chapter 7 localization & positioning

Chapter 7Localization & Positioning

112/04/241 Jang Ping Sheu

Means for a node to determine its physical position with respect to some coordinate system (50, 27) or symbolic location (in a living room)

Using the help of Anchor nodes that know their positions Directly adjacent nodes Over multiple hops

Goals of this chapter


7.1 Properties of localization and positioning procedures

7.2 Possible approaches 7.3 Mathematical basics for the lateration problem 7.4 Positioning in multi-hop environments 7.5 Positioning assisted by anchors

Outline


Physical position versus logical location Coordinate system: position Symbolic reference: location

Absolute versus relative coordinate Centralized or distributed computation Localized versus centralized computation Accuracy and precision:

Accuracy: how close is an estimated position to the real position? Precision: the ratio with which a given accuracy is reached

Scale (indoors, outdoors, global, …) Limitations: GPS for example, does not work indoors Costs: time, space, and energy consumption

7.1 Properties of localization and positioning procedures


Proximity A node wants to determine its position or location in the proximity

of an anchor (Tri-/Multi-) lateration and angulation

Lateration : when distances between nodes are used Angulation: when angles between nodes are used

Scene analysis The most evident form of it is to analyze pictures taken by a

camera Other measurable characteristic ‘fingerprints’ of a given location

can be used for scene analysis e.g., RADAR Bounding box

to bound the possible positions of a node

7.2 Possible approaches


Using information of a node’s neighborhood Exploit finite range of wireless communication

e.g., easy to determine location in a room with infrared (room number announcements)

Proximity (range-free approach)


(Tri-/Multi-)lateration and angulation Using geometric properties Lateration: distances between entities are used Angulation: angle between nodes are used

(x = 2, y = 1)

(x = 8, y = 2)

(x = 5, y = 4)

r1

r2

r3

Trilateration and triangulation (range-based approach)


To use (multi-)lateration, estimates of distances to anchor nodes are required.

This ranging process ideally leverages the facilities already present on a wireless node, in particular, the radio communication device.

The most important characteristics are Received Signal Strength Indicator (RSSI), Time of Arrival (ToA), and Time Difference of Arrival (TDoA).

Trilateration and triangulation (cont.)Determining distances


Send out signal of known strength, use received signal strength and path loss coefficient to estimate distance

Distance estimation RSSI (Received Signal Strength Indicator)


Problem: Highly error-prone process : Caused by fast fading, mobility of the environment Solution: repeated measurement and filtering out incorrect

values by statistical techniques Cheap radio transceivers are often not calibrated

Same signal strength result in different RSSI Actual transmission power different from the intended power Combination with multipath fading Signal attenuation along an indirect path is higher than along a direct

path Solution: No!

Distance estimationRSSI (cont.)


Distance estimationRSSI (cont.)

DistanceDistance Signal strength

PDF

PD

F

PDF of distances in a given RSSI value


Use time of transmission, propagation speed

Problem: Exact time synchronization Usually, sound wave is used But propagation speed of sound depends on temperature

or humidity

Distance estimation ToA (Time of arrival )


Use two different signals with different propagation speeds Compute difference between arrival times to compute

distance Example: ultrasound and radio signal (Cricket System)

Propagation time of radio negligible compared to ultrasound

Problem: expensive/energy-intensive hardware

Distance estimationTDoA (Time Difference of Arrival )


RADAR system: Comparing the received signal characteristics from multiple anchors with premeasured and stored characteristics values.

Radio environment has characteristic “fingerprints” The necessary off-line deployment for measuring the signal

landscape cannot always be accommodated in practical systems.

Scene analysis


Bounding Box

The bounding box method proposed in uses squares instead of circles as in tri-lateration

to bound the possible positions of a node.

For each reference node i, a bounding box is defined as a square with its center at the position of this node (xi, yi), with sides of size 2di (where di is the estimated distance) and with coordinates (xi –di, yi–di) and (xi+di, yi+di).


Bounding Box (cont.)

Using range to anchors to determine a bounding box

Use center of box asposition estimate

C

A

B

d


References N. Bulusu, J. Heidemann, and D. Estrin. “GPS-Less Low Cost

Outdoor Localization For Very Small Devices,” IEEE Personal Communications Magazine, 7(5): 28–34, 2000.

C. Savarese, J. Rabay, and K. Langendoen. “Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks,” In Proceedings of the Annual USENIX Technical Conference, Monterey, CA, 2002.

A. Savvides, C.-C. Han, and M. Srivastava. “Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors,” Proceedings of the 7th Annual International Conference on Mobile Computing and Networking, pages 166–179. ACM press, Rome, Italy, July 2001.

S. Simic and S. Sastry, “Distributed localization in wireless ad hoc networks,” UC Berkeley, Tech. rep. UCB/ERL M02/26, 2002.


7.3 Mathematical basics for the lateration problem


Solution with three anchors and correct distance values Assuming distances to three points with known

location are exactly given

Solve system of equations (Pythagoras!) (xi , yi) : coordinates of anchor point i, ri : distance to anchor i (xu, yu) : unknown coordinates of node


Solution with three anchors and correct distance values (cont.)


Rewriting as a matrix equation:

Trilateration as matrix equation

)()()()()()(

2 23

22

23

22

23

22

23

21

23

21

23

21

2323

1313

yyxxrryyxxrr

yx

yyxxyyxx

u

u

)()()()(2)(2 23

21

23

21

23

211313 yyxxrryyyxxx uu

)()()()(2)(2 23

22

23

22

23

222323 yyxxrryyyxxx uu


What if only distance estimation available?

Use multiple anchors, overdetermined system of equations

Use (xu, yu) that minimize mean square error, i.e,

Solving with distance errors

iii rr _


Look at square of the of Euclidean norm expression (note that for all vectors v)

Look at derivative with respect to x, set it equal to 0

Minimize mean square error


7.4 Positioning in multi-hop environments


Assume that the positions of n anchors are known and the positions of m nodes is to be determined, that connectivity between any two nodes is only possible if nodes are at most R distance units apart, and that the connectivity between any two nodes is also known

The fact that two nodes are connected introduces a constraint to the feasibility problem – for two connected nodes, it is impossible to choose positions that would place them further than R away

Connectivity in a multi-hop network


Multi-hop range estimation How to estimate range to a node to which no direct

radio communication exists? No RSSI, TDoA, … But: Multi-hop communication is possible

A

C

B

X


Multi-hop range estimation (cont.)

Idea 1: (DV-Hop) Start by counting hops between anchors then divide known distance

Count Shortest hop numbers between all two nodes. Each anchors estimate hop length and propagates to the

network. Node calculates its position based on average hop length

and shortest path to each anchor.


DV Hop

L1 calculates average hope length :

So do L2 and L3 :

Node A uses trilateration to estimate it’s position by multiplying the average hope length of every received anchor to shortest path length it assumed.

5.172640100

42.16527540

90.1556

10075

i

jijii h

yyxxc

22 )()(


DV-Distance

Idea 2: If range estimates between neighbors exist, use them to improve total length of route estimation in previous method (DV-Distance)

Distance between neighboring nodes is measured using radio signal strength and is propagated in meters rather than in hops.

The algorithm uses the same method to estimate but shortest distance length are assumed.


• Must work in a network which is dense enough DV-hop approach used the hop of the shortest path to approximately estimate the distance between a pair of nodes

• Drawback: Requires lots of communications

anchor

anchor

Multi-hop range estimation (cont.) DV-Based Scheme


Number of anchors Euclidean method increase accuracy as the number of

anchors goes up The “distance vector”-like methods are better suited for

a low-ratio of anchors Uniformly distributed network

Distance vector methods perform less well in non-uniformly networks

Euclidean method is not very sensitive to this effect

Discussion


7.5 Positioning assisted by anchors


By pure connectivity information Idea: decide whether a node is within or outside of a

triangle formed by any three anchors However, moving a sender node to determine its position

is hardly practical ! Solution:

inquire all its neighbors about their distance to the given three corner anchors

APIT (Approximate Point in Triangle)


APIT (cont.)

Inside a triangle

Irrespective of the direction of the movement, the node must be closed to at least one of the corners of the triangle

A

CB

M


APIT (cont.)

Outside a triangle:

There is at least one direction for which the node’s distance to all corners increases

A

CB

M


Approximation: Normal nodes test only directions towards neighbors

A

C

1

23

4

M

B

A

CB

A. Inside Case B. OutSide Case

1

23

4

M

APIT (cont.)


Grid-based Aggregation Narrow down the area where the normal node can

potentially reside

-1-1-10011100

-1-1-10122200

0-1-10112211

00-10112210

0001111100

0001110100

0001000000

-1-1-10000

-1-10100

0-1011

00-1010

00011100

00011000

0001100000

anchor node normal node

1

2

APIT (cont.)


