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IIT Bombay 3 19 th Dec 2008 Tracking Boundary Fronts Compute confidence band with high accuracy. Compute confidence band with high accuracy. δ Width of the band Estimate band with minimum communication overheads Estimate band with minimum communication overheads n, δ Boundary Front 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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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
IIT Bombay IIT Bombay 33 1919thth Dec 2008 Dec 2008
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
IIT Bombay IIT Bombay 44 1919thth Dec 2008 Dec 2008
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
IIT Bombay IIT Bombay 55 1919thth Dec 2008 Dec 2008
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
IIT Bombay IIT Bombay 66 1919thth Dec 2008 Dec 2008
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
IIT Bombay IIT Bombay 77 1919thth Dec 2008 Dec 2008
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
IIT Bombay IIT Bombay 99 1919thth Dec 2008 Dec 2008
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 )