Target Tracking with Binary Proximity Sensors

1. Target Tracking with Binary Proximity Sensors N. Shrivastava, R. Mudumbai, U. Madhow, S. Suri Presented By Shan Gao

2. Contents • Introduction • Spatial Resolution • Velocity Estimation • OccamTrack • Particle filter approach • Geometric post-processing • Simulation & Experiments

3. Introduction • Binary proximity sensors • Only know the existence of target(s) • No information about the number of targets, velocity, distance etc. • Signature: 000,100,110,010,011,001,000

4. Spatial resolution • Theorem 1 • If a network of binary proximity sensors has average sensor density ρ and each sensor has sensing radius R, then, the worst-case L∞ error in localizing the target is at least Ω(1/ρR). • Theorem 2 • Consider a network of binary proximity sensors, distributed according to the Poisson distribution of density ρ, where each sensor has sensing radius R, then the localization error at any point in the plane is of order 1/ρR. • P[X>x] ≈ e-2ρRx

5. Velocity Estimation A trajectory exhibiting high frequency variations cannot be captured by binary sensors.

6. OccamTrack • Assume ideal binary sensing. • O(m3)

7. Non-ideal sensing • OccamTrack’s performance is poor. • 0 - target is s.w. outside Ri • 1 - target is s.w inside R0

8. Particle Filtering • At any time n, we have K particles (or candidates), with the current location for the kth particle denoted by xk[n]. • At the next time instant n+1, choose m candidates for xk[n+1] uniformly at random from the patch F. K mK • Pick K candidates with the best cost functions to get the set xk[n+1]. • The final output is simply the particle (trajectory) with the best cost function.

9. Cost Function • Penalty on changes in the vector velocity • To keep with lowpass trajectory. • Geometric Postprocessing • Particle filtering provides no guarantees of a clean or minimal description. • Merge points within distance Δ

10. Simulation – Non-Ideal Sensing

11. