1. Architectures and Applications for Wireless Sensor Networks (01204525) Localization
Chaiporn Jaikaeo
Department of Computer Engineering Kasetsart University
Materials taken from lecture slides by Karl and Willig

2. Overview
Basic approaches
Trilateration
Multihop schemes

3. Localization & positioning
Determine physical position or logical location
Coordinate system or symbolic reference
Absolute or relative coordinates
Metrics
Accuracy
Precision
Costs, energy consumption, …

4. Main Approaches Based on information source Proximity
(Tri-/Multi-)lateration and angulation
Scene analysis
Radio environment has characteristic “signatures”

5. Estimating Distances – RSSI
Compute distance from Received Signal Strength Indicator
Problem: Highly error-prone process
PDF
PDF
Distance
Signal strength
Distance

6. Estimating Distances – Others
Time of arrival (ToA)
Use time of transmission, propagation speed, time of arrival to compute distance
Time Difference of Arrival (TDoA)
Use two different signals with different propagation speeds
Example: ultrasound and radio signal

7. Determining Angles Directional antennas Multiple antennas
Measure time difference between receptions

8. Range-Free Techniques
Overlapping connectivity
Approximate point in triangle

9. Overview
Basic approaches
Trilateration
Multihop schemes

10. Trilateration
Assuming distances to three points with known location are exactly given
Solve system of equations
(x1,y1)
(x2,y2)
(x3,y3)
(xu,yu) r1 r2 r3

11. Trilateration as Matrix Equation
Rewriting as a matrix equation:
Example: (x1, y1) = (2,1), (x2, y2) = (5,4), (x3, y3) = (8,2), r1 = , r2 = 2, r3 = 3

12. Trilateration with Distance Errors
What if only distance estimation ri' = ri + i available?
Use multiple anchors
Overdetermined system of equations
Use (xu, yu) that minimize mean square error, i.e,

13. Minimize Mean Square Error
Look at derivative with respect to x, set it equal to 0:
 Normal equation
Has unique solution (if A has full rank), which gives desired minimal mean square error

14. Example: Distance Error
Anchors' positions and measured distances:
0.5
(x,y) r
(2,1) 5
(5,4) 1
(8,2) 4
(3,1) 2
(7,5) 3
(2,8) 7
(4,6)
Solve

15. Overview
Basic approaches
Trilateration
Multihop schemes

16. Multihop Range Estimation
No direct radio communication exists
Idea 1: Count number of hops, assume length of one hop is known (DV-Hop)
Idea 2: If range estimates between neighbors exist, use them
Improve total length of route estimation in previous method (DV-Distance)

17. Iterative Multilateration

18. Probabilistic Position Description
Position of nodes is only probabilistically known
Represent this probability explicitly
Use it to compute probabilities for further nodes

19. Conclusions
Determining location or position is a vitally 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)
Multilateration problematic (convergence, accuracy)