Summary

The DMLP signal architecture presented in the previous chapter reduces the over-

all amount of eddy field noise, but does not eliminate it entirely. This chapter presents a

method to detect and further mitigate eddy field noise in the DMLP system. A model is

developed to describe the eddy fields produced by the pseudorandom beacon signals.

This model is then used to modify the estimation process, which extracts individual bea-

con field estimates from the measurement data, to take into account the effects of eddy

fields. The improved estimator is effective at detecting and mitigating eddy field noise,

as demonstrated by experimental results.



65

5 Solving for Position and Attitude

This chapter describes the next link in the signal processing chain (Figure 2.7)

that began in Chapter 3. In that chapter, the sensor recorded measurements of the local

magnetic field, which included a superimposed mix of signals from many beacons. The

signals from individual beacons were distinguished, and an estimate of the magnetic field

due to each beacon within range was obtained. Although the signal architecture proposed

in Chapter 3 reduces the amount of eddy field noise, it can still be a dominant source of

error in certain circumstances, such as when the sensor is close to a metallic object. The

techniques of Chapter 4 modify the magnetic field estimates to further reduce eddy noise.

This chapter now describes a method to take those magnetic field estimates, along

with the known beacon locations and parameters, and produce an estimate of sensor posi-

tion and attitude. Although the equations relating the magnetic field estimates to sensor

position and attitude are nonlinear, the technique reliably converges to the correct solu-

tion, even with no a priori knowledge of state.

To provide background, the initial section of this chapter surveys the solution al-

gorithms of existing magnetic-based systems. Although they are targeted at fundamen-

tally different applications, and are of limited use in the DMLP system, this discussion

helps establish a list of characteristics that are desirable for the new solution algorithm.



66

Then, the new position and attitude solution algorithm, designed specifically for the

DMLP system, is described in detail. Finally, the advantages of this new algorithm,

when applied to the DMLP system, are examined. One advantage of particular interest is

investigated in further depth: the solution technique enables the system to assume a new

geometry. Specifically, the beacons may consist of only one coil, rather than sets of three

orthogonal coils (the prevailing geometry among commercially available systems). This

geometry addresses both primary challenges to magnetic field positioning systems - the

coverage volume for a given power consumption is increased and the system eddy noise

is reduced.

5.1 Survey of Solution Methods

Magnetic fields have been used as the basis for several interesting types of posi-

tioning systems, and multiple algorithms can be found that operate on magnetic field

measurements to produce position information. However, a survey of existing solution

methods reveals that many are designed for applications that are fundamentally different

from the DMLP system, and are of limited use in the DMLP architecture. This survey

helps establish a list of desirable characteristics for the DMLP solution algorithm.

Several existing solution methods (e.g., [68-71]) are designed for applications

such as tracking an actor moving around on a stage. These techniques are specific to sys-

tems with small coverage volumes, using a small number of beacon coils (typically 3).

Thus, these solution methods do not take advantage of the numerous beacon signals that

are present in a DMLP application. Further, systems using these solution methods em-

ploy feedback from the sensor to generate the beacon signals. That is, the sensor uses the

current beacon signals to determine its location, then communicates this information to

the beacons. That location is used to determine the next set of beacon signals. This de-

sign constrains the number of sensor units that can operate in a given area and adds com-

plexity to the overall system.

In addition, solution methods [68-71] are developed for a specific beacon geome-

try, three co-located coils oriented in orthogonal directions (the prevailing geometry

among commercially available systems). In Section 5.3, it is shown that, for a building-

wide application, it is advantageous to break from this paradigm and use only one coil at



67

each beacon location. Finally, the solutions produced by these methods have ambigui-

ties. Other sensors, or a priori knowledge, can be used to choose among the various pos-

sibilities. In the DMLP system, it is desirable for the sensor to determine its location

immediately, with no a priori knowledge of location, allowing the sensor to start from an

arbitrary, unknown location.

Other solution methods are targeted at applications fundamentally different from

the DMLP system. For example, References [72, 73] are specific to problems with less

than six degrees of freedom. Reference [74] uses several sensors, at known locations, to

track the movement of a dipole magnetic field – the inverse of the DMLP application.

Although existing solution methods are successful in the applications they are de-

signed for, they are not particularly well suited for the DMLP application. Thus, this

brief survey establishes a list of desired characteristics for the position and attitude solu-

tion algorithm in the DMLP system. This desired solution algorithm: (i) incorporates

measurements from a large number of coils at multiple locations, (ii) uses simple beacons

that do not require feedback from the sensors, (iii) does not produce ambiguous results,

(iv) needs no a priori knowledge or additional sensors, and (v) estimates all six degrees

of freedom of the sensor.

In the next section, a new algorithm to solve for position and attitude is presented

that has these characteristics. Further, it is (arguably) simpler than existing methods, de-

coupling the position solution and attitude solution stages. This allows a large body of

previous research to be leveraged for the attitude estimation problem. Finally, as dis-

cussed in Section 5.3, this algorithm enables a new system geometry where only one bea-

con coil is used at each location. This improves the DMLP system in two important re-

spects: the coverage volume for a given power consumption is increased and the system

eddy noise is reduced.



68

5.2 New Solution Algorithm

5.2.1 Problem Statement

Consider a building with numerous beacons, each producing a dipole magnetic

field, as shown in Figure 5.1. A sensor unit measures the magnetic field vector at its lo-

cation in space, which contains a superimposed mix of signals from several beacons. As

discussed in previous chapters, the sensor processes the measured magnetic field vector

to distinguish the unique signals from which it is composed. The result is an estimate of

the magnetic field vector created by each individual beacon, Bi . The goal is to take the

estimates Bi , the known beacon locations, and the known beacon parameters (e.g. the size

of each beacon coil, number of turns, etc.) and produce an estimate of sensor position and

attitude.

Note that, for the solution algorithm, it is not important how the magnetic field es-

timates Bi are obtained. The beacons could use the pseudorandom code structure detailed

in Chapter 3, with the sensor processing the measurements by means of the discrimina-

tion techniques presented there. However, this solution algorithm is still applicable even

if the system uses TDMA or FDMA approaches to obtain the estimates Bi .

Assume the estimates Bi have been obtained for n nearby beacons. A minimum

of 3 beacons is required for this solution method (typically 3-8 beacons will be within

range.) The magnetic field is a vector quantity, and the magnetic field estimates of n

beacons in each of 3 sensor axes result in a total of 3n component measurements. For the

case where all beacons are oriented in the +z direction, the 3n measurements are related

to the position of the sensor by the following 3n equations:

5/)2)(2)(2)(2(

5/))((3

5/))((3

ir

i y y

i x x

i z z k

iz B

ir

i z z

i y yk

iy B

ir

i z z

i x xk

ix B

−−−−−=

−−=

−−=

(5.1)

where k = µ 0 NIa/4π and

i = 1...n identifies a particular beacon

r I = ( ( x - xi)2 + ( y - yi)

2 + ( z - z i)2 )1/2

x, y, z = sensor position



69

xi , yi , z i = position of beacon i Bix , Biy , Biz = estimate of magnetic field created by beacon i

(in x-, y-, or z- directions)

However, these equations are written for magnetic field estimates ( Bi ) with re-

spect to the building-fixed ( x, y, z ) coordinate frame. The actual measurements are taken

in the local (u, v, w) sensor coordinate frame. One method to relate these frames is to use

a direction cosine matrix:

=

iz

iy

ix

iw

iv

iu

B

B

B

C C C

C C C

C C C

B

B

B

333231

232221

131211

(5.2)

The direction cosine matrix itself only contains 3 unique pieces of information (the atti-

tude could be expressed as 3 Euler angles). The six constraint equations associated with

the direction cosine matrix are:

x

y

z

u

vw

B1

Bi

B2

sensor

beacon

Figure 5.1. In the DMLP system, the sensor measures the magnetic field of each

nearby beacon. Given these measurements, plus the known beacon locations and

parameters, the solution algorithm produces an estimate of the sensor position

and attitude.



70

1

1

1

1

1

1

2

33

2

23

2

13

2

32

2

22

2

12

2

31

2

21

2

11

2

33

2

32

2

31

2

23

2

22

2

21

2

13

2

12

2

11

=++

=++

=++

=++

=++

=++

C C C

C C C

C C C

C C C

C C C

C C C

(5.3)

The problem statement can be summarized as: given the 3n estimates ( Bix, Biy, and

Biz ) and the known beacon locations and parameters (e.g., k and xi in equation 5.1), but no

initial knowledge of state, solve equations 5.1–5.3 for the sensor position and attitude (6

independent unknowns).

5.2.2 Position Estimation

A conceptually simple way to find a solution to this set of nonlinear equations

(equations 5.1-5.3) is the brute force method – choose a trial sensor state, evaluate the

equations at that state, and record the residuals. The trial location that best “fits” the

equations is selected. However, this method was rejected for the DMLP system as im-

practical because of the massive amount of computation required. For example, if trial

locations are selected at 1 cm increments, a billion evaluations (each involving division

and square root operations) would be required to test a 10m x 10m x 10m volume.Another straightforward technique is to use the Newton-Raphson approach to

multidimensional root finding [75]. The solution procedure is to choose a reasonable ini-

tial estimate, linearize the equations about that estimate, and solve the linearized equa-

tions in a least-squares sense. This results in an incremental update to the state estimate,

and the process iterates until the updates become sufficiently small. However, when ap-

plied to these equations, this algorithm was found to have poor convergence properties.

Specifically, it has been found that the Newton-Raphson approach to solving equations

5.1-5.3 generally does not converge at all if the a priori position knowledge is inaccurate

by as little as 2 cm. Note that the simplest version of the Newton-Raphson technique was

tested – more complex versions (using “backtracking”, “hook step”, etc. [76]) may have

more success.



71

A step towards a potential solution is to combine the 3n component position equa-

tions 5.1 into n magnitude equations:

42/122 ))(3( iii r r z z k +−=i B (5.4)

Note that the sensor attitude has been decoupled from the position estimation problem.Equation 5.4 now represents n equations (for n beacons) with 3 unknowns ( x, y, z ). Tests

reveal that the simple Newton-Raphson approach can reliably solve equation 5.4, but

only if the initial estimate of position (the input to the algorithm) is “close” to the solu-

tion. For the typical distances between beacons and noise levels encountered in the

DMLP system, a priori knowledge of position needs to be accurate within approximately

50 cm in order for the Newton-Raphson technique to reliably solve equation 5.4 (the spe-

cific accuracy is a complicated function of the particular geometry).

A goal of the DMLP system, however, is to provide position estimates with no a

priori knowledge of state. Although there are no general methods that guarantee a solu-

tion to an arbitrary system of multiple nonlinear equations, further progress can often be

made by using additional insight specific to the problem [77]. Equation 5.4 can be re-

written using spherical coordinates as

32/12 )cos31( ii r k θ +=i B (5.5)

where θi is the angle between the axis of the ith beacon and the vector from the ith bea-

con to the sensor, as shown in Figure 2.1. Equation 5.5 represents n equations in n+3 un-

knowns ( x, y, z, θ i). However, the (1 + 3cos2θ)

1/2 term in equation 5.5 is bounded

1 ≤ (1 + 3cos2θ)

1/2 ≤ 2 ∀θ

so the characteristics of equation 5.5 are thus dominated by the 1/r 3 term. With this in-

sight, an approximate set of equations can be derived by replacing (1 + 3cos2θ)

1/2 by the

constant ‘1.5’ to obtain

3/5.1 ir k ≈i B (5.6)

The Newton-Raphson algorithm applied to equation 5.6 converges without any a

priori knowledge of position. Of course, the solution will differ from that of equation

(5.5) due to the approximation step. However, because the simplification does not affect

the dominant 1/r 3 term, the algorithm based on equation 5.6 reliably (see discussion be-

low) converges to a solution within 10 cm of the actual sensor position. Thus, equation



73

This problem has a long history, with well-known algorithms for the solution. It was first

posed by Wahba [78], motivated by the optimal estimation of the attitude of a satellite

(line of sight vectors to guide stars are measured in the satellite reference frame and

known in an earth-fixed reference frame). A solution appeared in [79], and a bibliogra-

phy of numerous improvements and modifications are referenced in [80]. For simplicity,

the singular value decomposition method, as described in [80], was used as the basis for

this experimental work (although examples of computationally faster methods appear in

[81,82]).

Following Reference [80], it can be shown that:

)(1)( T CAtraceC L −= (5.8)

where the auxiliary matrix A is defined as

∑=

=n

i

T

iivw A1

(5.9)

The singular value decomposition of A is then computed

T USV A = (5.10)

where U and V are orthogonal matrices, and S is diagonal. Note that matrices U and V

must be proper orthogonal (determinant of +1 instead of –1). This can always be accom-

plished – for example, if needed, a column can be multiplied by –1 and the sign of the

corresponding singular value adjusted accordingly. The solution, then, is simply:T

opt UV C = (5.11)

The elements of the direction cosine matrix, once estimated, contain all of the informa-

tion needed to convert to other attitude representations, such as Euler angles.

5.3 Advantages of the New Solution Algorithm

This solution algorithm is well suited to the DMLP application – it has the desired

characteristics that were established in the first section. The technique estimates all sixdegrees of freedom of the sensor, does not produce ambiguous results, and is able to in-

corporate measurements from a large number of coils at multiple locations. The algo-

rithm needs no a priori knowledge of state and does not require the beacons to receive

feedback from the sensors. Further, the method allows a large body of previous research

to be leveraged for the attitude estimation problem.



74

A final advantage is explored further in this section. The solution method enables

a new system geometry where only one beacon coil is used at each location, rather than

three coils per location (the prevailing geometry found in commercially available sys-

tems). The result of this geometry change is that both primary challenges to the DMLP

system are addressed. Specifically, the use of single coil beacons (enabled by the new

solution method) increases the system coverage volume for a given power consumption

and reduces the overall eddy field noise. To investigate this final advantage in further

detail, an analysis is carried out as a series of four steps.

The first step in the investigation is to define exactly the two solution algorithms

that are being compared. First, consider an existing solution algorithm (designated “A”)

that requires three co-located coils. Existing magnetic field positioning systems target

applications with relatively small coverage volumes, such as recording the motion of ac-

tors as they move on a stage. Commercial systems generally use a single beacon consist-

ing of three concentric coils, oriented in orthogonal directions. This allows a compact

unit – a sphere with these three coils inside can be hung over the center of a stage. Solu-

tion methods such as [68-71], appropriately, are designed for this standard geometry.

