Performance of a Precision IndoorPositioning System Usinga Multi-Carrier Approach

David Cyganski, John Orr, William MichalsonWorcester Polytechnic Institute

Supported by

National Institute of Justice, US Department of Justice

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Presentation Outline

Background/MotivationOverall System and Signal ArchitecturePerformance AnalysisResults, Further Work

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Project Focus

Precision, ad hoc, indoor/outdoorpositioning and associated exchange ofdata for situational awareness andcommand/control for

Firefighters Law enforcement officers Military First-responders Corrections officers

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System Overview

GPS Signal

Personnel Unit

Reference Unit,known location

Command and Control Unit

Phys Monitor

Reference Unit,known location

Reference Unit,known location

GPS referencePositioning signalSystem controlUser-Commander link

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Real-Time Deployable PersonnelGeolocation

Vehicles (red)driveup to a buildinganduse reference units(blue) to locateand display tracksof fire fighters.Exits and otherkey buildingfeatures may be“marked” on thefly.

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… with GIS (Geographic Info. Sys.)overlays.

If GIS information suchas complete floor plansare available, they canbe integrated with thetrack display to assistroute planning and other time-criticaldecisions.

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System Requirements

Number of dimensions: 3 Accuracy: +/- 1 ft Maximum range: 2000 ft Max number of simultaneous users: 100 Fundamental capabilities:

3-D location of each user relative to a chosen reference point Relative locations among users Graphical display at base station Graphical path information on all users Self rescue information to users (audio)

Enhancements: Physiologic information telemetry Integration with stored databases: geographic and structural

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Differences from GPS

Small operational area (< ~1km2)Major focus is indoorsAbsolute geo reference may not be neededUser devices may be activeOverall system cost must be kept lowEntire system must be self-initializing, self-

monitoring

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System Principles

Positioning based on Time Difference ofArrival

Roving Units are simple (transmitters ofperiodic signals)

Signal processing is DFT-based as inOFDM (Orthogonal Frequency DivisionMultiplex)

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Impulse-UWB vs. Multi-Carrier-UWB

Wide (ultra-wide) bandwidth is needed formultipath rejection, but ultra-narrow timepulses are not needed.

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The OFDM Concept

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Lessons Learned from OFDM

High data rate transmission via multicarriermodulation does not require a single wideband channel with: Low distortion (in amplitude and/or phaseresponse) Narrow pulses Uniform noise Absence of interferers Precise synchronization

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Proof of Concept Demonstration inAudio

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Proof of Concept Demonstration

Uses audio, not RF - greatly eased troubleshooting Top audio frequency has wavelength in air of 4.5 in. 1:1 scale behavior with an RF bandwidth of 2.625

GHz Implements real-time location system using

MATLAB Off the shelf microphone/speaker components can

be used thanks to the OFDM like channelization Displays true location solution as well as multipath

solutions

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Transmitted Signal

0

1[2 ( ) ]

0

( ) m

Mj f m f t

m

s t Ae! "

#+ $ +

=

=%

M carriers

Carrier spacing = Δf

Each carrier has arbitrary phase Φm

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Signal Format

Carriers:Δf

δf

Δf = Kδf δf = fs/N

BW = B = M Δf

M: # Carriers

N: # DFT frequency samples

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DFT Receiver Processing Architecture

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Received Signal

0 0 0

1[2 ( )( ) ]

0

( ) k m

Mj f m f t t

k k

m

s t A e! " #

$+ % + $ +

=

=&

t0: user clock offset; τk0: path delay

In the simple (no multipath) case, any 2 of the M carriersmay be used to identify a phase difference and hence atime and distance difference between two receiver sites.

There is phase and hence distance ambiguity, withambiguity distance of c/Δf where c is the velocity of thewave. For our situation, Δf may be chosen sufficientlysmall to eliminate the ambiguity.

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Frequency Sampling of ReceivedSignal

The mth Fourier coefficient of the kth reference receiver:

0 0[ 2 ( ) ]k m mj f m f

km kS A e! " # $% + & + +

=

[ ]mj

m kS A e!

