marios karagiannis 13/10/2010. distance estimation many localization techniques (ranged based)...
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MultilaterationMethods for clustering intersection points for wireless
sensor networks localization with distance estimation errorMarios Karagiannis
13/10/2010
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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
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Error modelsLinear error model
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Error modelsConstant error model
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Error modelsRandom error model
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Error modelsLogarithmic error model
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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
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Experiment
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Experiment results (sample)
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Experiment results (slice)
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Experiment results (slice)
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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
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ExamplesNo error in distance calculations
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ExamplesError in distance calculations
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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
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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
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Technique 1 Example
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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
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Technique 2 Example
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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)
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Technique 3 Example
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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
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ResultsNetwork 1
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ResultsNetwork 2
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ResultsNetwork 3
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ResultsNetwork 4
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Thank youQuestions?