Given field measurements from all three coils in a set, a position and attitude solution can

be formed using these existing methods.

One set of three coils cannot be used to cover the large volumes expected in

DMLP applications (see the discussion in Chapter 2). However, a straightforward ap-

proach could be used to extend this existing solution method to larger coverage areas.

Although commercially available systems generally use one set of three coils, consider an

example where multiple triple-coil beacons are placed around a building. If the sensor

measures the magnetic fields from all three coils in a set, its position and attitude can be

established using the existing method. Further, if the sensor is in such a location that it

can also measure the signals from all three coils in another set, those signals could be

used to form a second position solution. In this case, the two position solutions (one as-

sociated with each set of three coils) would likely be very similar. To arrive at a final

position solution, the two position solutions could be averaged. Algorithm A is depicted

in Figure 5.2(a).

In contrast, recall from the previous section that the new solution algorithm (des-



75

ignated “B”) incorporates measurements from any beacon. That is, no concept of a set of

beacons is required. Figure 5.2(b) depicts solution algorithm B for comparison.

The second step in the investigation is to determine the relation between the solu-

tion algorithms and the coverage volumes of the beacons. The coverage volume of a sin-

gle coil is shown in Figure 5.3(a). Figure 5.3(b) depicts a cross section of the coverage

volumes of three concentric, orthogonal coils. The intersection of the coverage volumes

of the three coils in Figure 5.3(b) is designated region I. That is, in region I the signal

from all three coils may be received. The union of the coverage volumes of the three coils

is designated region U. That is, in region U the signal from one or more coils may be re-

ceived.

The seemingly subtle difference between algorithms A and B is actually quite

significant, as follows. Solution method A may only be used in region I, where the sig-

Measurements from

all three coils in a setExisting solution

method

Average

Existing solution

method

Solution

Measurements from all three coils

in another set (if available)

Solution New solution

method

(a)

(b)

Measurement

from any coil

Figure 5.2. Comparison of existing and new solution methods.



76

nals from all three coils are present. In contrast, solution method B may make use of the

signal from any coil. Thus, algorithm B gains at least one usable signal anywhere in

region U. Using numerical analysis, the volume of region I is determined to be only 62%

of the volume of region U. In other words, 38% of the total coverage volume (the region

in U but not in I) is effectively wasted by using solution algorithm A – method B can

make use of the one or two signals in this area, but method A cannot.

The third step in the investigation is to consider the placement of the beacons. A

reasonable approach to outfitting a building with beacons is shown in Figure 5.4. The

beacons are located in planes, corresponding to the crawlspaces between floors of a

building. This location has several advantages, as described in Chapter 2 (e.g., access to

electrical outlets, the beacons are unobtrusive, it is relatively easy to place beacons in an

efficient, regular array). The beacons in alternating planes are staggered as shown in the

figure, which results in a larger coverage volume than if they were not staggered.

Finally, by utilizing the information from the first three steps of the investigation,

the advantages of solution method B over method A can be determined (the fourth step of

the investigation). First, consider algorithm A in a system with triple-coil beacons placed

as shown in Figure 5.4. In this analysis, the system is required to provide continuous

(a) (b)

I

U

Figure 5.3. The coverage volume of one coil is shown in (a). In (b), a cross sec-

tion of the coverage volume of three coils is depicted. Volume I is covered by all

three coils, while volume U is covered by one or more coils.



77

coverage, and thus every location in space is covered by all three signals from at least one

set of coils. That is, every location is within region I from at least one set of coils. A

cross section of the beacon placement is shown in Figure 5.5(a). In this baseline case, the

distance between beacons is denoted as 1 unit for comparison purposes.

Next consider algorithm B in the exact same scenario – triple-coil beacons, con-

tinuous coverage, using the same beacon placement pattern (Figure 5.4). The new solu-

tion algorithm enables beacons to be placed further apart for a given power consumption,

as shown in Figure 5.5(b). To demonstrate, consider the center location, equally distant

from all four beacons. At this location, a signal can be received from only one coil in

each triple-coil beacon. Existing solution method A relies on three signals coming from

one set of beacons and cannot produce a solution here, but new solution method B can.

The result is shown in Figures 5.6(a) and (b). Existing solution method A, in a system of

triple-coil beacons, uses the geometry shown in Figure 5.6(a). New solution method B,

in a system with triple-coil beacons, uses the geometry shown in Figure 5.6(b), where

beacons are placed 26% further apart. New solution algorithm B allows 200% (1.26 x

Figure 5.4. Example placement of beacons in a building.



78

1.26 x 1.26) of the volume of Figure 5.6(a) to be covered with the same number of bea-

cons and the same overall power consumption. An alternative way of stating the advan-

tage of the new method is that the volume in Figure 5.6(a) can now be covered using only

25% of the power.

However, an even more exciting geometry is made available by the new solution

method, shown in Figure 5.6(c). Here, a single coil at each beacon location consumes the

total power of a triple-coil beacon from Figure 5.6(a). This results in a system with 121%

of the coverage volume of Figure 5.6(a). Alternatively, the power consumption could be

reduced 32% for the same coverage volume. But notice that only one coil has been used

at each beacon location, not three. Therefore only 1/3 the number of signals need to be

used. In an FDMA system, only 1/3 the frequencies are required. With TDMA, only 1/3

the time slots are needed. In a CDMA system, the codes can be shorter and slower. That

is, regardless of the multiple access approach, this geometry (enabled by the new solution

method) lowers the overall spectral content of the beacon signals. As discussed in Chap-

ter 2, this results directly in lower eddy field noise. Thus, the new solution method and

the single-coil geometry of Figure 5.6(c) result in a larger coverage volume for a given

1 1.26

(a) (b)

Figure 5.5. A cross section view of the coverage volume of four triple-coil beacons

is shown. In (a), existing solution methods may be used. In (b), the new solution

may be used. The new solution algorithm allows the beacons to be spaced further

apart for the same power consumption, while still providing continuous coverage.



79

power consumption and reduced system eddy field noise.

5.4 Summary

An algorithm is presented which takes magnetic field estimates, along with the

known beacon locations and parameters, and produces an estimate of sensor position and

attitude. Although the equations relating the magnetic field estimates to sensor position

and attitude are nonlinear, the technique reliably converges to the correct solution, even

with no a priori knowledge of state. The solution method has several advantages over

existing methods because it is designed specifically for the DMLP application. The most

important advantage is that beacons with one coil can be employed, resulting in both lar-

ger coverage volume for a given power consumption and reduced system eddy field

noise.

1.26

1.26

1.26

1

1

1

0.81

0.81

1.87

(a) (b) (c)

Figure 5.6. The placement of beacons is shown for three different cases: (a) tri-

ple-coil beacons and existing solution method A, (b) triple-coil beacons and new

solution method B, and (c) single-coil beacons and new solution method B. Case

(c) allows 21% more coverage volume (for the same power consumption) than

case (a) while requiring only 1/3 of the frequency content (lowering eddy noise).



80

∫



81

6 Iron Noise Mitigation

The previous three chapters have described the DMLP signal processing chain,

starting with a sequence of magnetic field measurements and ending with an estimate of

sensor position and attitude. Each of these stages has been designed to combat eddy field

noise, a source of error caused by conductors in the environment. However, as described

in Chapter 2, there is a second, separate mechanism by which certain objects in the envi-

ronment (ferromagnetic materials) may introduce error into the position and attitude es-

timates. The principal offender in most scenarios is iron (though other materials, such as

nickel and cobalt, are ferromagnetic as well), and this distortion is referred to here as iron

noise. This chapter presents a method to detect and mitigate this source of error.

Unlike eddy field noise, iron noise cannot be detected from any individual beacon

signal. However, this disturbance can be observed by considering a collection of several

beacon signals. After a brief background section, this approach to detecting iron noise is

introduced with a one-dimensional example. Next, a model is developed of the effects of

iron distortion in three dimensions. Several assumptions and simplifications in the model

are required to yield a tractable mitigation technique. An algorithm is then presented

which examines the magnetic field readings for ferromagnetic distortion and, if iron noise



82

is detected, characterizes the source and computes a correction. Finally, experimental

results are presented, quantifying the performance of the technique.

This iron noise mitigation algorithm requires both a position and attitude estimate

(from Chapter 5) and estimates of the beacon field vectors (Chapters 3 and 4), and is thus

the last stage in the signal processing chain. It is the most computationally expensive

step and, because of the approximate model, produces modest results (a 40% reduction in

iron noise is typical). Thus, this stage may be considered optional in environments (e.g.,

an office building or apartment complex) where large amounts of iron are not likely to be

encountered.

6.1 Background

As described in Chapter 2, ferromagnetic materials respond to external magnetic

fields (e.g., the beacon fields) by creating magnetic fields of their own. These magnetiza-

tion fields sum with the beacon signals, introducing error into the position and attitude

estimates. Positioning systems based on ELF magnetic fields can mitigate this error

source through calibration. For example, the sensor is placed at a surveyed location and

the difference between its actual estimate and the known truth value ( i.e., what it should

estimate in a perfect environment) is recorded. This is repeated at numerous locations

throughout the operating area, and a map of corrections is built. There are several varia-

tions on this technique [83, 84]. This a priori calibration is effective for large, stationary

iron objects, and a DMLP installation can certainly utilize this technique.

The focus of this chapter is fundamentally different from calibration. The algo-

rithm presented here attempts to detect and mitigate iron noise dynamically, while the

system is in normal operation. As an example, consider a mobile robot navigating a

building using the DMLP system. Unexpectedly, an iron object is placed immediately

next to the sensor, and its position estimation errors grow to 10 or 20 cm. Calibration

offers no defense against this unforeseen iron source. However, the algorithm presented

in this chapter can detect the presence of this iron distortion “on the fly”, compensating

for its effects in real time while the sensor continues to operate normally.

Calibration and the mitigation algorithm presented here are complementary tech-

niques, and both may be used in the same positioning system. Calibration is most effec-



83

tive against large, stationary ferromagnetic objects. The algorithm presented here is most

effective against smaller iron clutter, not “captured” in the calibration, that the sensor

may unexpectedly encounter.

Although the mitigation proves only modestly successful, this technique is a po-

tentially valuable step for magnetic field-based positioning systems. An extensive litera-

ture search indicates that this is the first attempt to dynamically detect and mitigate

distortion caused by ferromagnetic objects in the environment.

6.2 Introduction to the Approach

Reducing the errors caused by ferromagnetic objects in the environment proves to

be a more difficult challenge than correcting for the effects of eddy fields. In Chapter 4,

the mitigation technique for eddy field noise operates on each beacon signal individually.

That is, even with only one beacon signal present, the effects of eddy fields on that signal

can be detected and accounted for (for example, see the Experimental Results section of

Chapter 4). Unfortunately, the distortions caused by the presence of iron cannot be de-

tected in the signal from any individual beacon. However, this section introduces an ap-

proach that examines a collection of beacon signals. That is, when several beacon signals

are combined into a position solution, the disturbance can be observed.

First, it is necessary to briefly review the sensor signal processing and define an

important new metric. As described in Chapter 3, the sensor unit takes a sequence of

measurements of the vector magnetic field at its location. These measurements contain

the superimposed signals from multiple beacons. In Chapters 3 and 4, algorithms are

presented which take the sequence of measurements and produce estimates of the vector

magnetic field, at the sensor’s location, produced by each individual beacon. The vari-

able Bi designates the magnetic field vector of the ith beacon. The solution method in

Chapter 5 then takes the estimates Bi and produces an estimate of sensor position and atti-

tude.

At this point, the sensor has enough information to perform an interesting compu-

tation. The location and parameters of each beacon are known to the sensor a priori, and

an estimate of sensor position and attitude has been obtained from the solution algorithm.

Thus, it is possible (using the dipole model in equation 2.3) to compute the theoretical



84

value of each beacon field at the sensor location. The magnetic field vector produced by

the ith beacon, determined by computation, at the estimated sensor position and attitude

is defined as Bi c.

Now an important metric may be introduced. A residual is defined as the differ-

ence between Bi (produced directly from measurements) and Bi c (computed at the esti-

mated sensor location):

c

i i i B B R −= sbC / (6.1)

Note that the sensor parameterizes the (measured) vectors Bi in sensor frame coordinates,

while the (computed) vectors Bi c are in building frame coordinates. Rotation matrix C b/s

transforms vectors from sensor frame coordinates to building frame coordinates (C b/s is

the matrix inverse of rotation matrix C , an output of the solution algorithm in Chapter 5).

Residuals are parameterized in building-frame coordinates.

The residuals are a measure of the quality of the position estimate. If the residuals

are small in magnitude (compared to, for example, the expected noise level in Bi ), then

the position estimate is trustworthy. That is, all of the estimates Bi have approximately

the value that would be expected for a sensor that is truly at the estimated location. How-

ever, if the residuals are large, the position estimate is suspect. That is, the position solu-

tion algorithm converged to an estimate, but each measured Bi value does not agree well

with the value expected at the estimated location. Discrepancies between Bi and Bi c

, cap-

tured by the residual metric, indicate that some type of noise or disturbance has affected

the estimates.

It is through the computation of residuals that iron noise becomes observable. To

demonstrate, consider the following one-dimensional example. A simple coordinate sys-

tem is constructed in Figure 6.1, with one beacon at location (0 m) and one beacon at lo-

cation (3 m). In this example, the sensor is constrained to lie along the line between the

beacons, and its position along this line is to be estimated. Each beacon field is described

by

3/1 r B = (6.2)

where: B = beacon field (mG)

r = distance from beacon (m) along the one dimension of freedom

In this simple example, the only source of noise is the presence of a ferromagnetic object.



85

First, consider the case where no iron is present. The sensor, located at (1 m),

measures the magnetic field at its position. From these measurements, the amplitude of

beacon 1 (B1) is estimated as 1 mG and the amplitude of beacon 2 (B2) as 0.125 mG.

From these estimates, the sensor determines its position to be (1 m). Given the known

beacon locations and parameters, the sensor computes the expected beacon fields at its

estimated location – B1c is 1 mG and B2

c is 0.125 mG. Thus, the residuals have zero

magnitude and the position solution is judged to be reliable.

In contrast, consider the effects of an iron mass placed “above” the sensor, as

shown in Figure 6.2. As described in Chapter 2, iron responds to an external field (pro-

Beacon 1 Beacon 2

0 1 2 3

B1

B2

Sensor

Figure 6.1. In this one-dimensional example, the sensor measures the fields pro-

duced by two beacons.

Sensor

0 1 2 3

Beacon 1 Beacon 2

B1

B2

Iron

Figure 6.2. An iron mass is placed next to the sensor in the one-dimensional exam-

ple. The iron, stimulated by the beacon fields, creates a field of its own and causes

the sensor to overestimate the size of the beacon signals. This iron noise causes er-

ror in the position estimate, but its presence can be detected in the residuals.



86

duced by the beacons) by creating a field of its own. Modeling the iron field as a simple

dipole oriented in the direction of the external field, the iron and beacon fields add con-

structively, as shown in the figure. The sensor takes measurements of the sum magnetic

field and, in this example, estimates B1 to be 1.1 mG and B2 as 0.138 mG. Neither esti-

mate, considered by itself, gives any indication that iron distortion is present. The sensor

uses B1 and B2 as inputs to a simple solution algorithm, and estimates its position as

(1.017 m).

However, at location (1.017 m), the expected amplitude of beacon 1 (B1c) is 0.951

mG and B2c is 0.128 mG. There is a discrepancy between the measured beacon field val-

ues and the values expected at the estimated location – the residuals are non-zero. Thus,

the sensor has detected the presence of a distortion by examining the residuals.

Note that in this simple example, the iron caused all of the beacon field estimates

to be too large. In three dimensions, the effects of iron are more complex. As described

in Chapter 2, a single iron source may cause the fields from some beacons to be overes-

timated while at the same time causing the fields from other beacons to be underesti-

mated. In the next section, a model of the effects of iron in three dimensions is devel-

oped.

In summary, the distortion due to iron is not detected from the measurements of

any one beacon. However, iron noise can be observed by considering a collection of sig-

nals from multiple beacons. The particular approach taken by this noise reduction tech-

nique is to attempt to observe and mitigate the effects of iron through the computation of

residuals.

6.3 Iron Noise Model

As described in Chapter 2, a ferromagnetic object in the environment responds to

a beacon field by creating a magnetic field of its own. This magnetic field combines with

the beacon field in the measurements taken by the sensor. Thus, the estimate of the bea-

con magnetic field (the output of Chapters 3 and 4), Bi , is the sum of the actual beacon

field, Bi true, and the distortion caused by the ferromagnetic object, F i .

i

true

i i F B B += (6.3)



87

In this section, a simple model is developed for the effect (F i ) that a ferromagnetic

object has on the estimate of a beacon magnetic field ( Bi ). Note that it is the effect of the

ferromagnetic object on the beacon field estimate that is modeled in this section, as op-

posed to the magnetization field itself. This effect (F i ) on the beacon field estimate has

units of Gauss. This approach is taken to simplify the discussion – the introduction of the

magnetic field strength vector (generally given the symbol H ) and the actual unit for a

magnetization field (the Oersted) can be avoided.

Several assumptions are required to form the model. The mitigation technique

would not be possible without these simplifications, but they do reduce its effectiveness.

First, it is assumed that the field generated by the iron in response to a beacon field can

be modeled as a dipole field. This assumption is sound if the sensor is “far” from the

iron, compared to the physical size of the iron object itself. However, as shown by the

experimental results in Section 6.5 (which demonstrate modestly successful iron noise

mitigation), this assumption is at least moderately accurate even when the iron is “near”

then sensor. Second, it is assumed that the distortion is the result of one dipole source

(i.e., one iron object close to the sensor). Third, the orientation of the iron dipole field is

assumed to lie along the beacon field vector that excited it (i.e., the ferromagnetic mate-

rial is isotropic). Fourth, the field generated by the iron is assumed to be proportional to

the applied field (i.e., the ferromagnetic material is linear ). Although ferromagnetic de-

posits are generally not perfectly isotropic or linear, these are fair first-order approxima-

tions for many types of ferromagnetic materials. Finally, it is assumed that the distance

between the iron and the sensor is small compared to the distance to the nearest beacon.

This enables the approximation that the beacon field vector is the same (in magnitude and

direction) at the location of the sensor as at the location of the iron object.

With these assumptions, the effect of a ferromagnetic object on the estimate of

beacon magnetic field Bi (at the sensor’s location) is modeled as (Figure 6.3)

))sin()cos(2( θ r BF c

i i ) )

iik θ θ +≈ (6.4)

where the dipole axis of F i is oriented in the direction of the beacon magnetic field vector

Bi c. The unit vector in the direction of Bi

c is designated c

i B . The proportionality con-

stant k absorbs the size, permeability, and distance of the iron object.



88

In Figure 6.3, the bearing vector (v) is the displacement vector between the iron

and the sensor. The unit vector in this direction is designated v . The bearing angle (θi)

is the angle between c

i B and v . An important point to note is that, using this approxi-

mate model, v always lies in the plane defined by c

i B and F i (this fact will be used

later).

References to θi in equation 6.4 can be written in terms of c

i B and v :

)cos(ˆˆiθ =• v B c

i (6.5)

)sin(ˆˆiθ =× v B

c

i (6.6)

Note that the bearing unit vector is parameterized in building reference frame coordi-

nates, and contains only two independent pieces of information (since it has a magnitude

of 1). The unit vector c

i B is also parameterized in building frame coordinates.

Figure 6.3. The field produced by the iron in response to beacon i is modeled as a

dipole directed along vector Bic.

v

r

θ ˆ

i

Bi c (beacon field)

Iron

Sensor

F i



89

Therefore, from equations 6.4 through 6.6, F i is a function of the unknowns v

and k :

( )k f ,vF i = (6.7)

Thus, this approximate model allows the effects of iron distortion to be described usingonly three independent parameters – the direction in space to the iron, v (2 independent

pieces of information), and the “strength” of the iron source, k . In other words, if v and

k are known, the complete effects of the iron distortion can be calculated using equations

6.4 through 6.6.


A final assumption now enables the mitigation technique. It is assumed that dis-

crepencies between Bi and Bi c, captured by the residual vectors in the second section, are

caused by ferromagnetic distortion that can be described by the model developed in the

third section. Specifically, it is assumed

i i F R ≈ (6.8)

and therefore the residuals can be used to estimate the three model parameters that char-

acterize the iron source. Once the iron source has been characterized, its effects can be

estimated and accounted for. This mitigation algorithm consists of four steps, detailed

next.

The first step in the algorithm is to determine if ferromagnetic distortion appears

to be present. This determination is based on the residuals, which are computed from Bi

and Bi c (equation 6.1). In any measurement system, including the DMLP system, there

are always some sources of noise preventing perfect measurements (for example, thermal

noise is always present in the DMLP system, as described in Chapter 8). Thus, the re-

siduals never have a magnitude of exactly zero, even when there is no iron nearby.

Therefore, as with the eddy field mitigation algorithm in Chapter 4, a threshold is set sothat small, random fluctuations in the magnetic field measurements do not trigger the iron

mitigation algorithm.

In the DMLP prototype system (Chapter 8), the following criteria worked well: if

two or more residuals have a magnitude greater than 0.6 mG, the presence of iron noise is

indicated and the mitigation will be performed. This experimentally determined thresh-



90

old value is strict enough that the iron mitigation technique was never falsely triggered by

thermal noise, and yet the presence of nearby iron was reliably detected. If no iron is de-

tected, the mitigation algorithm terminates at this point.

Note that the detection of iron, even without the mitigation steps that follow, may

be quite useful. For example, a mobile robot could record on its internal map areas where

iron distortion is indicated. Later routes could be planned to avoid these areas.

The second step in the algorithm is to estimate the parameters ( v and k ) that

characterize the iron distortion. First, the bearing unit vector (the line in space containing

the sensor and the iron source) is estimated as follows. Recall, from Figure 6.3, that Bi c

and F i , for each beacon i, define a plane containing v . Also recall that, by assumption,

Ri = F i . Thus ni , a vector normal to the plane containing v , Bi c, F i , and Ri , can be calcu-

lated by:

i

c

i i R Bn ×= ˆ (6.9)

The vector v , which lies in the plane defined by Bi c and Ri , is therefore normal to ni :

0ˆ =•i

nv (6.10)

At this point, the vector ni associated with each beacon i is calculated (equation

6.9). The two vectors with the largest magnitudes are selected – the indices of these vec-

tors are defined as A and B. The plane containing B Ac and R A (normal to vector n A) and

the plane containing B Bc and R B (normal to vector n B) can be used to determine v . The

bearing vector lies in both planes, and thus lies along the intersection of these two planes.

Equivalently, the bearing vector is normal to both n A and n B, and can therefore be com-

puted as:

B A nnv ˆˆˆ ×= (6.11)

where An and Bn are the unit vectors in the directions of n A and n B, respectively.

Note that there is a sign ambiguity in the bearing vector – it actually only repre-

sents the line in space along which both the sensor and iron are located. The direction

which it points (from the sensor to the iron or from the iron to the sensor) is unobserv-

able, and does not affect the final output of the mitigation algorithm.



91

Once v has been determined, it is straightforward to estimate k and thus complete

the characterization of the iron source. Taking the magnitude of both sides of equation

6.4 yields:

)cos31(2

i

k θ += c

i i

BF (6.12)

Every term in equation 6.12, except for k , is now known (with the help of equation 6.5).

Equation 6.12, written with respect to the beacon with index ‘A’ (determined previously),

becomes:

)cos31(2

Ak θ += c

A A BF . (6.13)

Similarly, equation 6.12, written with respect to the beacon with index ‘B’, becomes:

)cos31(2

Bk θ += c

B B BF (6.14)

Equations 6.13 and 6.14 are each solved for k . These two values of k are averaged to ar-

rive at the final estimate of k .

The third step in the mitigation algorithm is to estimate the effect that the iron dis-

tortion has on the measurements. Parameters characterizing the iron source, v and k ,

were estimated in the last step. With the estimates, the effect of the iron distortion (F i ) is

straightforward to calculate, using equations 6.4 through 6.6.

The final step in the mitigation algorithm is to account for the effects of the iron

distortion. The effect that the iron distortion has on the beacon field estimates was com-

puted in the previous step. Thus, the effect of the iron distortion F i is subtracted from the

beacon estimate Bi . The result is a modified estimate Bi (labeled Bi true

in equation 6.3).

These modified beacon field estimates, which have been corrected for the effects of iron

distortion, are then passed through the solution algorithm (Chapter 5) a second time. A

new position and attitude estimate, in which the effects of ferromagnetic distortion have

been mitigated, is obtained.

This final step has two effects. By subtracting F i , the bias in the position esti-

mates due to iron noise is reduced. However, the random fluctuation in the position es-

timates (the “scatter” in Chapter 8) increases. Therefore, an adjustment is made to the

final step of the algorithm. Instead of subtracting the instantaneous value of F i , a low-

pass filtered value of F i is used instead. In the DMLP prototype system (Chapter 7), po-

sition estimates and F i estimates are calculated every 0.1 s (10 Hz), but the F i estimates



92

are filtered to a 1 Hz bandwidth before being applied in the correction. The result is that

the mitigation technique reduces the bias caused by iron distortion while not significantlycontributing to increased scatter.


Several experiments were conducted during the development and testing of this

mitigation algorithm. The experiments were performed using the prototype DMLP sys-

tem (described in the next chapter), where signals from eight beacons are available. The

following simple test procedure was used. Each experiment started without an iron ob-

ject in the test environment, to provide a reference. Then, while the sensor estimates

were recorded, an iron object was placed near the sensor.

One typical experiment is examined in detail in Figures 6.4 through 6.7. In this

experiment, a 6.4 kg iron mass was placed next to the sensor. Figure 6.4 shows the mag-

nitude of two of the residual vectors versus time as the experiment was conducted. Ini-

Figure 6.4. The magnitudes of two residual vectors rise measurably as a ferro-

magnetic mass is placed near the sensor, triggering an indication that iron noise

is present.

0 5 10 15 20 25 30 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

residuals

(magnitude)

iron

indication

(binary flag)

time (s)

m a g n i t u d e o f r e s i d u a l s ( m G )



94

Figure 6.6. An iron mass is placed next to the sensor (at approximately 17 s),

causing a 28% error in the estimate of B1x. With the mitigation algorithm, the

estimate of B1x is only 7.2% in error.

Figure 6.7. The iron mass causes a 30% error in the estimate of B2x. The mitiga-

tion algorithm reduces the error to 13%.

0 5 10 15 20 25 30 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

3 . 0

3 . 5

B1x uncorrected

B1x corrected

truth

iron

indication

time (s)

B 1 x

- c o r r e c t e d a n d u n c o r r e c t e d ( m G )

0 5 10 15 20 25 30 - 2 . 5

- 2

. 0

- 1 . 5

- 1 . 0

- 0 . 5

0

0 . 5

1 . 0

B2x uncorrected

B2x corrected

truth

iron

indication

time (s)

B 2 x

- c o r r e c t e d a n d u n c o r r e c t e d ( m

G )



95

estimate of B1x jumped to 3.03 mG – iron noise caused a 28% error. However, the cor-

rected estimate of B1x (i.e., F 1x has been subtracted) remained at 2.54 mG – an error of

only 7.2%. Thus, the error in this particular signal component was reduced by 74%.

Figure 6.7 shows a similar result in the estimate of a different beacon signal – B2x.

In this case, the nominal value (i.e., with no iron object) for B2x was –1.86 mG. When the

iron was placed near the sensor, the uncorrected value jumped to –2.42 mG (30% error)

while the corrected value changed to –2.11 mG (13% error). The mitigation algorithm

reduced the noise in this signal component by 55%.

Each of these Bi values is an input to the position and attitude solution algorithm.

When the iron was near the sensor and uncorrected Bi values were used, a 16.2 cm error

was created in the (3-D) position estimate. However, when the corrected Bi values were

passed through the solution algorithm, the error in the position estimate was only 8.5 cm.

Thus, for this experiment, the mitigation algorithm reduced the effect of iron noise on the

position estimate by 48%.

Multiple additional experiments were conducted in a similar manner but with dif-

ferent parameters (e.g., location in the experiment area, distance and bearing between the

sensor and the iron). The overall results can be roughly summarized as follows. A 6.4 kg

mass of iron at a distance of 20 cm or more is “far” from the sensor, and does not signifi-

cantly affect the position estimates. At approximately 5-10 cm distance, the position es-

timates are affected (generally a 5 to 15 cm total error). At this distance, the algorithm

reliably detects the presence of the iron, and generally reduces the bias due to the iron

distortion by 20% to 50%. On average, the algorithm provided noise mitigation of ap-

proximately 40%.