112/04/24 38

MCL (Monte-Carlo Localization)

Assumptions Time is divided into several time slots Moving distance in each time slot is randomly chosen

from [0, Vmax ] Each anchor node periodically forwards its location to

two-hop neighbors Notation

R - communication range


112/04/24 39

MCL (cont.)

Each normal node maintains 50 samples in each time slot Samples represent the possible locations The sample selection is based on previous samples Sample (x , y) must satisfy some constraints

Located in the anchor constraints


112/04/24 40

MCL (cont.)

Anchor constraints Near anchor constraint

The communication region of one-hop anchor node ( near anchor )

Farther anchor constraint The region within ( R, 2R ]

centered on two-hop anchor ( farther anchor )

Near anchor constraint

RA1

RR

Farther anchor constraint

A1

N1

N1N2


112/04/24 41

MCL (cont.)Environment

Anchor nodeNormal node

A1

A2

A3

A4

N1


112/04/24 42

MCL (cont.)Initial Phase

N1

A1

A2

A3

A4


Sample in the last time slot


112/04/24 43

RR R

MCL (cont.)Prediction Phase & Filtering Phase

N1

A1

A2

A3

A4

Vmax


Sample in the last time slot Sample in this time slot


112/04/24 44

R

MCL (cont.)Prediction Phase & Filtering Phase

N1

A1

A2

A3

A4

Vmax

Vmax

Vmax


RR



112/04/24 45

MCL (cont.)Estimative Location

N1

A1

A2

A3

A4

the average of samples

EN1


Estimative position Sample in this time slot


112/04/24 46

MCL (cont.) Repeated Prediction Phase & Filter Phase

Vmax

N1A1

A2

A3

A4

R

In the next time slotAnchor nodeNormal node



There are three phases in the DRLS algorithm. Phase 1 – Beacon exchange

Phase 2 – Using improved grid-scan algorithm to get initial estimative location

Phase 3 – Refinement

DRLS Distributed Range-Free Localization Scheme


Beacon exchange via two-hop flooding

N1

Near anchorNormal node

A1

A2

A3

A4

N2

N3 Farther anchor

DRLS (cont.)Beacon Exchange


DRLS (cont.)Improved Grid-Scan Algorithm

A2

A3

A1

N

Normal nodeAnchor node

right sideleft side

up side

down side

Calculate the overlapping rectangle



Divide the ER into small grids The initial value of the grid is 0

0

0

0

0

00

0 0

0

A2

A3

A1

0 0

0

0

0

0

N

0

Anchor nodeNormal nodeEstimative location



2

2

2

3

33

3 3

3

A2

A3

A1

1 1

2

2

2

2

N

N’2

Anchor nodeNormal nodeEstimative location

Initial estimative location Apply centroid formula to grids with the maximum grid

value


Repulsive virtual force (VF) Induced by farther anchor nodes

Dinvasion : the maximum distance that the farther anchor invades the estimative region along the direction from the farther anchor towards the initial estimative location

DRLS (cont.)Refinement


VFA3

DinvasionA3

VFA4

DinvasionA4

VFA5

DinvasionA5

VFi : virtual force induced by farther anchor i Dinvasioni : the maximum distance that

the farther anchor i invades the estimative region along the direction from i towards the initial estimative location

Vi,j : the unit vector in the direction from the farther anchor i towards the initial estimative location j

VFi = Vi,j˙Dinvasioni

A4

A5

A1

A2

NN’A3



RVF

Resultant Virtual Force (RVF) RVF = ΣVFi

A4

A5

A1

A2

NN’A3

N’



DA3max

Dimax : the maximum moving

distance caused by the farther anchor i

Di : the moving distance caused by the farther anchor i

A4

A5

A1

A2

NN’A3

L3

ab

cd e f

DinvasionA3

Di

Dimax

=Dinvasioni

Dinvasionimax

DinvasionA3max


112/04/2455

Di = N’e × cd

ce

Jang Ping Sheu

Dmovei : the moving vector caused by the farther anchor i

Vi,j : the unit vector in the direction from the farther anchor i towards the initial estimative location j

Dmovei = Vi,j˙Di

estimative region

DmoveA3

DinvasionA3

DmoveA4

DinvasionA4

DmoveA5

DinvasionA5

A4

A5

A1

A2

NN’A3



Dmove: the final moving vector Dmove = Σ Dmovei

Dmove

A4

A5

A1

A2

NN’A3

N’



Improvements Dynamic number of samples

According to the overlapping region of anchor constraints Restricted samples

Anchor constraints The estimative locations of neighboring normal nodes

Predicted moving direction of the normal node Be used to increase the localization accuracy

IMCL Improved MCL Localization Scheme


Phase 1- Sample Selection Phase

Phase 2- Neighbor Constraints Exchange Phase

Phase 3- Refinement Phase

IMCL (cont.)


