1. IPSN 2012 Yu Wang, Rui Tan, Guoliang Xing, Jianxun Wang, and Xiaobo Tan NSLab study group 2012/07/02 Reporter: Yuting 1

2.  Introduction  System Model  Movement Scheduling  Evaluation  Conclusion 2

3.  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 3

4.  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 4

5.  Introduction  System Model  Movement Scheduling  Evaluation  Conclusion 5

6.  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 6

7.  Assume some initial condition ◦ A total of A cm 3 of substance is discharged at location (x s,y s ) and t=0  t>0: (x 0,y 0 ) = (x s +u x t, y s +u y t) ◦ Distance from any location (x, y) to the source: d = d(x, y) = ◦ Concentration at (x, y): c(d,t)   Di ff usion profile Θ = {x 0, y 0,α, β} (β->t, α->A) 7

8.  Can't use Bayesian (need prior probability)  Assume constant-speed advection, then reading of sensor i : z i = c(d i, t)+b i +n i ◦ b i : bias ◦ n i : noise ~ N(0, ς 2 ), assume {n i } are independent ◦ Takes K samples in a short time and average them, then z i ~ N( c(d i, t)+b i, σ 2 ), where σ 2 = ς 2 /K  =>  Log-likelihood: 8

9.  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(Θ k )  (x i,y i ): coordinates of sensor i 9 L X 1, L Y 1 are 1×N vectors L X 2, L Y 2 are N×1 vectors

10.  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 x 0 and y 0 ( Can also use CRB(α), CRB(β) )  ω is function of (x 0,y 0 ), (x i,y i ), for all i => use estimated (x 0,y 0 ) instead  If sensors are randomly distributed around the diffusion source => ε=0 => 10

11.  Introduction  System Model  Movement Scheduling  Evaluation  Conclusion 11

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13.  φ i = ∠(∇ i ω)  ||∇ i ω||: steepness of the metric ω  Proportionally allocate the movement steps according to sensor’s gradient magnitude:  Complexity: O(N) 13

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15.  SNR-based ◦ Move toward the estimated source location to increase SNR ◦ Complexity: should be O(N)  Simulated Annealing ◦ Given movement orientations {φ i |∀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 15

16.  Introduction  System Model  Movement Scheduling  Evaluation  Conclusion 16

17.  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 17

18.  Fig4: Simple clustering method Nodes randomly assigns itself a cluster ID Average of results from all clusters 18

19. 19 12cm from the water surface

20.  Greedy algorithm does not account for the interdependence of sensors in providing the overall profiling accuracy 20

21.  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 annealing in terms of both time complexity and optimality 21

22.  The variances decrease with increasing A  Both the greedy and radial algorithms can achieve a high accuracy 22

23.  (Fig12) δ: source location bias ◦ Diffusion source appears at (δ, 0) ◦ Sensors are not randomly deployed around source 23

24.  (Fig 14) Fix each di and randomly deploy sensors in different quadrant of plane  Deployment with max ω is still an open issue 24

25.  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 25

26.  Introduction  System Model  Movement Scheduling  Evaluation  Conclusion 26

27.  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 27