6.6 Summary

The mitigation of iron noise proves to be a more difficult challenge than correct-

ing for the effects of eddy fields. However, this chapter presents a method that can detect

this error source by observing a collection of several beacon signals. Then, using a sim-

plified model of iron noise, the parameters describing the distortion can be estimated and



96

a correction can be computed. The algorithm, confirmed experimentally, reliably detects

the presence of iron distortion and achieves a modest level of mitigation.



97

7 The Prototype System

A prototype DMLP system, incorporating the innovations presented in the last

several chapters, was designed and constructed to demonstrate position and attitude sens-

ing in a cluttered environment. The focus of this chapter is the implementation of the

four main parts of the prototype system – the beacons, beacon network, sensor box, and

processor. The results of the experiments performed with this system are detailed in the

next chapter.

7.1 Overview

The DMLP system, as described in the preceding chapters, is based on extremely

low frequency magnetic fields. Inexpensive beacons, installed at known locations

throughout the building, are responsible for creating these magnetic signals. The beacon

fields are generated according to the CDMA signal architecture presented in Chapter 3.

The beacons must be synchronized to use this signal architecture. The beacon network

provides this synchronization as well as a communication link for monitoring the beacons

from a central location.

By measuring the beacon magnetic fields, a small, low-power sensor can deter-

mine its position and orientation anywhere in the building. In the prototype, the sensor is



98

implemented as two separate components, a sensor box and a processor . The sensor box

samples the local magnetic field (a vector quantity) at the proper times and reports the

data to the processor. The processor, using the techniques presented in the preceding

chapters, distinguishes the fields produced by individual beacons, implements algorithms

to mitigate eddy and iron noise, and produces an estimate of the position and attitude of

the sensor box with respect to the building-fixed beacons. The processor for the DMLP

prototype is a laptop PC.

These four main components of the prototype system – the beacons, beacon net-

work, sensor box, and processor – are individually described in the following sections.

7.2 Beacons

Beacons are responsible for creating the low frequency magnetic field signals. To

accomplish this task, the prototype beacons (one is pictured in Figure 7.1) consist of three

main components – a coil, a power amplifier, and an electronics box.

Electrical current flows through the coil to create a dipole magnetic field (de-

picted in Figure 2.1). The current is switched in polarity to implement the signal struc-

ture described in Chapter 3. The power amplifier is used to force the desired current

through the coil inductance. In the prototype system, each coil consists of 80 turns of

wire wrapped on 36 cm diameter core, resulting in a coil inductance of 4 mH and a resis-

tance of 1.2 Ω. At the end of each chip period, when magnetic field measurements are

made by the sensor (described later), the current running through the coil is 2 A. This

yields a magnetic field amplitude of 16 mG at 1 m distance and 0.25 mG at 4 m distance

(measured at θ = 90°, as defined in Figure 2.1). For comparison, the earth’s magnetic

field amplitude, measured at the surface, is approximately 300-500 mG.

The electronics box commands the power amplifier and controls the operation of

the beacon, as shown in Figure 7.2. A Motorola MC68HC11E2 microcontroller (the

“HC11”) is at the heart of each beacon. Upon receiving the “Sync” (synchronization)

signal from the beacon network (described in the next section), it outputs the next chip in

the pseudorandom code sequence. This output commands the amplifier to produce the

proper current through the coil, creating the appropriate magnetic field.



99

Figure 7.1. A prototype beacon. In the DMLP system, beacons generate low fre-

quency magnetic field signals that permeate a building.

Figure 7.2. Prototype beacons consist of a coil, power amplifier, and a beacon

electronics box (containing the functionality inside the dashed line).



100

The digital command from the HC11 is converted to an analog signal (labeled

“Command”) through a D/A converter. The difference between the “Command” signal

and the “Sense” signal (representing the current actually flowing through the coil) is fed

to the control law (a simple gain). The output of the control law, an amplified “Error”

signal, directs the power amplifier. A resistor of low value (0.1Ω) but high heat dissipa-

tion (2W) is used to sense the current flowing through the coil to complete the control

loop. All of the components in the dashed box in Figure 7.2 are inside the beacon elec-

tronics box.

This “closed loop” design provides a simple way to enhance the performance of

the beacon. Figure 7.3 shows the relationship between the “Command” signal, the power

amplifier drive voltage, and the current flowing through the coil. When a change in po-

larity is commanded, the error signal is multiplied by the control law gain. This large

signal causes the amplifier to apply its maximum control authority (about 50V in the pro-

totype system), motivating the current to rapidly change direction through the coil induc-

tance. The amplifier relaxes only when the actual current flowing through the coil

closely matches the desired current. By the end of the chip period, the amplifier is apply-

ing just enough voltage to keep the current flowing through the small resistance of the

Figure 7.3. Relationship between the command signal, amplifier drive voltage,

and coil current in a prototype beacon.



101

coil wire and sense resistor. The result is a beacon that can change polarity much faster

than the “L/R” time constant of the coil. This enables the use of a larger coil inductance,

which translates into additional turns of wire and larger magnetic fields.

This enhanced performance could also be achieved open loop, with a command

profile generated by the HC11. However, the closed loop arrangement is not only sim-

ple, but provides secondary advantages. The design rejects disturbances within the bea-

con, such as changes in transistor parameters as the amplifiers warm up, and also miti-gates the differences between beacon amplifiers.

Each HC11 is programmed with its pseudorandom code. Gold codes of length 63

are used, and a code sequence completes in 0.1 seconds. Thus, the prototype system is

representative of a large DMLP installation, employing the same signal structure that

would be used in a system with thousands of beacons. The codes are shown in Table 7.1

in octal form (i.e., an octal value of 6, which is [1 1 0] in binary, represents a code se-

quence of [1 1 –1]).

The communication signals “Sync”, “ToBeac”, and “FromBeac” are carried by

the beacon network to each beacon electronics box, where they are translated from

RS485 to TTL electrical levels. Only the “Sync” signal is necessary for operation, but the

HC11 also responds to a limited set of commands sent over the beacon network (the

Table 7.1. Pseudorandom codes (written in octal notation) used in the prototype

system.



102

“ToBeac” and “FromBeac” lines). These signals and the beacon network are described

further in the next section.

One lesson learned from the prototype design is that linear power amplifiers are

not well suited for DMLP beacons. The amplifier used in the prototype system (an off-

the-shelf audio amplifier) was inexpensive, easy to obtain, and had ample control author-

ity (power supply rails at +/-50V). However, at the end of each chip period, when only 2

V is required to maintain 2 A of current through the (approximately) 1 ohm coil resis-

tance, 48 V of potential is “dropped” across the power transistors in the linear amplifier.

Thus, for a significant part of each chip period, 96 W are dissipated inside the amplifier

while only 4 W are applied to the coil. In the future, the use a PWM (pulse width modu-

lated) power amplifier in the beacons should prove beneficial.

7.3 Beacon Network

The beacons in the DMLP system must be synchronized to implement the signal

architecture described in Chapter 3. The primary purpose of the beacon network (Figure

7.4) is to connect each beacon to a central timekeeping source, the Timing Box, to enable

this synchronization.

The Timing Box generates the “Sync” signal, which is distributed over the net-

work to all of the beacons. In the prototype system, the signal consists of a repeating se-

quence of 63 pulses, as shown in Figure 7.5. Each pulse prompts the beacons to progress

to the next chip in their respective pseudorandom code sequences. The pulses have a

width of 10 us, except for the first pulse in the sequence, which has a width of 100 us.

This long pulse marks the beginning of a code cycle, when each beacon must produce the

first chip in its sequence. Since the prototype system produces estimates at 10 Hz, a code

cycle (63 chips) must complete every 0.1s. Therefore each pulse is separated by

(0.1s/63) 1.587ms.

The beacon network enables synchronization at two levels – on both the chip and

the code timeframes. First, the beacons are synchronized at the chip level. Based on the

rising edge of the “Sync” signal, all beacons generate the next chip in their code sequence

at the same time. This allows the sensor unit to sample the sum magnetic field at the end

of each chip period, when the beacon fields have stabilized. Thus, this synchronization is



103

required to be accurate within a few percent of a chip period. Note that this timing re-

quirement is not difficult to achieve - even 1000 m of cable adds only microseconds of

delay, which is small compared to a chip length.

Second, the beacons are synchronized at the code level. Based on the long start-

ing pulse of the “Sync” signal, all beacons maintain their relative code alignment. For

example, when a beacon is first powered up, it waits for the starting pulse to begin gener-

ating its magnetic signal. Similarly, if a beacon falls behind by 1 chip (e.g., due to noiseon the “Sync” line), it realigns itself at the next starting pulse.

The beacon network is implemented in a bus configuration – all beacons receive

the same “Sync” signal. Electrically, RS485 signals are used, allowing numerous trans-

mitters and receivers to be attached to the same line. This standard uses differential sig-

naling for noise immunity and allows long cable lengths. Physically, the signals are car-

Figure 7.4. The beacon network is used to synchronize and monitor the beacons.

Figure 7.5. The “Sync” signal, carried by the beacon network to all beacons.



104

ried by category 5 ethernet cable, which is inexpensive, readily available in different

lengths, and has 8 conductors (two wires are used by the “Sync” signal, and four other

wires are used by the two signals described next).

The Timing Box has a secondary purpose – in addition to synchronization, it pro-

vides communication between the beacons and a central control station, the Monitor PC.

The Timing Box converts RS232 signals from the PC’s serial port to RS485 signals on

the beacon network. The PC sends simple commands on the “ToBeac” line, and the bea-

cons respond, one at a time, on the “FromBeac” line.

A limited set of commands is implemented in the prototype system, mainly to

monitor the health and status of the beacons. Each beacon records diagnostic informa-

tion, such as an unexpected starting pulse on the “Sync” signal (indicating a timing pulse

has been missed) and the temperature of each beacon (although overheating was not a

problem in the prototype system, and temperature sensors were not installed). The soft-

ware on the Monitor PC periodically polls each of the beacons, and displays the status

information. Further, the amplitude of each beacon magnetic field can be set from the

Monitor PC, and beacons can be enabled or disabled.

7.4 Sensor Box

The sensor box (in Figures 7.6 and 7.7) is a small, low-power electronics module

that takes measurements of the vector magnetic field at its location. This data is then sent

to the processor, where it is used to estimate the position and attitude of the sensor box

with respect to a building-fixed reference system.

Magnetic field sensing is accomplished using three Honeywell magnetoresistive

transducers. These semiconductors generate a voltage proportional to the applied mag-

netic field. They are sensitive to fields along only one axis, allowing three separate sen-

sors, aligned in orthogonal directions, to capture vector measurements of the magnetic

field. The three sensors are contained in two physical packages, one Honeywell

HMC1001 (one-axis) and one HMC1002 (two-axis).

Several technologies exist to measure magnetic fields – a comparison of tech-

niques can be found in [85]. The magnetoresistive approach was chosen because it is well

suited to the requirements of the DMLP sensor. The Honeywell semiconductors are in-



105

Figure 7.6. The prototype sensor box takes vector magnetic field measurements

and reports them to the processor. The sensor semiconductors are located under

the circle.

Figure 7.7. Block diagram showing the functionality inside the sensor box.



106

expensive, directional, available in a small packages, and have good sensitivity. Among

the various approaches, magnetoresistive sensors offer superior resolution and noise

characteristics, without resorting to large coils or cumbersome SQUID equipment.

The three signals from the transducers are amplified and conveyed through a first

order low pass filter. The signals are then digitized by an Analog Devices AD974 ana-

log-to-digital converter. This A/D converter features high speed (10us conversion time)

and good resolution (16 bits). The high speed allows the three signals to be sampled

nearly simultaneously. The high resolution is motivated by the large dynamic range of

the signals in the DMLP system – a signal from a nearby beacon may be a thousand times

stronger than signals from further beacons.

An HC11 microcontroller, similar to those used inside the beacons, controls the

A/D conversion process. When a timing pulse arrives on the “Sync” signal, the HC11

waits for approximately 1.5 ms (almost an entire chip period) and then initiates conver-

sions on the three signal channels (one from each axis). The results are read by the

HC11. The conversion is very fast, and it takes only a small fraction of a chip period to

obtain the three digital measurements. The reason that the measurements are taken at the

end of a chip period is that the beacon fields do not instantaneously assume their proper

values (see Figure 7.3). Waiting until the end of the chip period allows the beacon fields

to stabilize (experimentally, it takes approximately 75% of a chip period for the beacon

fields to reach their final values). The measurement data (one 16-bit sample from each of

three axes) is then sent over a RS232 serial link to the solution processor (described in the

next section).

In the prototype system, the “Sync” signal (generated by the Timing Box) is car-

ried to the Sensor Box by either a cable or a wireless link. The wireless link is an off-the-

shelf RF video link, modified slightly to transform the output signals into the proper digi-

tal levels.

7.5 Processor

The magnetic field measurements (output from the sensor box) are used by the

processor to produce a position and attitude estimate. In the prototype system, a laptop

PC is used to do this processing in real time.



107

The implementation of the signal processing in the prototype system is depicted in

Figure 7.8. Details of the various stages in the signal processing chain can be found in

the preceding chapters. The first step is to read and verify a complete data set – 63 meas-

urements from each of the 3 sensors. The HC11 in the sensor box adds information to the

data stream to ensure that only complete packets are accepted. Once a complete set of

data has been obtained, the detection algorithm (Chapters 3 and 4) is used to distinguish

the beacon fields and to provide eddy field noise mitigation. Given estimates of several

beacon field vectors, along with the known beacon locations and parameters, the next

stage computes a position and attitude solution (Chapter 5). An algorithm then examines

the beacon field vectors and the position and attitude solution to detect and mitigate the

effects of iron in the environment (Chapter 6). Finally, the results are displayed in real

time and recorded.

The prototype signal processing is coded in C and runs in a DOS environment.

Several of the routines use fairly complex matrix manipulation – for example, a matrix

Figure 7.8. Implementation of the signal processing chain inside the processor.



108

inversion in the attitude estimation step. Numerical Recipes in C [86] proved to be a

valuable tool in the implementation of the prototype processor.

The laptop PC was a useful platform in the development stage of the DMLP sys-

tem. The code development tools are self-hosted, making programming straightforward.

Intermediate results along the signal processing chain can be displayed in real time, eas-

ing debug and promoting a greater understanding of the system in operation. For imple-

mentation in an actual system, however, an embedded processor can be integrated with

the sensor unit to create a physically small and rugged device.