=

results in.

multiplied by

where the clock offset is 0 02 ( )m f m f t! "= + #

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0 02 ( )k kf t! "# = $ %where

Which represents samples of a sinusoid withsampling index m and frequency 2πΔf(t0-τk0). Hence,given Δf, the time difference can be found.

0

0 0 0 0

( 2 )

[2 ( )] 2

k m

k

k

jm f

km m k

jm ft f j f tk

j mk

S S A A e

A A e

B e

! " #

! " !

$ % +& &

% $% +&

'

=

=

= ,

Frequency Sampling of ReceivedSignal (cont.)

Frequency Delay

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Sample Result for 1 Signal

“Freq Index” corresponds to carrier frequenciesin the transmitted signal “comb.”

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Sinusoidal Frequency Estimation

Estimation of the frequencies of sinusoidsin noise (not necessarily harmonicallyrelated) is an old/fertile field

We use the state space approach: Exact solution (without noise) for P

frequencies given M > 2P Fouriersamples (comb frequencies)

Direct solution, good noise performance Model-based (P must be estimated a

priori)

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Positions from Frequencies

Given the frequencies, TDOAs of all paths immediatelyfollow

Can reject multipath TDOAs based on inconsistencywith a single source (computation-intensive)

Given time synchronization with transmitter, TDOAbecomes TOA and direct paths can be identified directly

Or, make the system unambiguous range cell largerthan the maximum physical operations area, and ordersolutions to identify shortest path

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Steps in Determination ofPosition Errors

Error in frequency estimation given signal structure,noise, signal strength

Error in position estimate given frequency error,system geometry

RF Channel performance: needed transmit power Engineering rules: position error vs. transmitted

signal power given system structure Note: This initial analysis contains some simplying

assumptions, including perfect synchronizationamong reference receivers

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Bound on Frequency Estimate

{ }2

1

2

3

2 6

cME

n

k

!="#

Cramer Rao Bound for a frequency estimate ofone sinusoid:

σn is the noise standard deviationc1 is the amplitude of the sinusoidM is the number of carriers

where

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Bound on Delay Estimate

sTPB

N

22

02

8

3

!"# =

Put in terms of known or measurable parametersthe bound on variance of the delay estimate is:

where

N0 is noise PSD

B is signal bandwidth

T is period of transmitted signal

Ps is received signal power

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Position Estimate Error

])[(ˆ 1

0

!= AATrcr

T

r "#$$

Standard deviation of the position estimate isapproximately (asymptotically correct for large r0 ):

where

c is the speed of light

r0 is the overall distance from target to references

σδτ is TDOA error standard deviation

A is the matrix of relative positions of reference stations!"! ## 2$

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Example for a Particular Geometry

hw0

0w0

h0w

00w

h00

A =

BhTP

whNc

s

r

!"

22

0256

8

1ˆ

+=

6 reference stations:1 at (0, 0, 0),1 at (0, 0, h), etc.

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RF Performance Effects

2

0

2

2

16 r

GGP

s

rectranstransP

!

"=

Friis Transmission Formula for received power Ps:

)10(4 10/

0

NF

aTN !=

Noise power for given receiver noise figure(dB) and antenna noise temperature (Kelvin):

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Specific Example

TPBh

wfwhX

trans

rmax

22

8 251019.2ˆ

+=

!"

• Same geometry, omnidirectional antennas• Noise figure of 3 dB, Antenna temperature of 290K• Path attenuation of shortest wavelength (fmax)

or

EFh

wwhX

r

22

8 251019.2ˆ

+=

!"

where F = (B/fmax) and E = PtransT

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Performance Nomograph

Nomograph for 6sensor examplegeometryintroducedearlier, h = 5 m,desired positionstd. dev. of 10 cm.

Example:1 – 1.2 GHz BW,w = 21 m, energyneeded is 2x10-12

W-sec or 2 µWfor T=1 µsec

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Conclusions

This analysis provides encouragingresults on system performance

Analysis has been verified withsimulation

Continuing work will tighten theperformance bounds and remove thesimplifying assumptions

Implementation of an RF proof-of-concept system is underway