Architectures and Architectures and Applications for Applications for Wireless Sensor Wireless Sensor

Networks (01204525)Networks (01204525)

LocalizationLocalization

Chaiporn JaikaeoChaiporn Jaikaeochaiporn.j@ku.ac.thchaiporn.j@ku.ac.th

Department of Computer EngineeringDepartment of Computer EngineeringKasetsart UniversityKasetsart University

Materials taken from lecture slides by Karl and Willig

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OverviewOverview Basic approachesBasic approaches TrilaterationTrilateration Multihop schemesMultihop schemes

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Localization & Localization & positioningpositioning Determine Determine physical positionphysical position or or

logical locationlogical location Coordinate system or symbolic referenceCoordinate system or symbolic reference Absolute or relative coordinatesAbsolute or relative coordinates

MetricsMetrics AccuracyAccuracy PrecisionPrecision Costs, energy consumption, … Costs, energy consumption, …

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

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Main ApproachesMain Approaches Based on Based on

information sourceinformation source ProximityProximity (Tri-/(Tri-/

Multi-)Multi-)lateration lateration and and angulationangulation

Scene analysis Scene analysis Radio environment Radio environment

has characteristic has characteristic “signatures” “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 – Estimating Distances – RSSI RSSI Compute distance from Compute distance from RReceived eceived

SSignal ignal SStrength trength IIndicatorndicator

Problem: Highly error-prone processProblem: Highly error-prone process

Distance

PD

F

DistanceSignal strength

PD

F

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Estimating Distances – Estimating Distances – OthersOthers Time of arrival (ToA)Time of arrival (ToA)

Use time of transmission, propagation Use time of transmission, propagation speed, time of arrival to compute speed, time of arrival to compute distancedistance

Time Difference of Arrival (TDoA)Time Difference of Arrival (TDoA) Use two different signals with different Use two different signals with different

propagation speedspropagation speeds Example: ultrasound and radio signalExample: ultrasound and radio signal

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Determining AnglesDetermining Angles Directional antennasDirectional antennas

Multiple antennasMultiple antennas Measure time difference between Measure time difference between

receptionsreceptions

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Range-Free TechniquesRange-Free Techniques Overlapping connectivity Overlapping connectivity

Approximate point in triangleApproximate point in triangle

?

?A

B

C

D

F

G

E

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OverviewOverview Basic approachesBasic approaches TrilaterationTrilateration Multihop schemesMultihop schemes

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TrilaterationTrilateration Assuming distances to Assuming distances to

three points with known three points with known location are exactly givenlocation are exactly given

Solve system of equationsSolve system of equations((xx11,,yy11))

((xx22,,yy22))

((xx33,,yy33))

((xxuu,,yyuu))

rr11rr22

rr33

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Trilateration as Matrix Trilateration as Matrix EquationEquation Rewriting as a matrix equation: Rewriting as a matrix equation:

Example: Example: ((xx11, , yy11) = (2,1), () = (2,1), (xx22, , yy22) = (5,4), ) = (5,4), ((xx33, , yy33) = (8,2), ) = (8,2), rr11 = 10 = 100.50.5 , , rr22 = 2, = 2, rr33 = 3 = 3

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Trilateration with Trilateration with Distance ErrorsDistance Errors What if only distance estimation What if only distance estimation rrii'' = = rrii + + ii

available?available? Use multiple anchorsUse multiple anchors

Overdetermined system of equationsOverdetermined system of equations

Use Use ((xxuu, , yyuu)) that minimize mean square that minimize mean square error, i.e, error, i.e,

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Minimize Mean Square Minimize Mean Square ErrorError

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

Normal equationNormal equation Has unique solution (if A has full rank), Has unique solution (if A has full rank),

which gives desired minimal mean which gives desired minimal mean square errorsquare error

Example: Example: Distance Distance ErrorError Anchors' positions and measured Anchors' positions and measured

distances: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

SolveSolve bAxAA TT ˆ

0.5

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OverviewOverview Basic approachesBasic approaches TrilaterationTrilateration Multihop schemesMultihop schemes

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Multihop Range Multihop Range EstimationEstimation No direct radio communication existsNo direct radio communication exists

Idea 1: Count number of hops, Idea 1: Count number of hops, assume length of one hop is known assume length of one hop is known ((DV-HopDV-Hop))

Idea 2: If range estimates between Idea 2: If range estimates between neighbors exist, use themneighbors exist, use them Improve total length of route estimation Improve total length of route estimation

in previous method (in previous method (DV-DistanceDV-Distance))

X

B

A

C

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Iterative Iterative MultilaterationMultilateration

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Probabilistic Position Probabilistic Position DescriptionDescription Position of nodes is only probabilistically Position of nodes is only probabilistically

knownknown Represent this probability explicitlyRepresent this probability explicitly Use it to compute probabilities for further Use it to compute probabilities for further

nodesnodes

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ConclusionsConclusions Determining location or position is a Determining location or position is a

vitally important function in WSN, but vitally important function in WSN, but fraught with many errors and fraught with many errors and shortcomingsshortcomings Range estimates often not sufficiently Range estimates often not sufficiently

accurateaccurate Many anchors are needed for acceptable Many anchors are needed for acceptable

resultsresults Anchors might need external position Anchors might need external position

sources (GPS)sources (GPS) Multilateration problematic Multilateration problematic

(convergence, accuracy)(convergence, accuracy)