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Accuracy-Aware Aquatic Diffusion Process Profiling

UsingRobotic Sensor Networks

IPSN 2012Yu Wang, Rui Tan, Guoliang Xing, Jianxun Wang, and Xiaobo Tan

NSLab study group 2012/07/02Reporter: Yuting

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Introduction System Model Movement Scheduling Evaluation Conclusion

Outline

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Goal◦ Detect and monitor aquatic environments◦ Diffusion profile:

Concentration contour maps Elapsed time of diffusion Total amount of discharged substance Location of original source

Movement Scheduling◦ Improve the profiling accuracy◦ Constraints on sensor mobility and energy budget

Introduction (1)

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System Model◦ Diffusion Process◦ MLE-based Diffusion Profiling◦ Profiling Accuracy Metric◦ Two scheduling algorithm

Experiments◦ Validation of the diffusion model◦ Evaluation by real data traces (on telosB)

simulation using MATLAB◦ Impact of several factors on profiling accuracy

Introduction (2)

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Introduction System Model Movement Scheduling Evaluation Conclusion

Outline

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Fickian diffusion-advection model:

◦ t: time elapsed since the discharge of substance◦ c: substance concentration◦ D: diffusion coefficient

Characterize speed of diffusion, depend on (1) species of solvent (2) discharge substance (3) environment factors (ex: temperature)

◦ u: advection speed Usually Dx=Dy, and Dz can be omitted

Diffusion Process Model (1)

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Assume some initial condition◦ A total of A cm3 of substance is discharged at

location (xs,ys) and t=0 t>0: (x0,y0) = (xs+uxt , ys+uyt)

◦ Distance from any location (x, y) to the source:d = d(x, y) =

◦ Concentration at (x , y): c(d,t)

Diffusion profile Θ = {x0, y0 ,α, β} (β->t, α->A)

Diffusion Process Model (2)

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Can't use Bayesian (need prior probability) Assume constant-speed advection, then

reading of sensor i : zi = c(di , t)+bi +ni◦ bi : bias◦ ni : noise ~ N(0, ς2), assume {ni} are independent◦ Takes K samples in a short time and average

them, then zi ~ N( c(di , t)+bi , σ2), where σ2 = ς2 /K

=>

Log-likelihood:

ML Estimation

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A theoretical lower bound on the variance of parameter estimators (Θ here)

Inverse of the Fisher information matrix (FIM) J, J = , is taken over all z

= CRB(Θk) (xi,yi): coordinates of sensor i

Cramér-Rao Bound (CRB)

LX1 , LY1 are 1×N vectorsLX2 , LY2 are N×1 vectors

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Previous works take det(J) as the metric, but it's too problem-dependent

This paper use a novel metric based on CRB

Larger ω indicates more accurate estimation of x0 and y0 ( Can also use CRB(α), CRB(β) )

ω is function of (x0,y0), (xi,yi), for all i=> use estimated (x0,y0) instead

If sensors are randomly distributed around the diffusion source => ε=0=>

Profiling Accuracy ω

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Introduction System Model Movement Scheduling Evaluation Conclusion

Outline

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Assumption◦ Sensors move straight in each profiling iteration◦ Moving distance is always multiple of l meters, where l is

referred to as "step" Profiling iteration has short time duration

◦ Sensor’s straight movement does not cause significant errors Problem statement: s.t.

◦ M: total steps that can be allocated (in one iteration)◦ Li: the largest distance sensor i can move (in one iteration)◦ l: unit of step◦ mi: # of steps (in one iteration)◦ φi: movement orientation (in one iteration)◦ Complexity:

Movement Scheduling

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φi = ∠(∇iω) ||∇iω||: steepness of the metric ω Proportionally allocate the movement steps

according to sensor’s gradient magnitude:

Complexity: O(N)

Greedy Algorithm

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Fx the sensor closest to the estimated source location Only schedule other sensors di* = =

,where Dynamic programming algorithm:

Ω(i, m): maximum ω when the first i sensors are allocated with m steps

Complexity: O((N-1)M2) ~ O(N3)

Radial Algorithm

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SNR-based◦ Move toward the estimated source location to

increase SNR◦ Complexity: should be O(N)

Simulated Annealing◦ Given movement orientations {φi |∀i}, uses

brutal-force search to find the optimal step allocation

◦ Then search for optimal movement orientations by simulated annealing algorithm

◦ Complexity: exponential with respect to N

Two Additional Baseline Algorithms

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Introduction System Model Movement Scheduling Evaluation Conclusion

Outline

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The performance of profiling are affected by these errors (GPS, motor)

Iterative approach avoid error accumulation◦ Sensors update their positions and report to cluster

head (in each iteration)

Average GPS error: 2.29(m) Robotic fish speed: expect 2.5m/min when tail

beats at 23° amplitude and 0.9Hz frequency◦ Error not mentioned in the paper

Localization And Control Errors

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Fig4: Simple clustering methodNodes randomly assigns itself a cluster IDAverage of results from all clusters

Computation Overhead

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Diffusion Model Validation & PRR

12cm from the water surface

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Greedy algorithm does not account for the interdependence of sensors in providing the overall profiling accuracy

Movement Scheduling Result

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10 sensors, 15 profiling iterations Greedy and radial: curves with and without

simulated movement control and localization errors almost overlap => no error accumulation

Radial:better than annealingin terms of bothtime complexityand optimality

Profiling Accuracy Result (1)

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The variances decrease with increasing A Both the greedy and radial algorithms can

achieve a high accuracy

Profiling Accuracy Result (2)

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(Fig12) δ: source location bias◦ Diffusion source appears at (δ, 0)◦ Sensors are not randomly deployed around source

Some Impact On Profiling (1)

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(Fig 14) Fix each di and randomly deploy sensors in different quadrant of plane

Deployment with max ω is still an open issue

Some Impact On Profiling (2)

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Shortest distance path from sensors to cluster head Trace-driven simulations

◦ Nodes transmit packet to the next hop with success p = PRR retrieved from the communication traces

◦ Nodes re-transmit the packet for 10 times before it is dropped until success

◦ Packet to the cluster head includes:sensor ID, current position, measurement

◦ Packet to the sensor includes:moving orientation, distance

# of packet (re-)transmissions in an iteration:mean 158, standard deviation 28(30 sensors are randomly deployed)

Delay will be within seconds at most

Communication Overhead

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Introduction System Model Movement Scheduling Evaluation Conclusion

Outline

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Strength◦ Reduce computation and hardware cost◦ Real hardware implementation of lots of

mathematical model Weakness (also their future work)

◦ Cluster head needed◦ May not work on wavy environments◦ GPS and Zigbee may not work in deep water◦ It seems that the system can't be done in real

time

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