Network Kernel Architectures

and Implementation(01204423)

Localization

Chaiporn Jaikaeochaiporn.j@ku.ac.th

Department of Computer EngineeringKasetsart University

Materials taken from lecture slides by Karl and Willig

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Overview Basic approaches Trilateration Multihop schemes

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Localization & positioning Determine physical position or

logical location Coordinate system or symbolic

reference Absolute or relative coordinates

Metrics Accuracy Precision Costs, energy consumption, …

http://www.mathsisfun.com/accuracy-precision.html

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Main Approaches Based on

information source Proximity (Tri-/

Multi-)lateration and angulation

Scene analysis Radio environment

has characteristic “signatures”

Length known

Angle 1

Angle 2

(x = 2, y = 1)

(x = 8, y = 2)

(x = 5, y = 4)

r1

r2

r3

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Estimating Distances – RSSI Compute distance from Received

Signal Strength Indicator

Problem: Highly error-prone process

Distance

PD

F

DistanceSignal strength

PD

F

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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

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Determining Angles Directional antennas

Multiple antennas Measure time difference between

receptions

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Range-Free Techniques Overlapping connectivity

Approximate point in triangle

?

?A

B

C

D

F

G

E

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Overview Basic approaches Trilateration Multihop schemes

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Trilateration Assuming distances to

three points with known location are exactly given

Solve system of equations(x1,y1)

(x2,y2)

(x3,y3)

(xu,yu)

r1r2

r3

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Trilateration as Matrix Equation Rewriting as a matrix equation:

Example: (x1, y1) = (2,1), (x2, y2) = (5,4), (x3, y3) = (8,2), r1 = 100.5 , r2 = 2, r3 = 3

3

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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,

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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

Example: Distance Error Anchors' positions and measured

distances:

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(x,y) r

(2,1) 5

(5,4) 1

(8,2) 4

(3,1) 2

(7,5) 3

(2,8) 7

(4,6) 4

7.2

5.5x̂

Solve bAxAA TT ˆ

0.5

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Overview Basic approaches Trilateration Multihop schemes

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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)

X

B

A

C

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Iterative Multilateration

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Probabilistic Position Description Position of nodes is only probabilistically

known Represent this probability explicitly Use it to compute probabilities for further

nodes

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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)