MultilaterationMethods for clustering intersection points for wireless

sensor networks localization with distance estimation errorMarios Karagiannis

13/10/2010

Distance estimationMany localization techniques (ranged based)

require distance estimationMany estimation techniques have been

proposedRF and Ultrasound ToARSSI strengthEtc.

These techniques have something in commonErrors in estimation

Error modelsLinear error model

Error modelsConstant error model

Error modelsRandom error model

Error modelsLogarithmic error model

Which ones is closer to reality?We’ve run an experiment

We used RSSI strength52 positions6 anchors

Built a map of RSSI strengths for each anchor

Extracted a couple of “slices” from the mapCompared with error models

Experiment

Experiment results (sample)

Experiment results (slice)

Experiment results (slice)

Error existsBut how do we reduce it with not extra

information available?We use geometry!Step 1: We draw circles

Center is the nearby anchorRadius is the (erroneous) calculated distance

ExamplesNo error in distance calculations

ExamplesError in distance calculations

And then what?Step 2: We calculate the intersection points

of all the circlesStep 3: We find the barycenter of a subgroup

of these intersection points.How? Using any of the following filtering

techniques

Technique 1We examine each pair of circles.If they intersect:

For each intersection point(IP1 and IP2) we assign 0 Favor Points

For Each Circle (C’) different than the two circles in the pair If d(IP1,Center Of C’)>d(IP2,Center Of C’)

Points(IP1)++; Else Points(IP2)++;

If Points(IP1)>0 and Points(IP2)==0) IP1 is included in the cluster

If Points(IP2)>0 and Points(IP1)==0) IP2 is included in the cluster

If (Points(IP1)>0 and Points(IP2)>0) Nothing is included in the cluster

Technique 1 Example

Technique 2We examine all intersection pointsIf an intersection point is in all each circle C

(d(IP,center(C))<R(C) where R(C) is the radius of circle C) then the point is included in the cluster

Technique 2 Example

Technique 3Same as technique 1 but with stricter

conditionsThe Favor Points of any Intersection Point

must be equal to the total number of circles – 2 (because we subtract the two circles that are producing the intersection points)

Technique 3 Example

ResultsWe simulated using 4 networksAnd 200 iterations for each method on each

networkSize Nodes Radius Mean

Conn.

1m x 1m 100 0.04 4.582

1m x 1m 100 0.05 7.199

1m x 1m 100 0.06 10.394

1m x 1m 100 0.07 13.96

ResultsNetwork 1

ResultsNetwork 2

ResultsNetwork 3

ResultsNetwork 4

Thank youQuestions?