7.6 Summary

The focus of this chapter is the implementation of the four main parts of the

prototype DMLP system – the beacons, beacon network, sensor box, and processor. Bea-

cons, installed in known locations throughout the building, are responsible for creating

the low-level fields. The beacon network is a communication link responsible for syn-

chronizing and monitoring the beacons. The sensor box is a small, low-power electronics

module that takes measurements of the local vector magnetic field. The processor , using

these measurements, distinguishes the fields produced by individual beacons, implements

algorithms to mitigate eddy and iron noise, and produces an estimate of the position and

attitude of the sensor box with respect to the building-fixed beacons.



109

8 Experimental Demonstrations

A prototype DMLP system, incorporating the innovations presented in Chapters 3

through 6, was constructed to experimentally demonstrate position and attitude sensing in

a cluttered environment. The specific design and implementation of the prototype hard-

ware are detailed in Chapter 7. This chapter presents and analyzes the experimental re-

sults obtained with the system.

First, experiments conducted in an “uncluttered” environment are considered,

quantifying the nominal performance of the prototype system. Then, the system is then

presented with several challenging scenarios, and results in cluttered environments are

examined. The DMLP prototype system demonstrates a position accuracy of several cen-

timeters and an attitude accuracy of several degrees even in the midst of considerable

line-of-sight obstructions. Further, these experimental results are not the product of a

perfect “laboratory” environment – the experimental area surroundings are representative

of a challenging industrial setting.

8.1 Test Results in an Uncluttered Environment

The prototype DMLP system, shown in Figure 8.1, is installed in a 4 m by 4 m

experiment area. Eight beacons are located at the corners of this area – the upper four



110

beacons are mounted on ladders at a height of 2.7 m, while the lower ones rest on the

floor. The grid lines on the floor, spaced at 1 m intervals, are used as a truth system. The

lower right corner of the grid, as shown in the picture, is the origin of the building-fixed

coordinate system. The X and Y axes are in the horizontal plane (the X axis is directed

from the origin to the far right corner of the grid) and the Z axis is directed upwards.

The prototype system produces position estimates at 10 Hz using beacon pseudorandom

codes with a length of 63 chips. Thus, the signals used in the prototype system are ap-

propriate for a system with thousands of beacons. More information about the design and

construction of the prototype hardware can be found in Chapter 7.

A typical experiment is shown in Figure 8.2. The sensor, mounted on a test stand,

measures the local magnetic field vector. The laptop computer processes this data, using

the techniques described in earlier chapters, to estimate position and attitude. Estimates

are displayed in real-time and recorded for further analysis. The “true” sensor state is

surveyed with respect to the grid using construction-grade techniques (e.g., plumb bob

and tape measure).

The first experiment provides a measure of the nominal performance of the posi-

tioning system. The sensor is placed at 9 “intersections” on the grid – locations (1 m, 1

Figure 8.1. The prototype DMLP system and experiment area.



111

m), (1 m, 2 m), etc through (3 m, 3 m). At each position, the sensor generates and recordsapproximately 300 estimates (taking about 30 s). The estimated values of position in the

horizontal (X-Y) plane are plotted in Figure 8.3.

To quantify the results of this experiment, the error in the estimates may be di-

vided into two categories. First, the estimates at a given location are not all identical –

there is scatter in the estimates. Second, the average position estimate at a particular lo-

cation does not perfectly match the surveyed “truth” value – there is bias in the estimates.

The scatter and bias in the estimates generated by the prototype DMLP system are ana-

lyzed individually, as follows.

The random scatter in the position estimates is approximately Gaussian in distri-

bution and has a (1-sigma) standard deviation of 2.3 cm in the X axis, 2.5 cm in the Y

axis, and 2.8 cm in the Z axis. This scattering effect is caused by thermal noise inherent

in the sensor electronics. The random motion of electrons in the sensor and amplifier

Figure 8.2. A typical experiment. The sensor box (mounted on the tripod) takes

measurements of the magnetic field vector while the laptop computer processes

the data to determine position and attitude. The results can be compared to the

grid truth system.



112

semiconductors adds noise to the magnetic field measurements. These fluctuations in the

magnetic field readings produce jitter in the position and attitude estimates. This thermal

noise is expected, and is one of the most common forms of noise encountered in elec-

tronic systems [87]. The scatter in the estimates could potentially be reduced through

improved electronics (e.g., amplifiers with better noise figures).

It is interesting to note that, even though the thermal noise is the same at all loca-

tions in the experimental area, the scatter in the position estimates does not have the same

shape at all locations. Recall that the magnetic field readings are transformed into posi-

tion estimates by the solution algorithm, and that the amplitudes of the beacon fields are

related to the sensor position through a nonlinear set of equations (Chapter 5). Noise in

the magnetic field measurements transforms into error in the position estimates in a way

that depends on the particular geometry of the magnetic fields at a given point in space.

Thus, the scatter in the position estimates may be greater in some locations than in others,

and greater in some directions than in others. A similar effect occurs in other types of

positioning systems (e.g., Dilution of Precision (DOP) in the GPS system [88]). The ge-

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

3.5

4

X (m)

Y(m)

Figure 8.3. Graph of position estimates (in the horizontal plane) gener-

ated by the DMLP sensor in nine separate locations.



113

ometry of the DMLP prototype (with all beacons oriented in the vertical direction) results

in modestly better accuracy in the X and Y axes than in the Z axis. This geometry was

selected because vertical accuracy is generally less important for mobile robotic applica-

tions.

Next, bias in the experimental results is considered. The average magnitude of

the bias in the position estimates is 4.3 cm in the X axis, 4.2 cm in the Y axis, and 5.9 cm

in the Z axis. Two sources for this bias have already received considerable attention –

eddy field noise and iron noise. As described later in this section, the experimental area

is hardly a pristine environment, even without any occlusions purposely placed in the

area. Thus, some portion of the bias in the experimental results is attributable to eddy

field and iron noise stemming from the imperfect surroundings. Further, some level ofeddy field and iron noise is produced by objects that are part of the test itself ( e.g., batter-

ies inside the sensor box, the tripod), though components were chosen to minimize this

effect.

However, there are numerous other factors that contribute to bias in the prototype

system. In the sensor unit, the three semiconductors that measure magnetic fields are not

actually located at a point in space; rather, there is a separation of over 1 cm between

them. These transducers are not sensitive along one axis only (i.e., there is a certain

amount of cross-axis sensitivity) and they do not have identical gains. The sensors, am-

plifiers, and A/D converter each have various nonlinearities. The three transducers are

not completely orthogonal, and the analog multiplexer used by the A/D converter may

allow some “cross-talk” coupling between the channels.

Outside the sensor unit, there are additional sources of bias. The beacons change

their nominal field levels over time with heating, though this is minimized by the closed

loop design. The coils are not perfectly wound and do not create fields that exactly

match the model (equation 2.3). Further, the truth system itself contributes to the bias.

The floor in the area is not smooth, which caused difficulties in laying down the truth

system grid. The truth system grid is only accurate to approximately 0.5 cm (i.e., the grid

lines are not perfectly square or straight), leading to errors in both the beacon locations



114

and the “true” sensor position. Additionally, the ladders are not seated well on the rough

floor, producing tilt in the beacon orientations.

The bias sources thus appear to be divisible into two distinct categories – inherent

noise sources and engineering limitations. Inherent noise sources, such as eddy field

noise and iron noise, are fundamental limitations of the system. As described in Chapter

2, if conductors or ferromagnetic objects are present, a magnetic field positioning system

by its nature will experience some amount of bias error. In contrast, bias sources in the

second category (e.g., non-orthogonal semiconductor alignment, imperfect truth system)

are not fundamental to the system, and can potentially be mitigated through “straightfor-

ward” engineering improvements.

This discussion of error in the prototype system has, to this point, been specific tothe position measurements. Similar experiments were conducted to investigate the accu-

racy of the attitude estimates. In these experiments, the sensor was placed at a number of

locations in various orientations and the measurements were recorded. With orientation

expressed in terms of Euler angles, the scatter in the attitude measurements has a standard

deviation of 1.4 degrees. The average magnitude of the bias is 3.5 degrees. The underly-

ing causes for the scatter and bias in the attitude estimates are the same as those that gen-

erate the errors in the position estimates.

A different type of experiment, shown in Figure 8.4, provides additional perspec-

tive on the nominal performance of the system. In this experiment, the sensor is pulled

along a straight track (running along the x=2 m grid line) at a speed of approximately 0.1

m/s. The experiment is repeated with the track in the other horizontal direction, and the

position estimates from these two trials are shown in Figure 8.5. The magnitudes of the

“cross-track” errors (i.e., distances from the grid line) average 2.4 cm.

Finally, to conclude this analysis of nominal system performance, it must be noted

that the experimental results obtained here are not the product of a perfect “laboratory”

environment. The prototype environment is actually representative of an industrial set-

ting, such as a factory or warehouse. As shown in Figure 8.6, the site is surrounded by

numerous large ferromagnetic and conductive objects. For example, an entire (ferromag-

netic) iron scaffold, extending over 10 m in height, is stationed less than 2 m from the



115

Figure 8.4. The sensor is pulled along a track.

0 1 2 3 40

1

2

3

4

X (m)

Y(m)

Figure 8.5. Sensor X-Y position estimates as it is travels along the grid lines x=2

m and y=2 m.



116

(upper right) corner of the experiment area. Further, the floor on which the system is lo-

cated presents an unusually harsh environment – multiple layers of iron rebar are present

in the floor along with iron “briquettes” embedded in the concrete (their original purpose

was radiation shielding). In spite of these challenging surroundings, the prototype system

achieves an accuracy of a few centimeters.

8.2 Test Results with Occlusions

The highlight of this research was a series of experiments conducted with signifi-

cant line-of-sight obstructions. The results, presented here, demonstrate that the DMLP

system can accurately measure position and attitude in a very cluttered environment. A

simple test procedure was used for these experiments. First, the sensor output was re-

corded in an uncluttered environment (i.e., other than the equipment necessary for the

test, no other objects were near the sensor). Then, various objects were placed near the

sensor and the estimates were recorded, leaving all other parameters unchanged. Differ-

Figure 8.6. Wider view of the prototype DMLP experiment area, showing the

non-ideal environment.



117

ences between the two sets of estimates are reported as the errors caused by the addition

of the objects.

As a first example, consider the experiment shown in Figure 8.7. Over 100 kg of

wood and concrete are placed immediately around the sensor, occluding the lines-of-sight

to all eight beacons. However, these materials, like many common construction materi-

als, are characterized by permeability values close to that of empty space (Chapter 2) and

have virtually no effect on the magnetic field measurements. As expected, the introduc-

tion of this considerable obstruction causes negligible changes in the position and attitude

estimates.

The DMLP sensor accurately measures position and attitude in the midst of non-

ferromagnetic and nonconductive materials (Figure 8.7), and also when large ferromag-

netic or conductive objects are several meters away (Figure 8.6). To test the limits of

system performance, then, experiments were performed in surroundings that are more

challenging for the DMLP system. Figures 8.8 through 8.11 show several experiments

where iron masses and conductive objects are located near the sensor.

Figure 8.7. The sensor accurately estimates its position and attitude even though

surrounded by over 100 kg of wood and concrete.



118

In Figure 8.8, the sensor is placed between two stainless steel bowls, forming a

Faraday cage. This environment, which clearly defeats approaches based on vision or

electromagnetic waves, causes an error in the horizontal plane of only 0.3 cm. In Figure

8.9, a significant cast iron mass is placed only centimeters above the sensor. This object

creates a 4.8 cm error in the horizontal position estimate. The same object, when placed

15 cm from the sensor, causes no noticeable error. A cylinder composed of galvanized

steel is placed over the sensor in the experiment shown in Figure 8.10. This considerable

obstacle produces a 10.5 cm X-Y plane error.

To gain further insight into system performance, the “track” experiment shown in

Figure 8.4 is modified. This time (Figure 8.11), the sensor is pulled along the track

through a (ferromagnetic) steel duct used in ventilation systems. The sensor estimates are

shown in Figure 8.12 along with the output from the previous experiment (without the

duct) for comparison. This significant occlusion poses no difficulty for the DMLP sys-

tem – the differences between the estimates with and without the duct are almost unob-

servable (i.e., the differences are within the random scatter). In this experiment, the

Figure 8.8. The sensor accurately estimates its position and attitude even though

it is inside two steel bowls (one above and one directly below).



119

Figure 8.9. The sensor maintains accurate position and attitude estimates even

though a substantial cast iron object is placed only centimeters away.

Figure 8.10. The sensor generates accurate position and attitude estimates even

inside a steel can.



120

Figure 8.11. The sensor slides along a track through a steel duct.

0 0.5 1 1.5 2 2.5 3 3.5 40

1

2

3

4

X (m)

Y(m)

Figure 8.12. Experimental results (X-Y position estimates) while sliding the sen-

sor along the track shown in Figure 8.10, with and without the steel duct occlu-

sion. The rectangle represents the location of the occlusion.



121

magnitudes of the differences between the estimated path and the true path (along the x=2

m grid line) average only 1.7 cm.

The experiment shown in Figure 8.13 proved to be an effective demonstration of

the full range of system capabilities. For this experiment, a grid with lines spaced at 0.1

m intervals was installed in the experimental area. The sensor was moved to various po-

sitions and attitudes while real-time estimates were displayed for observers on the proces-

sor screen. In addition, various objects (e.g., the wood and steel bowls used previously)

were placed around the sensor. The sensor maintained accurate estimates throughout the

experiment. As an example, a snapshot of this experiment is captured in Figure 8.13. In

the picture, the bottom left corner of the grid is at location (1 m, 1 m), the top right is at

location (2 m, 2 m), and the true sensor position is (1.40 m, 1.30 m, 0.97 m). As shown,

the sensor generated an estimate (1.37 m, 1.32 m, 0.93 m) that is inaccurate by a few cen-

timeters. Analyzing the measurements generated from three of these demonstrations

(consisting of several thousand estimates), the magnitude of the errors in the X and Y po-

sition components averaged only 2.7 cm.

Figure 8.13. The sensor is moved around on a grid, and various objects are

placed over it, while the estimate of position and attitude is displayed in real time.



122

A final experimental demonstration must be described which, although it did not

generate numerical results, qualitatively allowed observers to gain better insight into the

system capabilities. The sensor was placed on a small remotely operated vehicle, as

shown in Figure 8.14. An operator navigated the robot along a specific path using the

position estimates reported by the DMLP system. The path, which was marked on the

experiment area floor, traversed a number of challenging obstacles, passing between

desks, under a table, and through a section of steel duct. Several of the beacons were lo-

cated behind the modular walls, and the sensor often did not have a clear line of sight to

any of the beacons. No truth system, other than the observers’ eyes, was present to quan-

tify the estimate error. However, the robot, navigating by the DMLP sensor estimates,

clearly remained within several centimeters of the desired path (marked on the floor),

even in the cluttered office environment. The difficulty in finding a positioning technol-

ogy that could serve as a truth sensor for this test highlights the utility of the DMLP sys-

tem.

