Accuracy-Aware Aquatic Accuracy-Aware Aquatic Diffusion Process Diffusion Process

Profiling Using Robotic Profiling Using Robotic Sensor NetworksSensor Networks

Yu Wang, Rui Tan, Guoliang Xing, Jianxun Wang, Xiaobo Tan

Michigan State University

• Diffusion profiling• source location, concentration, diffusion speed• high accuracy, short delay

• Physical uncertainties– temporal evolution, sensor biases, environmental noises

04/19/2012 IPSN'12, Beijing, China 2

Harmful Diffusion ProcessesHarmful Diffusion Processes

Unocal oil spillSanta Barbara, CA, 1969http://en.wikipedia.org

BP oil spill,Gulf of Mexico, 2010

http://en.wikipedia.org

Chemicals/Waste Water PollutionUK, 2009, Reuters

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Traditional ApproachesTraditional Approaches

• Manual sampling – labor intensive– coarse spatiotemporal

granularity

• Fixed buoyed sensors– expensive, limited coverage, poor adaptability

• Mobile sensing via AUVs and sea gliders– expensive (>$50K), bulky, heavy

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Aquatic Sensing via Robotic Aquatic Sensing via Robotic FishFish

• On-board sensing, control, and wireless comm.

• Low manufacturing cost: ~$200-$500

• Limited power supply and sensing capability

Smart Microsystems Lab, MSU

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Problem StatementProblem Statement

diffusion source

robotic sensors

•Maximize profiling accuracy w/ limited power supply

•Collaborative sensing: source location, concentration, speed•Scheduling sensor movement to increase profiling accuracy

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RoadmapRoadmap

• Motivation

• Background

• Profiling and Accuracy Modeling

• Movement Scheduling

• Trace Collection & Evaluation

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Diffusion Process ModelDiffusion Process Model

• Concentration at position (x,y,z) and time instance t

• Diffusion and water speed• Diffusion profile (source loc, α, β)

)exp(),( 2dtdc

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Sensor Measurement ModelSensor Measurement Model

• Sensor measurement• Actual concentration

– distance to diffusion source– elapsed time

• Sensor bias• Random noise,

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Collaborative Diffusion Collaborative Diffusion Profiling Profiling

• Each sensor samples periodically• Samples from different sensors are fused

via Maximum Likelihood Estimation (MLE)

• How to model the accuracy of profiling? • How does the accuracy metric guide the

movement of sensors?

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Cramér-Rao Bound (CRB)Cramér-Rao Bound (CRB)

• Lower bound of estimate variance• Highly non-linear expression

e.g.

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row vectors of all sensor coordinates

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A New Accuracy MetricA New Accuracy Metric

• Sum of contributions of individual sensors

fixed in each profiling iteration node i's contribution tooverall profiling accuracy

),,( minddf ii distance b/w source

and sensor i min distance

to source

diffusion parameter

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Sensor Movement SchedulingSensor Movement Scheduling

Objective: find movement schedule for each sensor, s.t. profiling accuracy ω is maximized

Constraint:

• Movement Schedule: {orientation, # of steps}

MmN

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number of steps for sensor i

• Assign orientation– Find di

* that maximizes – If di > di

*, toward estimated source, otherwise

away from

• Allocate moving steps

– Maximize Σω(Δi), Δi – # of steps of sensor i

– Decomposition → dynamic programming

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Radial Scheduling AlgorithmRadial Scheduling Algorithm

di*

),,( minddf ii

diffusion source

robotic sensors

Putting All TogetherPutting All Together

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2

3

• Collaborative profiling• Sampling• TX samples to node 2• Profiling via MLE estimation Estimated source location

• Movement scheduling• Orientation determination • DP-based step allocation

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Evaluation MethodologyEvaluation Methodology

• Trace collection– Rhodamine-B diffusion model– On-water Zigbee communication– GPS localization, robotic fish movement

• Trace-driven simulation– Profiling accuracy, scalability etc.

• Implementation on TelosB motes– Computation complexity

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Rhodamine-B DiffusionRhodamine-B Diffusion

discharge Rhodamine-B in saline water periodically capture diffusion with a camera expansion of contour → diffusion evolution

grayscale

model verification

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On-water ZigBee On-water ZigBee CommunicationCommunication

• PRR measurement using ZigBee radios on Lake Lansing

• 50% drop of comm. range compared to on land

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GPS and Movement ErrorsGPS and Movement Errors

• GPS localization errors– groundtruth vs. GPS measurement– average error is 2.29 m

• Robotic fish movement– 3m×1m water tank– tail beating frequency: 0.9 Hz,

amplitude: 23o

expected speed: 2.5 m/min

Linx GPS module

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Trace-driven SimulationsTrace-driven Simulations

• Profiling accuracy vs. elapsed time

profiling accuracy improves as time elapses

< SNR-based scheduling >orientation: gradient-ascent of

SNR# of steps: proportion to SNR

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Time ComplexityTime Complexity

• Implemented MLE estimation and scheduling algorithm on TeobsB motes

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ConclusionsConclusions

• Collaborative diffusion profiling using robotic fish– New accuracy profiling metric– Movement scheduling algorithm

• Evaluation in trace-driven simulation & real implementation

– High accuracy & low overhead

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Trace-driven SimulationsTrace-driven Simulations

• Profiling accuracy vs. number of sensors

profiling accuracy improves as more sensors are deployed