C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 1

Locationing in Distributed Ad-hocLocationing in Distributed Ad-hocWireless Sensor NetworksWireless Sensor Networks

Chris Savarese, Jan Beutel, Jan Rabaey

ICASSP 2001

University of California at Berkeley

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 2

• Introduction to PicoRadio and triangulation

• A brief look at other research in the field

• Using redundancy to improve accuracy in position estimates

• Establishing initial position estimates

Presentation OutlinePresentation Outline

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 3

PicoRadio OverviewPicoRadio Overview

• Ad-hoc network of many sensors, monitors, and actuators (>100 total)

• No infrastructure

• Distributed computation

• Highly dynamic

• Limited radio range

• Every node capable of acting as repeater

• Obstacles

• Sensor data requires location tag to be useful

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 4

Positioning: The ProblemPositioning: The Problem

Reference Positions, Map Database

Other Networking Nodes, Distance and Geometric

Constellation

Finding the position of networking nodes

Relative positioning vs. Absolute positioning

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 5

Positioning 101Positioning 101

Triangulation Core Computation

• Least Squares

• Minimum Mean Squared Error

Measured Data

• Time of Arrival, Time Difference of Arrival require high clock

• Angle of Arrival too expensive – requires antenna arrays

• Preferred method: Received Signal Strength (RSSI)

• Ranges subject to as much as 50% error

Geometric Interpretation

• 2-D requires 3 anchors

• 3-D requires 4 anchors

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 6

• Dr. Yao, UCLA

• A Protocol for Distributed Node Location

• Does not consider error in range measurements

• Dr. Srivastava, UCLA

• Location Discovery in Ad-Hoc Wireless Networks

• Propagated awareness from closely packed anchors

• Kris Pister, Berkeley

• Smart Dust

• Centralized computation

Other ResearchOther Research

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 7

• Improve dilution of precision by incorporating redundancy into triangulation solution

• Exploit high connectivity

Exploiting RedundancyExploiting Redundancy

• Iteration on every node

• Receive neighbors’ positions

• Range estimation

• Position calculation

• Broadcast result to neighbors

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 8

Individual TriangulationIndividual Triangulation

0 0.5 10

0.2

0.4

0.6

0.8

1

Delaunay Mesh of 25 Networked Nodes

x

0 0.5 10

0.2

0.4

0.6

0.8

1

Solution on 25 Ranges and 50% Error

x

0 0.5 10

0.2

0.4

0.6

0.8

1

50 Solutions and Mean

x

0.4 0.45 0.5 0.55 0.60.4

0.45

0.5

0.55

0.6

Zoom on Error

x

dx 0.0054

dy 0.0058

1% error

Position iterated on 25 ranges with 50% error

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 9

010

3020

5040

0

20

60

40

6

5

4

3A

vera

ge P

osit

ion

Err

or (

%)

Initial Position Error (%)

Range Error (%)

Network-wide triangulationNetwork-wide triangulation

• Average position error more sensitive to range error than to initial position estimate error

• Convergence problem related to quality of initial positions

Parameters:

• 10 nodes, 3 anchors

• 25 iterations, 30 trials

• Given initial estimates, nodes reposition themselves with respect to their neighbors

• Iterate until desired accuracy achieved

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 10

• Assumption Based Coordinates (ABC)

• n0 assumed to be at (0,0,0)

• n1 assumed to be at (r01,0,0)

r01 = RSSI range between n0 and n1

• n2 at (

Assumptions:

• n3 at (

Assumption:

r012 + r03

2 - r132

2r01

, r032-x3

2-y32 )

r032 – r23

2 + x22 + y2

2 - 2x2x3

2r01

,

r012 + r02

2 - r122

2r01

, r022-x2

2 , 0)x

y

z

n0 n1

n2

n3• positive square root

• z2 = 0

• positive square root

Establishing Initial Position EstimatesEstablishing Initial Position Estimates

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 11

• Triangulation via Extended Range and Redundant Association of Intermediate Nodes

• ABC algorithm creates maps

• Target node waits to beincluded in 3 maps

• Extended rangescalculated fromrespective maps

• Triangulation bytarget node basedon extended ranges

• Iterate network-widetriangulation

TheThe TERRAINTERRAIN AlgorithmAlgorithm

1

2

3

radio range

extended range

intermediate node

C. Savarese, J. Beutel, J. Rabaey; UC Berkeley ICASSP 2001 12

• Position estimates accurate to within 6%

• Working to understand convergence/divergence cases

• Characterizing convergence time and energy cost

• Exploring means of lowering energy consumption

• Minimize expensive start up cost

• Optimize core triangulation algorithm

• Adapting algorithms to include confidence metrics

• Scaling simulations to include much larger node populations

Conclusions and Future WorkConclusions and Future Work