Plume Tracking in Sensor Networks. Glenn Nofsinger PhD Thesis Defense August 22, 2006. Outline. Motivation and Problem Statement Other Work Theoretical Background 2-Step Algorithm Experiments Results and Conclusions. Motivation.
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Plume Tracking in Sensor Networks
PhD Thesis Defense
August 22, 2006
Mobile scout robots
Static sensor networks
with high density
cheap fixed sensors
with high resolution sensors,
low sensor density
Theoretical Background (1)
Theoretical Background (2)
Theoretical Background (6)
Theoretical Background (7)
Radii of location for rising and falling edges of agent detection – one for each edge is possible in binary sensor
Analytical approach no longer useful, need statistical methods.
Leads to Bayesian formulation
Typical Sensor Response Curve
Theoretical Background (9)
Relationship between a posteriori distribution, a priori distribution, and the likelihood function
Theoretical Background (10)
MMSE –minimum-mean-squared error. It is the mean posterior density. Equal weight to obs.
MAP- maximum a posteriori, maximizes the posterior distribution
ML- maximum likelihood, considers information in measurement only
Theoretical Background (11)
Theoretical Background (12)
Theoretical Background (13)
Theoretical Background (14)
Sensor “Hits” (x,y,t)
Output: N Tracks
For each track
1.1 Track Initialization –All new observations potentially create tracks. The terminal node on track is designated leader node
Detail of likelihood function for track association
2-Step Algorithm (10)
Track Assisted State Estimation
Gradual update of estimated source position, as sensor data is aggregated along the path ABCD.
2-Step Algorithm (11)
Final estimated likelihood map after integration of ABCD, and renormalization for easier viewing.
Final update of estimated source position, as sensor data is aggregated along the path ABCD.
Initialize, setup scenarios
And control batch runs
Main loop –
Fick’s law for diffusion implemented numerically using standard 2D centered difference scheme
Concentration of Agent assumed=0 at boundaries, agent “floats off screen”
Same code used for forward diffusion and backward belief state propagation
Data Imported from web
YYYY MM DD hh mm DIR SPD GDR GSP GTIME 2004 12 31 23 00 116 7.5 999 99.0 9999
2004 12 31 23 10 115 6.7 999 99.0 9999
2004 12 31 23 20 134 7.2 999 99.0 9999
2004 12 31 23 30 136 8.2 999 99.0 9999
Likelihood performance metrics
Results and Conclusions (2)
Results and Conclusions
Mean wind Speed scaled into 4 groups
Standard deviation of direction divided into 4 groups
This produced 16 total wind categories
Mean wind speed
Zone: low wind
Wind direction Std. deviation
Results and Conclusions (3)
Results and Conclusions (4)
Results and Conclusions (5)
Results and Conclusions (6)
Results and Conclusions (7)
To what extent can
we differentiate two sources
as a function of sensor
In this example, two sources in constant wind can superimpose to create a 3rd peak
The goal of this sensor network is to correctly identify exactly 2 sources, not 3
We want to construct a belief map after each trial, and look at
the value of the cell where the actual source was released.
Once we introduce tracking, we get sharper regions with higher
Values per cell. This allows us to compare the predicted map
with ground truth on any selected trial.
Likelihood Map M
The inverse scale here is E-5, which is likelihood that
The source was released from that particular cell.
Typical values for a single cell are between 10E-3 and 10E-5
Known release event : A
Forward Probability, P(B|A)
Inverse Probability, P(A|B)
Known detection event : B