Dynamic sample number Sampling Region

The overlapping region of anchor constraints

Difficult to calculate Estimative Region (ER)

A rectangle surrounding the sampling region

A1

A2

A3

R

R

R

ER

N

IMCL (cont.) Sample Selection Phase



The number of samples ( k )

k =

• ERArea — the area of ER• ERThreshold — the threshold value• Max_Num — the upper bound of sample number

In our simulations, ERThreshold = 4R2

Threshold

Area

ERERNumMax _

k ≦ Max_Num

A1A2

A3

R

R

R

ER

N



Using the prediction and filtering phase of MCL Samples are randomly selected from the region

extended Vmax from previous samples Filter new samples

Near anchor constraints Farther anchor constraints


N2

IMCL (cont.) Effective Location Estimation

An additional normal nodes constraint Samples must locate on the communication region of

neighboring normal nodes The localization error may increase

Send the possible location region to neighbors instead of the estimative position N1

N3

EN1

EN2


The possible location region The distribution of samples are selected in phase I

IMCL (cont.) Neighbor Constraints Exchange Phase

Step 1: Sensor A constructs a coordinate axis and uses (Cx ,Cy) as originStep 2: The coordinate axis is separated into eight directions

Central position in phase 1

45°135°

225° 315°

90°

270°

180° 0°(Cx ,Cy)


θ

45°90°135°

180° 0°

225°270°

315°


Step 3: The samples are also divided into eight groups according to the angle θ with (Cx , Cy)

(Cx ,Cy)

(Sx ,Sy))(tan 1

xx

yy

CSCS

Valid samples in current time slot

Central position in phase 1112/04/2465 Jang Ping Sheu

45°90°135°

180° 0°

225°270°

315°


Step 4: Using the longest distance within group as radius to perform sector

the possible location region described by eight sectors and (Cx , Cy)

Sample in the this time slot

Central position in phase 1

112/04/24

66 Jang Ping Sheu

Neighbor constraint Extend R from the possible located region

Neighbor constraint

90°45°135°

180° 0°

225°

270°

315°

(Cx ,Cy)

R Each sensor broadcasts its neighbor constraint region once



IMCL (cont.) Refinement Phase

Samples are filtered Neighbor constraints

Receive from neighboring normal nodes Moving constraint

Predict the possible moving direction When sample is not satisfy the constraints

Normal node generates a valid sample to replace it



S1

S2

Neighbor constraints Sample S1 is a valid sample

Satisfied both neighborconstraints of N2 and N3

Sample S2 is an invalid sample Only satisfied the neighbor

constraint of N3



Et-2

Et-1

θ Δ Φ

Δ Φ (Cx , Cy)

(Cx , Cy)

In time slot t if (Cx , Cy) is located in {θ±ΔΦ} from Et-2

Prediction is right

if (Cx , Cy) is located outside of {θ±ΔΦ} from Et-2

Prediction is wrongThus, we do not adopt the moving constraint!

Moving constraint The prediction of nodes moving direction is [θ±ΔΦ ]



If prediction is right, sample must be located in {θ±ΔΦ} from Et-2

Sample 1 satisfies moving constraint

Sample 2 does not satisfy moving constraint

Et-2

Et-1

θ Δ Φ

Δ Φ (Cx , Cy)

Sample 1

Sample 2


IMCL (cont.) Estimative Position

Normal node calculates the estimative position Et (Ex , Ey) of samples

Ex =

Ey =

k

ixk

i1

sample of coordinate

k

iyk

i1

sample of coordinate

number sample , k


Determining location or position is a really important function in WSN, but fraught with many errors and shortcomings Range estimates often not sufficiently accurate Many anchors are needed for acceptable results Anchors might need external position sources (GPS)

Conclusions


References J. Hightower and G. Borriello. “Location Systems for Ubiquitous Computing,”

IEEE Computer, 34(8): 57–66, 2001. J. Hightower and G. Borriello. “A Survey and Taxonomy of Location Systems

for Ubiquitous Computing,” Technical Report UW-CSE 01-08-03, University of Washington, Computer Science and Engineering, Seattle, WA, August 2001.

