IIT Bombay IIT Bombay 1919thth Dec 2008 Dec 2008

Tracking Dynamic Boundary Fronts

using Range Sensors

Subhasri Duttagupta (Ph. D student), Subhasri Duttagupta (Ph. D student), Prof. Krithi RamamrithamProf. Krithi Ramamritham

Dept of Computer Sc. & Engg, Indian Institute of Technology,

Bombay, India

IIT Bombay IIT Bombay 1919thth Dec 2008 Dec 2008

Early Warning System For Early Warning System For Landslide Prediction using Sensor Landslide Prediction using Sensor

NetworksNetworks

Traffic Management on Traffic Management on Highways Highways

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Tracking Boundary FrontsTracking Boundary Fronts• Compute confidence band with Compute confidence band with

high accuracy.high accuracy. δ δ Width of the band Width of the band

• Estimate band with minimum Estimate band with minimum communication overheadscommunication overheads

n, δ BoundaryFront

Tracking

When is the tornado going to hit the city? [Manfredi et al. 2005]

n = number of observations

k, loss of coverage

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Combining Spatial and Temporal Combining Spatial and Temporal Estimation at Estimation at a locationa location

Feedback improves the accuracy Feedback improves the accuracy of of TemporalTemporal Estimation Estimation

yesSpatial

Estimation

no

Multiple Observations

Temporal Estimation

Feedback from Spatial

change > threshold

ObservationSpatial Estimation

How to estimate

Temporal Estimation When to update

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Placement of Estimation PointsPlacement of Estimation Points

• GoalGoal: Minimize : Minimize LOCLOC of interpolated band of interpolated band • Start with a small set of equidistant points and perform spatial Start with a small set of equidistant points and perform spatial

estimation at these pointsestimation at these points• Add more estimation points in the region of Add more estimation points in the region of high variancehigh variance (variance (variance

implies spatial variation)implies spatial variation)

regions with high variance

)2|)(ˆ(|1)( 1 iin yxdIn

xxPE

Prediction Error FunctionPrediction Error Function can represent can represent LOC without the knowledge of actual boundary

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Comparison of DBTR, SE, TEComparison of DBTR, SE, TE• DBTR performs DBTR performs

better by better by 2-4 2-4 %%• DBTR utilizes DBTR utilizes

benefits of both benefits of both the techniquesthe techniques

• Difference in Difference in accuracy does not accuracy does not change with change with δ.δ.

• Spatial Estimation provides more accuracy for lower Spatial Estimation provides more accuracy for lower δδ• Temporal Estimation has better accuracy for larger Temporal Estimation has better accuracy for larger δδ

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ConclusionsConclusions Tracking dynamic boundary fronts using Tracking dynamic boundary fronts using

range sensorsrange sensors• DBTR tracks both spatial and temporal variations with low DBTR tracks both spatial and temporal variations with low

communication overheadscommunication overheads• Spatial estimationSpatial estimation technique uses technique uses kernel smoothing kernel smoothing to reduce to reduce

the effect of noisethe effect of noise• Temporal estimationTemporal estimation technique uses technique uses Kalman filterKalman filter model- model-

based approach updates estimate before the boundary moves based approach updates estimate before the boundary moves out of confidence bandout of confidence band

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Sensing nodes Cluster heads

TE(xp1 )

actual boundary

xp1

TE(xp2 )

xp2

h neighborhood

Location of Spatial Estimation (SE) Location of Spatial Estimation (SE) and Temporal Estimation (TE)and Temporal Estimation (TE)

SE(xp1, xp2 )

SE(xp1 )