Figure 8.14. The DMLP system is used to navigate a robot through a cluttered of-

fice environment. The laptop screen (inset picture) displays the position estimates.



123

8.3 Summary

Experiments were conducted with the prototype DMLP system to demonstrate

position and attitude sensing over a range of scenarios, from uncluttered to badly clut-

tered environments. The results indicate that the system is capable of achieving a posi-

tion accuracy of several centimeters and an attitude accuracy of several degrees even in

the midst of considerable line-of-sight obstructions and surroundings representative of a

challenging industrial setting.



124

∫



125

9 Conclusions

This dissertation has presented the Distributed Magnetic Local Positioning sys-

tem, a sensing system that measures position and attitude even in a cluttered indoor envi-

ronment. The first chapters examined the motivation for the research, the concept for the

system, the characteristics that make it uniquely suited for its job, and the challenges in

its development. Several chapters then detailed the research innovations that enable the

DMLP system, the design of a prototype, and the results of experimental demonstrations.

To conclude this work, a summary of the research is first presented. The

strengths and limitations of the system are then discussed, examining the applications for

which it is well suited as well as scenarios where it is of limited use. Finally, several

concepts for extending this research are introduced.

9.1 Research Overview

A large amount of detailed information has been presented in this dissertation. As

an aid in comprehending the material, it is useful to review the research from a broad per-

spective. In this section, the main points of the previous eight chapters are briefly sum-

marized.



126

Chapter 1 – Introduction

Accurate sensing of

position and attitude is es-

sential in many applica-

tions, from personnel

tracking to mobile robot

navigation, but it is a very

challenging problem amid

the obstacles that often

clutter the real world. The

goal of this research is to

design a positioning system that is specifically suited to meet the challenges of operation

in an indoor environment. The resulting DMLP system produces position and attitude

measurements with no line-of-sight restrictions throughout an operating area that can

span a large building. Accuracy of several centimeters and a few degrees is delivered at

10 Hz, even surrounded by obstacles that defeat other approaches. The sensor units are

small (no baselines are required to determine attitude), and any number of the units may

be in operation, all providing drift-free position estimates in a common reference frame.

Chapter 2 – System Concept and Challenges

The system is based on extremely

low frequency magnetic fields, which have

excellent characteristics for penetrating line

of sight obstructions. Numerous beacons

distributed throughout a building create the

low-level fields. A mobile sensor unit sam-

ples the local magnetic field vector and pro-

processes the measurements to determine its

position and attitude.

Two challenges have prevented existing magnetic-based systems from being used

as building-wide positioning systems: the inherently short range of the beacon fields, re-

You are here:

x = 8.21 m Ø1 = 0º

y = 12.85 m Ø2 = 2º

z = 1.56 m Ø3 = 127º

Figure 9.1. The DMLP system provides position and

attitude sensing even in cluttered environments.

Figure 9.2. Numerous beacons dis-

tributed throughout a building cre-

ate low frequency magnetic fields.



127

quiring numerous beacons to achieve building-wide coverage, and the sensitivity to con-

ductors and ferromagnetic materials in the environment. The innovations in Chapters 3

through 6 address these challenges.

Chapter 3 – Signal Architecture

The architecture of the beacon sig-

nals proves to be a critical design parameter

for the DMLP system – higher frequency

content in the magnetic fields causes in-

creased eddy field noise and reduced posi-

tion and attitude estimate accuracy. A signal

structure based on pseudorandom codes is

presented that allows numerous beacons to

be used while maintaining low overall fre-

quency content. The new signal architecture

enables the DMLP system to have building-

wide coverage with low eddy field noise.

Chapter 4 – Eddy Field Noise Mitigation

The signal architecture presented in

the previous chapter greatly reduces eddy

field noise, but does not eliminate it entirely.

This chapter presents a method to detect and

further mitigate eddy field noise in the

DMLP system.

A model is developed to describe the

eddy fields produced by the pseudorandom bea-

con signals. Using the model, the estimation

process, which distinguishes the individual bea-

con fields, is modified to take into account the effects of eddy fields. Experimentally, the

improved estimator is quite effective at detecting and mitigating eddy field noise.

0 10 20 30 40 50 60

0

5

1 0

1 5

2 0

2 5

time (s)

B f i e l d ( m G )



E11 z

E21 z

E31 z

eddy

indication

(binary flag)

TDMA

FDMA

CDMA

number of beacons


101 102 103 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

Figure 9.3. The signal architecture

presented in Chapter 3 reduces eddy

noise in a system with many beacons.

Figure 9.4. Chapter 4 presents an

algorithm to detect and further

mitigate eddy field noise.



128

Chapter 5 – Solving for Position and Attitude

A solution algorithm is

presented in this chapter that

takes the beacon field meas-

urements, along with the

known beacon locations and

parameters, and produces an

estimate of sensor position and

attitude. The algorithm can

function in a system with nu-

merous beacons, and reliably

converges to the correct solution,

even with no a priori knowledge of state. The algorithm also enables an advantageous

system geometry (the use of one coil per beacon), resulting in both larger coverage vol-

ume for a given power consumption and reduced system eddy field noise.

Chapter 6 – Iron Noise Mitigation

The techniques in Chapters 3

through 5 are designed to combat eddy

field noise, a source of error caused by

conductors in the environment. How-

ever, there is a second, separate mecha-

nism by which certain objects in the en-

vironment (ferromagnetic materials) in-

troduce error into the position and atti-

tude estimates. This chapter presents a

method to detect and mitigate the effects

of this “iron noise.”

0 5 10 15 20 25 30 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

3

. 0

3 . 5

B1x uncorrected

B1x corrected

truth

iron

indication

time (s)

B 1 x

- c o r r e c t e d a n d u n c o r r e c t e d ( m

G )

x

y

z

u

vw

B1

Bi

B2

sensor

beacon

Figure 9.5. Chapter 5 presents an algorithm to

estimate the sensor position and attitude.

Figure 9.6. An algorithm to detect and

mitigate the effects of ferromagnetic

materials is presented in Chapter 6.



129

Chapter 7 – The Prototype System

A prototype DMLP system,

incorporating the innovations pre-

sented in the last several chapters,

was designed and constructed. The

focus of Chapter 8 is the implemen-

tation of the four main parts of the

prototype system: beacons, which

create the low-level fields; the bea-

con network , a communication link

responsible for synchronizing and

monitoring the beacons; the sensor box, a small, low-power electronics module that takes

measurements of the local vector magnetic field; and the processor , which processes the

measurements to produce an estimate of the position and attitude of the sensor box with

respect to the building-fixed beacons.

Chapter 8 – Experimental Demonstrations

Experimental results from the prototype demonstrate that the DMLP system is ca-

pable of sensing position and attitude, to an accuracy of several centimeters and degrees,

even in badly cluttered environments.

Figure 9.7. Chapter 7 examines the design

of a prototype DMLP system.

Figure 9.8. In Chapter 8, experimental results using the prototype DMLP system

demonstrate position and attitude sensing even in cluttered environments. In (a), left,

the sensor operates normally even though surrounded by construction materials. In

(b), right, a mobile robot uses the system to navigate a cluttered office environment.



130

9.2 Strengths and Limitations of the DMLP System

As mentioned in the first chapter, no single sensing system is optimal for all situa-

tions and environment. Every system has strengths and limitations, applications for

which it excels and scenarios where it is less well suited. In this section, conclusions are

drawn about the “pros and cons” of the DMLP system.

The DMLP system, in its current form, has limitations that make it less appropri-

ate for certain applications than other technologies. Four drawbacks in particular charac-

terize the system. First, as discussed in Chapter 2, the beacons have a short range. Thus,

the DMLP system is not suited for use in expansive buildings (e.g., navigating a small

blimp through a sports arena) or over large traverses (e.g., guiding vehicles across the

country – however, navigation through a parking garage is a different matter). Second,

the sensor unit is not of negligible cost. In some applications (e.g., tracking items leaving

a store), the mobile component of the system must be extremely inexpensive but does not

need position and attitude accuracy or the ability to penetrate metallic occlusions. RFID

tags [89] are more suitable for this type of task. Third, the DMLP system is less effective

in environments with large ferromagnetic deposits. Thus, the system is not particularly

suitable for tracking containers of ore through an underground iron mine (though other

systems, such as those using RF, are less effective in this type of environment as well).

Finally, the DMLP system requires a certain amount of installation time (to place and

survey the beacons) and infrastructure (for electrical power and communication). Thus,

the system is not currently appropriate for applications such as military urban reconnais-

sance (however, see the concept for a deployable DMLP system in the Future Investiga-

tion section, below).

Though not suitable for every task, the DMLP system has a unique combination

of strengths that make it a competitive positioning solution for a variety of applications.

The system operates with no line-of-sight restrictions, providing a distinct advantage

amid the obstacles that often clutter the real world. The system provides coverage

throughout a large building with an accuracy of a few centimeters and degrees, meeting

the needs of many mobile robot applications. Any number of sensor units may be in op-

eration, all providing drift-free position estimates in a common reference frame, resulting

in a system well suited for cooperative robotic applications. Finally, the sensor can be



131

miniaturized because it operates on measurements taken at a single point in space (in con-

trast to systems requiring baselines for attitude determination).

The DMLP system has these particular strengths and limitations because of the

tradeoffs made during its design. For example, the system can penetrate many line-of-

sight obstructions because it uses nearly steady state magnetic fields, but at the cost of a

relatively large power consumption. However, in a cluttered factory or warehouse,

power is readily available while unobstructed lines-of-sight are not. Thus, design trade-

offs were made so that the system would be well suited for the specific task of localiza-

tion in a cluttered indoor environment, even when those tradeoffs made it less suited for

other applications.

The design of the DMLP system makes it an effective solution across a broad ar-

ray of applications, from industrial automation (e.g., AGVs, inspection, cleaning, deliv-

ery, construction) to home robotics (e.g., security, automation, help for the disabled, en-

tertainment) and object tracking (e.g., personnel, cargo pallets, augmented reality). Each

of these applications can potentially benefit from a reliable positioning system with no

line-of-sight restrictions, absolute measurements, and building-wide range. Further dis-

cussion about the applications for a local positioning system, and about the strengths of

the DMLP system, can be found in Chapter 1.

It can be difficult to fully appreciate the utility of a positioning system before it is

installed and actually providing service. For example, the Global Positioning System,

originally designed for military use, has had invaluable impact across a full spectrum of

civilian applications. Similarly, a local positioning system that operates reliably in clut-

tered environments could have benefits in a variety of unexpected ways. Two brief case

studies follow, providing examples of specific applications where the DMLP system may

prove useful.

A Positioning System For the Home

During the construction of a home, measurements are taken repeatedly to find the

location for every wall, window, pipe, outlet and fixture. A DMLP system combined

with an electronic blueprint of the house could prove valuable during construction – effi-

ciency could be improved with a device that can immediately pinpoint its coordinates on



132

the construction site. Recall that the DMLP system maintains its highest levels of accu-

racy amid light construction materials, such as wood, brick, and concrete. After

construction, the positioning system remains installed, and the home enjoys the benefits

of increased automation (e.g., mobile robots providing cleaning, yard work,

entertainment, and security services).

A Positioning System For the International Space Station

A DMLP system could be installed on the International Space Station (ISS), pro-

viding position and attitude measurements throughout the inside of the station and for

several meters outside the station. A positioning system would benefit mobile robot ap-

plications, such as automated inspection [90], saving valuable astronaut time. Other for-

mation flying applications, such as docking a supply ship or extra-vehicular activity in

the Manned Maneuvering Unit (MMU), could be conducted using high level (task-level)

commands rather than low-level control. Similarly, the positioning system could also be

useful in the control of a large robotic arm. Significant performance improvements in

arm maneuvers can be achieved if endpoint sensing is available [91, 92]. This applies not

only to motion of the arm, but also in keeping it still (e.g., providing a steady platform for

an astronaut, attached to the end of the arm, to work).

In addition to motion control, a positioning system could be used to aid communi-

cation between the astronauts and engineers on the ground. For example, it may be de-

sirable for ground control to designate a particular location or item in the ISS frame to an

astronaut (e.g., “place the probe here”). Ground engineers could specify the point in ISS

coordinates, and the astronauts would see the location highlighted through an augmented

reality heads-up display in their helmets.

9.3 Future Investigation

Finally, the potential exists for the DMLP system, through further research, to be

extended, improved, and adapted to increase performance and utility. Several concepts

are presented that may provide direction for future investigation.



133

Deployable DMLP System

The ability to rapidly deploy the DMLP system may be a valuable extension of

the technology. Consider a scenario where several fire engines, each carrying one or

more beacon coils, are arrayed around a building (depicted in Figure 9.9). The coils have

a large diameter and, if the motor is left running, they have access a large amount of

power – conceivably tens of kW could be used to create the magnetic signals. Such po-

tent beacons would have a range of over one hundred meters. The locations of the bea-

cons are determined using a global navigation system, such as GPS, and relayed to the

sensor units. Thus, a temporary DMLP system could be rapidly deployed to an area

where positioning services are needed. With this approach, coverage could extend to

much of the building, reaching even to areas, such as inside an elevator, where other

technologies (e.g., RF-based) may lose effectiveness.

Initially, such a system could be used to simply track rescue workers. Eventually,knowledge of location and gaze direction could be combined with heads-up displays

(HUD) in the helmets of the emergency team. With access to building floor plans, such a

system could prove invaluable for rapid navigation. For example, an augmented reality

“path” could be displayed on the HUD to guide a rescue worker through a smoke-filled

area. Further, the availability of positioning information may enable increased use of ro-

Figure 9.9. The DMLP system could be rapidly deployed using emergency vehicles.



134

botics in emergency situations. The deployable DMLP concept has application to law

enforcement and military reconnaissance tasks as well.

Self-Initialization of Deployable DMLP System

The deployable DMLP system, described above, can be extended to provide fur-

ther utility. In this version, GPS is not needed to establish the beacon locations; instead,

the DMLP system initializes itself. Each vehicle at the scene contains both a beacon and

a sensor unit. Using the DMLP system alone, the vehicles determine their relative posi-

tions and attitudes and form a reference frame. Thus, a positioning system could be rap-

idly deployed inside a building or other location where GPS is unavailable.