A. Boukerche, H. Oliveira, E. Nakamura, and A. Loureiro. “Localization systems for wireless sensor networks”. IEEE Wireless Communications, December 2007.

R. Want, A. Hopper, V. Fal˜ao, and J. Gibbons. The Active Badge Location System. ACM Transactions on Information Systems, 10(1): 91–102, 1992.

A. Ward, A. Jones, and A. Hopper. A New Location Technique for the Active Office. IEEE Personal Communications, 4(5): 42–47, 1997.

P. Bahl and V. N. Padmanabhan. RADAR: An In-Building RF-Based User Location and Tracking System. In Proceedings of the IEEE INFOCOM, pages 775–784, Tel-Aviv, Israel, April 2000.

N. B. Priyantha, A. Chakraborty, and H. Balakrishnan. The Cricket Location-Support System. In Proceedings of the 6th International Conference on Mobile Computing and Networking (ACM Mobicom), Boston, MA, 2000.


References

N. Bulusu, J. Heidemann, and D. Estrin. “GPS-Less Low Cost Outdoor Localization For Very Small Devices,” IEEE Personal Communications Magazine, 7(5): 28–34, 2000.

C. Savarese, J. Rabay, and K. Langendoen. “Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks,” In Proceedings of the Annual USENIX Technical Conference, Monterey, CA, 2002.

A. Savvides, C.-C. Han, and M. Srivastava. “Dynamic Fine-Grained Localization in Ad-Hoc Networks of Sensors,” Proceedings of the 7th Annual International Conference on Mobile Computing and Networking, pages 166–179. ACM press, Rome, Italy, July 2001.

S. Simic and S. Sastry, “Distributed localization in wireless ad hoc networks,” UC Berkeley, Tech. rep. UCB/ERL M02/26, 2002. D. Niculescu and B. Nath. “Ad Hoc Positioning System (APS)”. In Proceedings of IEEE GlobeCom, San Antonio, AZ, November 2001.

C. Savarese, J. M. Rabaey, and J. Beutel. “Locationing in Distributed Ad-Hoc Wireless Sensor Networks”. In Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP 2001), Salt Lake City, Utah, May 2001.


References V. Ramadurai and M. L. Sichitiu. “Localization in Wireless Sensor Networks:

A Probabilistic Approach”. In Proceedings of 2003 International Conference on Wireless Networks (ICWN 2003), pages 300–305, Las Vegas, NV, June 2003.

M. L. Sichitiu and V. Ramadurai, “Localization of Wireless Sensor Networks with A Mobile Beacon,” Proc. 1st IEEE Int’l. Conf. Mobile Ad Hoc and Sensor Sys., FL, Oct. 2004, pp. 174–83.

N.Bodhi Priyantha, H. Balakrishnan, E. Demaine, S. Teller,”Mobile-Assisted Localization in Sensor Network”, IEEE INFOCOM 2005, Miami, FL, March 2005.

T. He, C. Huang, B. M. Blum, J. A. Stankovic, and T. Abdelzaher. Range-Free Localization Schemes for Large Scale Sensor Networks. Proceedings of the 9th Annual International Conference on Mobile Computing and Networking, pages 81–95. ACM Press, 2003.

F. Dellaert, D. Fox, W. Burgard, and S. Thrun, "Monte Carlo Localization for Mobile Robots", IEEE International Conference on Robotics and Automation (ICRA), 1999

L. Hu and D. Evans, "Localization for Mobile Sensor Networks," Proc. ACM MobiCom, pp. 45-47, Sept. 2004.


References J.-P. Sheu, P.-C. Chen, and C.-S. Hsu, “A Distributed Localization Scheme

for Wireless Sensor Networks with Improved Grid-Scan and Vector-Based Refinement,” IEEE Trans. on Mobile Computing, vol. 7, no. 9, pp. 1110-1123, Sept. 2008.

Jang-Ping Sheu, Wei-Kai Hu, and Jen-Chiao Lin, "Distributed Localization Scheme for Mobile Sensor Networks," IEEE Transactions on Mobile Computing Vol. 9, No. 4, pp. 516 - 526, April 2010.


chapter 7 localization & positioning

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jang ping sheujang ping

signal of known strength

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signal strength indicator

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lateration problem

positioning procedures7