Since each sensor is very close to a beacon, dynamic range will be a primary chal-

lenge in the implementation of this concept. Each sensor is exposed to a large signal

from the local beacon. This may prevent the sensor from properly measuring the rela-

tively weaker signals from other, more distant beacons. A potential solution is to attempt

to cancel the large local beacon field in the sensor’s measurement circuitry, leaving only

the signals from other beacons. Interestingly, “straps” are provided inside the HMC1001

and HMC1002 sensor semiconductors (used in the prototype system – refer to Chapter 7)

which can be used to offset an external field.

Miniature Sensor Unit

Decreasing the size of the sensor unit may enhance the utility of the DMLP sys-

tem. As discussed in previous chapters, the DMLP system takes vector measurements of

the magnetic field. This results in a unique characteristic – attitude can be determined by

measurements at one point in space, and baselines between sensors are not required. The

entire DMLP sensor unit (sensing, amplification, and processing) could conceivably be

incorporated into one semiconductor. This research may be particularly relevant to ef-

forts such as “micro” unmanned aerial vehicles (UAVs) and “swarms” of miniature ro-

bots.



135

Gradient Sensor

In the DMLP system, the sensor unit takes magnetic field measurements at one

location in space and processes them to determine position and attitude. On a larger ro-

bot, several sensors (especially miniature ones) could be fixed at various locations. The

data from multiple sensors can then be used to determine gradients in the magnetic field.

This increase in information may enable new approaches to eddy field and iron noise

mitigation.

Linear Beacons

The beacons presented in this work use relatively small coils of wire, creating di-

pole magnetic fields that diminish with the cube of the distance from the beacon (i.e.,

1/r 3). A large number of these beacons are distributed throughout a building to form the

positioning system. However, an entirely different beacon design may potentially be

more effective.

Consider an extremely large beacon, as shown in Figure 9.10. The distance be-

tween one side of the beacon and the building, ‘d’, and the size of the building itself, ‘b’,

are both small compared to the length of a side of the beacon, ‘s’. Given this geometry,

s

b

d

Figure 9.10. Concept for “linear” DMLP beacons.



136

the field inside the building is primarily due to the current flowing through only one side

of the beacon (the side nearest the building) – to first order, the other three sides of the

beacon do not significantly contribute. The result is that, in the vicinity of the building,

the magnetic signals from this “linear” beacon diminish directly with distance (i.e., 1/r,

rather than 1/r 3, decay) [93]. Of course, far from the beacon (at a distance of several ‘s’

lengths), the fields assume a dipole characteristic and decrease in amplitude with the cube

of the distance.

Only three or four large beacons would be needed to provide a positioning system

throughout the building. Such beacons may be easier to install (buried underground out-

side the building) and may provide higher efficiency (in terms of coverage volume per

power consumption). A network of many large beacons may be used to provide position-

ing services to a campus of buildings.

Distributed Metal Detection

Traditional metal detectors carry both a source and a sensor of electromagnetic

fields. Interestingly, the DMLP sensor unit is able to determine some information about

nearby metallic objects (Chapters 4 and 6) with no magnetic field generator on board.

This distributed approach to metal detection, where the field sensors and generators are

not collocated, may be a valuable extension of the DMLP technology.

An example application is landmine cleanup, as depicted in Figure 9.11. A large

central vehicle contains powerful beacon coils (three coils in orthogonal directions is an

effective arrangement), potentially with a range of 100 m (refer to the Deployable DMLP

System concept presented above). A “swarm” of small robotic vehicles carry out the

search within the coverage area provided by the central vehicle. The beacon fields thus

provide two essential services. First, since the search vehicles only need to carry minia-

ture magnetic sensors and not field generation equipment, they can be extremely agile,

small, and low power. Second, the fields provide a positioning system for the robotic

search vehicles relative to the central vehicle. The positioning system extends even into

rough terrain or heavy foliage.



137

9.4 Summary

To conclude this work, the main points of each of the preceding eight chapters are

briefly summarized, providing an overview of the research. The “pros and cons” of the

DMLP system are then discussed, examining the applications for which it is well suited

as well as scenarios where it is of limited use. Finally, concepts for future investigation

are proposed to further the development of this positioning system for cluttered environ-

ments.

Figure 9.11. Concept for distributed metal detection.



138

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139

Appendix A

Examination of an Alternate Signal Architecture

As described in Chapter 3, the architecture of the beacon signals is an im-

portant design parameter in the DMLP system. The signal structures used in small, exist-

ing magnetic positioning systems (based on TDMA and FDMA approaches) do not ex-

tend well to a building-wide application requiring a large number of beacons. Therefore,

in Chapter 3 a new signal architecture (based on pseudorandom codes) is presented which

can support a large number of beacons. This architecture then forms the foundation for

the succeeding chapters (e.g., the noise mitigation technique in Chapter 4 and the proto-

type system in Chapter 7)

However, there are many other possible architectures for the beacon sig-

nals. In this Appendix, an alternate signal architecture is considered which is based on

the TDMA and FDMA approaches but allows the reuse of frequency or time slots. It

performs significantly better than straightforward TDMA and FDMA structures in a sys-

tem with a large number of beacons, and approaches the performance of the Chapter 3

signal architecture. Although this alternate signal architecture is not currently used in the

DMLP system, it is interesting to examine its performance through simulation.



140

A.1 Alternate Signal Architecture

Briefly, the argument against using a TDMA or FDMA architecture for the

DMLP application can be summarized as follows (a detailed analysis can be found in

Chapter 3). In an FDMA system, as each new beacon is added, it is assigned the next

higher frequency (assuming all the lower frequency slots have been taken). In a TDMA

system, as each new beacon is added, the time slot allotted to each beacon becomes

shorter. In both cases, the overall frequency content of the beacon signals scales with the

number of beacons. Increasing frequency content in the beacon signals causes eddy field

noise to grow. The result is that the accuracy of systems using these structures degrades

rapidly (in the presence of eddy noise) as the number of beacons grows.

However, the straightforward TDMA and FDMA approaches can be modified to

create a more suitable architecture for a large number of beacons by allowing the reuse of

signals in remote neighborhoods. For example, beacon #1 generates a signal with a fre-

quency of 100 Hz and beacon #224 (far from beacon #1) also uses that same frequency.

Similarly, in a TDMA system, two beacons far from each other may share the same time

slot. In this architecture, two beacons sharing the same time or frequency slot must be

located far enough apart that a sensor cannot receive both signals at the same time.

With signal reuse, this alternate signal architecture can support a large

number of beacons. For example, consider a system with 1000 beacons. Using a

straightforward TDMA approach, 1000 unique beacon signals are needed. With a 10 Hz

update rate, beacon spectral content in this system extends past 10 kHz (refer to the ex-

ample in Chapter 3). But if the system uses only 50 unique beacon signals (each one

used by multiple beacons), spectral content (and eddy noise) is 20 times lower.

One potential problem is immediately apparent: if a sensor receives a 100

Hz signal, how can it determine whether the signal originated from beacon #1 or beacon

#224 (or some other beacon using the same signal)? To a limited extent, this challenge

may be answered by considering the combination of beacon signals received. As de-

scribed in Chapter 2, a sensor inside the coverage volume of the positioning system will

always receive multiple beacon signals. As long as the combination of signals in the vi-

cinity of beacon #1 is different from the combination of signals in the vicinity of beacon

#224, the proper neighborhood can be determined. For example, consider a neighbor-



141

hood with beacons #1, #2, and #3 transmitting at 100, 200 and 300 Hz, respectively. In a

remote neighborhood, beacons #224, #225, and #226 transmit at 100, 250, and 450 Hz,

respectively. By examining the combination of signals received, the sensor can deter-

mine in which of these neighborhoods it is located, and, correspondingly, which beacon

the 100 Hz signal comes from. Note that this is similar to the method used by the DMLP

system for initialization in Chapter 3 (Section 3.5).

However, this approach to discrimination is limited – if the number of

unique signals is not large enough, there can be separate locations where the same com-

bination of beacon signals is received. For example, there could be two places in the

building where a sensor receives a 100 Hz signal, a 200 Hz signal, and a 300 Hz signal.

Each such instance is referred to here as a duplication, and it prevents the sensor from

uniquely determining its location. Thus, there is a limitation on the amount of signal re-

use that can be achieved – the system must use a minimum number of unique signals to

prevent duplications. The simulation in the next section numerically investigates the

number of unique signals required to support a given number of beacons with no duplica-

tions. The results are then used to estimate the performance of the alternate signal archi-

tecture in the presence of eddy field noise.

A.2 Analysis

A MATLAB simulation is used to investigate a system of beacons operat-

ing with the alternate signal architecture. Given the total number of beacons in the sys-

tem ( N ) and the number of unique beacons signals (U ), the number of duplications in the

system (if any) is determined. The simulation applies to both the reuse of time slots in a

TDMA approach and the reuse of frequency slots in an FDMA approach.

The simulation operates as follows. First, N beacons are placed in a lattice

in a three dimensional workspace (Figure A.1). The spacing between beacons is desig-

nated s. Four beacons forming a square (with sides of length s) are called a “panel.” A

cubic volume with sides of length 2 s (containing 27 beacons) is referred to as a “cube.”

Second, each of the N beacons is randomly assigned one of the U available sig-

nals. Since only U unique signals are available, some signals are reused if U is less than

N . Signal assignment is subject to the following rule: two beacons may not use the same



142

signal if they are in the same cube. This requirement ensures that a sensor cannot “hear”

two beacons with the same signal at the same time.

To keep the simulation tractable, only one scenario is examined: the sen-

sor is located at the midpoint of a panel and receives signals from the four beacons on

that panel. Thus, the third step in the simulation is to compile a list of the set of beacon

signals received at each panel midpoint. That is, the simulation steps through every panel

midpoint in the building. At each panel midpoint, the set of four beacon signals is re-

corded.

Finally, the list of sets is examined for any duplications – locations where the sen-

sor receives the same set of four beacon signals.

A.3 Results

For each test, a value was chosen for N (total number of beacons) and for

U (number of unique signals) and results were obtained using the simulation. Ten simu-

lations were performed at each test point. Table A.1 presents results obtained with two

values of N (1000 and 4096 total beacons) and several values of U . The table shows the

average number of duplications found in the 10 runs (and the standard deviation of this

lattice of beacons

“panel” of beacons

X

Y Z panel midpoint

s

Figure A.1. The beacons in the simulation are arranged in a regular lattice.

Each “panel” in this lattice has four beacons at its corners.



143

number in parentheses). The “*” indicates that at least one of the simulations encoun-

tered zero duplications.

Table A.1 indicates that the alternate signal architecture, used in a system with

1000 beacons, requires approximately 80 unique beacon frequencies or time slots to

eliminate duplications. In a system of 4096 beacons, approximately 170 unique signals

are required. Thus, using the simulation, the number of unique signals required to

achieve zero duplications in a system with N beacons can be estimated.

Some indication of the performance of the alternate signal architecture can be

gained directly from Table A.1. For example, in a system with 1000 beacons, a straight-

forward TDMA approach employs 1000 beacon time slots. A TDMA system where the

beacon signals are reused requires only approximately 80 t ime slots. The Chapter 3 sig-

nal architecture uses codes of length 31 (approximately equivalent to 31 time slots). The

hypothetical optimal architecture discussed at the end of Chapter 3 (Section 3.6) employs

10 time slots. Thus, these signal architectures – TDMA, TDMA with reuse, CDMA, hy-

pothetical optimal – are listed in order of increasing t ime slot length, decreasing spectral

content, and increasing performance in the presence of eddy field noise.

Total Beacons ( N ): 1000

Unique

Signals (U ) Duplications

50 13.8 (3.5)

60 6.1 (2.8)

70 3.3 (1.4)

80 2.2 (1.7) *

Total Beacons ( N ): 4096

Unique

Signals (U ) Duplications

80 34.9 (6.6)

100 15.3 (3.3)

120 7.8 (2.4)

140 3.3 (0.9)

160 1.8 (1.0)

170 2.2 (1.5) *

Table A.1. For various values of N and U , the average number of duplications in

the simulated system is shown. Ten runs were made at each test point, and the

standard deviation of the number of duplications is given in parentheses. The “*”

designates that at least one of the ten simulations encountered zero duplications.



144

Further insight into the performance of the alternate signal architecture can be ob-

tained by applying the performance analysis used in Chapter 3. Recall from Chapter 3

that the performance analysis steps through various values of N . At each value, the signal

structure is determined, eddy field noise is simulated, and position estimates are gener-

ated. The error in the position estimates is then plotted as a function of N , showing how

the accuracy of a system using a given signal structure degrades in the presence of eddy

field noise. Using the results in Table A.1, as well as results obtained by running the

simulation at several other values of N , the Chapter 3 performance analysis can be ap-

plied to the alternate signal structure. The end result (Figure A.2) is that a comparison

can be made between the alternate signal architecture and the signal architectures pre-

sented in Chapter 3.

TDMA

FDMA

alternate

CDMA

“optimal”

number of beacons


101 102 103 0

0 . 2

0 . 4

0 . 6

0

. 8

1 . 0

Figure A.2. Predicted position error (m) versus number of beacons, considering

eddy noise. The alternate signal structure performs significantly better than

straightforward TDMA and FDMA structures, approaching the performance of

the Chapter 3 CDMA signal architecture.



145

The results shown in Figure A.2 are specific to a particular beacon geometry

(Figure A.1) and a particular scenario (sensor at a panel midpoint). However, these re-

sults suggest that the alternate signal architecture has the potential to perform signifi-

cantly better than straightforward TDMA or FDMA structures, approaching the perform-

ance of the Chapter 3 signal architecture.

A.4 Summary

An alternate signal architecture is presented which is based on straightforward

TDMA and FDMA approaches, but allows the reuse of beacon signals. Although this

alternate signal architecture is not currently used in the DMLP system, it is interesting to

examine its performance. First, a simulation is used to estimate the amount of signal re-

use that can be achieved. Then, the analysis from Chapter 3 is used to investigate the

performance of the alternate architecture, as measured by the error in the position esti-

mates, due to eddy noise, for a given number of total beacons in the system. The results

suggest that the alternate signal architecture has the potential to perform significantly bet-

ter than straightforward TDMA or FDMA structures, approaching the performance of the

Chapter 3 signal architecture.



146

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147

Bibliography

[1] Siegel, M., Gunatilake, P., “Remote Inspection Technologies for Aircraft Skin In-

spection,” IEEE Workshop on Emergent Technologies and Virtual Systems for In-

strumentation and Measurement, Ontario, Canada, May 1997.

[2] Prassler, E., Ritter, A., Schaeffer, C., Fiorini, P., “A Short History of Cleaning Ro-

bots,” Autonomous Robots, Special Issue on Cleaning and Housekeeping Robots,

Vol. 9, Issue 3, December 2000.

[3] Gambao, E., Balaguer, C., “Robotics and Automation in Construction,” IEEE Robot-

ics and Automation Magazine, March 2002.

[4] Iborra, A., Pastor, J., Alvarez, B., Fernandez, C., Merono, J., “Robots in Radioactive

Environments,” IEEE Robotics and Automation Magazine, December 2003.

[5] Rossetti, M. D., Kumar, A. and Felder, R., "Mobile Robot Simulation of Clinical

Laboratory Deliveries," The Proceedings of the 1998 Winter Simulation Conference.

[6] Montemerlo, M., Pineau, J., Roy, N., Thrun, S., Verma, V., “Experiences with a

Mobile Robotic Guide for the Elderly,” Proceedings of the AAAI National Confer-

ence on Artificial Intelligence, Edmonton, Canada, 2002.

[7] “Building 21st Century John Deere Tractors,” Modern Materials Handling , March

2001.



148

[8] Everett, H.R., Gage, D.W., "From Laboratory to Warehouse: Security Robots Meet

the Real World," International Journal of Robotics Research, Special Issue on Field

and Service Robotics, Vol. 18, No. 7, July 1999.

[9] Wardell, C. “Home Technology,” Popular Science, November 2000.

[10] Pfeiffer, E., “WhereWare,” Technology Review, September 2003.

[11] Gleicher, M., Ferrier, N., “Evaluating Video-Based Motion Capture,” Proceedings of

Computer Animation 2002, June 2002.

[12] Navab, N., “Developing Killer Apps for Industrial Augmented Reality,” IEEE Com-

puter Graphics and Applications, May/June 2004.

[13] IEEE Robotics & Automation Magazine, http://www.ncsu.edu/IEEE-

RAS/RAM/RAM.html.

[14] The International Journal of Robotics Research, http://www.ijrr.org.

[15] Proceedings of the IEEE 2004 International Conference on Robotics and Automa-

tion (ICRA 2004), http://www.icra2004.org.

[16] Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots

and Systems (IROS 2004), http://www.iros2004.org.

[17] NASA Space Telerobotics Program “Cool Robot of the Week” website,

http://ranier.hq.nasa.gov/telerobotics_page/coolrobots.html.

[18] Wyeth, G., Brown, B., “Robust Adaptive Vision for Robot Soccer,” Mechatronics

and Machine Vision in Practice, Research Studies Press, 2000.

[19] Cremean, L., Dunbar, W., van Gogh, D., Hickey, J., Klavins, E., Meltzer, J., Murray,

R., “The Caltech Multi-Vehicle Wireless Testbed,” Proceedings of the 2002 Confer-

ence on Decision and Control .

[20] Leonard, J., Durrant-Whyte, H., “Simultaneous Map Building and Localization for

an Autonomous Mobile Robot,” IEEE/RSJ International Workshop on Intelligent

Robots and Systems, Vol. 3, 1991.

[21] Se, S., Lowe, D., Little, J., “Local and Global Localization for Mobile Robots using

Visual Landmarks,” Proceedings of the IEEE Int. Conf. On Intelligent Robots and

Systems (IROS) 2001.

[22] Ward, A., Jones, A., Hopper, A., “A New Location Technique for the Active Of-

fice,” IEEE Personal Communications, Vol. 4, No. 5, October 1997.



149

[23] Rosenberg, B., “ ‘Indoor GPS’ Uses IR Light in Aerospace Metrology Realm,” Avia-

tion Week & Space Technology, December 9, 2002.

[24] Parkinson, B., Spilker, J., Axelrad, P., Enge, P., Global Positioning System: Theory

and Applications Volume II , American Institute of Aeronautics and Astronautics,

Inc., 1996.

[25] Elkaim, G., O’Connor, M., Bell, T., Parkinson, B., “System Identification and Ro-

bust Control of a Farm Vehicle Using CDGPS,” Proceedings of the Institute of

Navigation’s GPS conference (ION GPS), September 1997.

[26] Drane, C., Macnaughtan, M., Scott, C., “Positioning GSM Telephones,” IEEE

Communications Magazine, Vol. 36, No. 4, April 1998.

[27] Rabinowitz, M., Spilker, J., “A New Positioning System Using Television Synchro-

nization Signals,” Rosum Corporation white paper, available at

http://www.rosum.com/rosum_whitepapers.html.

[28] Kayton, M., Fried, W., Avionics Navigation Systems, Second Edition, John Wiley &

Sons, Inc., 1997, pp. 138-154.

[29] Hall, T., Counselman, C., Misra, P., “Radiolocation Using AM Broadcast Signals:

Positioning Performance,” proceedings of the Institute of Navigation’s GPS confer-

ence (ION GPS), September 2002.

[30] Kayton, M., Fried, W., Avionics Navigation Systems, Second Edition, John Wiley &

Sons, Inc., 1997, pp. 283-312.

[31] Fontana, R., Richley, E., Barney, J., “Commercialization of an Ultra Wideband Pre-

cision Asset Location System,” 2003 IEEE Conference on Ultra Wideband Systems

and Technologies, November 2003.

[32] Ladd, A., Bekris, K., Rudys, A., Marceau, G., Kavraki, L., Wallach, D., “Robotics-

Based Location Sensing using Wireless Ethernet,” Proceedings of the Eighth ACM

International Conference on Mobile Computing and Networking (MOBICOM), Sep-

tember 2002.

[33] Inan, U., Inan, A., Electromagnetic Fundamentals and Applications, Addison

Wesley Longman, 1997, pp. 1-103.

[34] Griffiths, D., Introduction to Electrodynamics, Prentice Hall, 1989, pp. 340-395.



150

[35] Everett, H., Sensors for Mobile Robots: Theory and Application, A.K. Peters, Ltd.,

1995, pp. 47-48.

[36] Petovello, M., Cannon, M., Lachapelle, G., “Quantifying Improvements from the

Integration of GPS and a Tactical Grade INS in High Accuracy Navigation Applica-

tions,” Proceedings of the Institute of Navigation 2003 National Technical Meeting

(ION NTM), January 2003.

[37] Borenstein, J., Feng, L., “Measurement and Correction of Systematic Odometry Er-

rors in Mobile Robots,” IEEE Transactions in Robotics and Automation, Vol. 12,

No. 6, December 1996.

[38] Ascension Technology Corporation, Burlington, VT, http://www.ascension-

tech.com.

[39] Polhemus, Colchester, VT, http://www.polhemus.com.


1995.

[41] Borenstein, J., Everett, H., Feng, L., Wehe, D., “Mobile Robot Positioning – Sensors

and Techniques,” Journal of Robotic Systems, Special Issue on Mobile Robots, Vol.

14, No. 4, 1997.

[42] Hightower, J., Borriello, G., “Location Systems for Ubiquitous Computing,” Com-

puter , Vol. 34, No. 8, IEEE Computer Society Press, August 2001.

[43] Werb, J., Lanzl, C., “Designing a Positioning System for Finding Things and People

Indoors,” IEEE Spectrum, September 1998.


1995, pp. 305-326.

[45] Luo, M., Akos, D., Pullen, S., Enge, P., Erlandson, B., Frodge, S., “Interference to

GPS from UWB Transmitters,” proceedings of the Institute of Navigation’s GPS

conference (ION GPS), September 2000.

[46] Code of Federal Regulations, Title 47 (Telecommunications), Chapter I (Federal

Communications Commission), Part 15 (Radio Frequency Devices), Section 15.3

Definitions (47CFR15.3) defines “RF” energy to be contained in the spectrum be-

tween 9 kHz and 3,000,000 MHz.



151

[47] Prigge, E., How, J., “Signal Architecture for a Distributed Magnetic Local Position-

ing System,” Proceedings of the First IEEE International Conference on Sensors

(Sensors 2002), June 2002.

[48] Prigge, E., How, J., “An Indoor Absolute Positioning System with No Line of Sight

Restrictions and Building-Wide Coverage,” Proceedings of the IEEE International

Conference on Robotics & Automation (ICRA 2000), April 2000.

[49] Asimov, I., Biographical Encyclopedia of Science and Technology, Doubleday,

1982.

[50] Goldhaber, A., Nieto, M., “Terrestrial and Extraterrestrial Limits on the Photon

Mass,” Review of Modern Physics, Vol. 43, 1971.

[51] Giancoli, D., Physics for Scientists and Engineers with Modern Physics, Second Edi-

tion, Prentice Hall, 1989.

[52] D. Griffiths, Introduction to Electrodynamics (Second Edition), Prentice Hall, 1989.

[53] Inan, U., Inan, A., Electromagnetic Fundamentals and Applications, Addison

Wesley Longman, 1997.

[54] Ibid , p. 61.

[55] Ibid , p. 93.

[56] Ibid , p. 84.

[57] Ibid , p. 87.

[58] Ibid , p. 95.

[59] Ibid , p. 7.

[60] Blood, E., “Device for Quantitatively Measuring the Relative Position and Orienta-

tion of Two Bodies in the Presence of Metals Utilizing Direct Current Magnetic

Fields,” United States Patent 4,945,305, July 1990.

[61] Kuipers, J., “Object Tracking and Orientation Determination Means, System and

Process,” United States Patent 3,868,565, February 1975.

[62] R. Peterson, R. Ziemer, D. Borth, Introduction to Spread Spectrum Communication,

Prentice Hall, 1995.

[63] Lupas, R., Verdu, S., “Linear Multiuser Detectors for Synchronous Code Division

Multiple Access Channels,” IEEE Transactions on Information Theory, January

1989.



152

[64] Kay, S., Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice

Hall, 1993.


and Applications Volume I , American Institute of Aeronautics and Astronautics, Inc.,

1996.

[66] Corbyn, J., “Pulse Induction Metal Detector,” Wireless World , March, 1980.

[67] Das, Y., McFee, J., Chesney, R., “Time Domain Response of a Sphere in the Field of

a Coil: Theory and Experiment,” IEEE Transactions on Geoscience and Remote

Sensing , Vol. GE-22, No. 4, July 1984.

[68] Raab, F., Blood, E., Steiner, T., Jones, H., “Magnetic Position and Orientation

Tracking System,” IEEE Transactions on Aerospace and Electronic Systems, Sep-

tember 1979.

[69] Raab, F., “Remote Object Position Locater,” United States Patent 4,054,881, October

1977.

[70] Kuipers, J., “SPASYN – An Electromagnetic Relative Position and Orientation

Tracking System,” IEEE Transactions on Instrumentation and Measurement , De-

cember 1980.

[71] Kuipers, J., “Tracking and Determining Orientation of Object Using Coordinate

Transformation Means, System and Process,” United States Patent 3,983,474, Sep-

tember 1976.

[72] Kalmus, H., “A New Guiding and Tracking System,” IRE Transactions on Aero-

space and Navigational Electronics, Vol. 9, March 1962.

[73] Olsen, R., Farstad, A., “Electromagnetic Direction Finding Experiments for Location

of Trapped Miners,” IEEE Transactions on Geoscience Electronics, October 1973.

[74] Wait, J., “Electromagnetic Induction Technique for Locating a Buried Source,” IEEE

Transactions on Geoscience Electronics, 1971.

[75] W. Press, S. Teukolsky, W. Vetterling, B. Flannery , Numerical Recipes in C, the Art

of Scientific Computing, Second Edition, Cambridge University Press, 1992, pp. 379-

383.

[76] Ibid , pp. 383-393.

[77] Ibid , p. 380.



153

[78] G. Wahba, “A Least Squares Estimate of Satellite Attitude,” SIAM Review, Vol. 7,

No. 3, p. 409, July 1965.

[79] J. Farrell, J. Stuelpnagel, “A Least Squares Estimate of Satellite Attitude,” SIAM Re-

view, Vol. 8, No. 3, p. 384, July 1966.

[80] F. Markley, “Attitude Determination using Vector Observations and the Singular

Value Decomposition,” Journal of the Astronautical Sciences, Vol. 36, No. 3, July-

September 1988.

[81] F. Markley, “Attitude Determination Using Vector Observations: A Fast Optimal

Matrix Algorithm,” Journal of the Astronautical Sciences, Vol. 41, No. 2, April-June

1993.

[82] M. Shuster, S. Oh, “Three-Axis Attitude Determination from Vector Observations ,”

Journal of Guidance and Control , January-February 1981.

[83] Livingston, M., State, A., “Magnetic Tracker Calibration for Improved Augmented

Reality Registration,” Presence, Vol. 6, No. 5, 1997.

[84] Birkfellner, W., Watzinger, F., Wanschitz, F., Ewers, R., Bergmann, H., “Calibration

of Tracking Systems in a Surgical Environment,” IEEE Transactions on Medical

Imaging , Vol. 17, No. 5, October 1998.

[85] Caruso, M., Bratland, T., Smith, C., Schneider, R., “A New Perspective on Magnetic

Field Sensing,” Sensors, December 1998.

[86] W. Press, S. Teukolsky, W. Vetterling, B. Flannery , Numerical Recipes in C, the Art

of Scientific Computing, Second Edition, Cambridge University Press, 1992.

[87] P. Horowitz and W. Hill, The Art of Electronics (Second Edition), Cambridge Uni-

versity Press, 1989, pp. 430-431.


and Applications Volume I , American Institute of Aeronautics and Astronautics, Inc.,

1996, pp. 474-477.

[89] Warrior, J., McHenry, E., McGee, K., “They Know Where You Are,” IEEE Spec-

trum, July 2003.

[90] J. Wagenknecht, S. Fredrickson, T. Manning, and B. Jones, "Design, Development

and Testing of the Miniature Autonomous Extravehicular Robotic Camera (Mini



AERCam) Guidance, Navigation, and Control System," 26th Annual American As-

tronautical Society Guidance and Control Conference, February 2003.

[91] Ballhaus, W., Experiments in High-Performance Control of a Multi-Link Flexible

Manipulator with a Mini-Manipulator, PhD thesis, Stanford University, 1994.

[92] Ballhaus, W., Rock, S., “End-Point Control of a Two-Link Flexible Robotic Manipu-

lator with a Mini-Manipulator: Initial Experiments,” Proceedings of the American

Control Conference, June 1992.

[93] D. Griffiths, Introduction to Electrodynamics (Second Edition), Prentice Hall, 1989,

p. 209.

a positioning system with no line-of-sight restrictions for cluttered environments

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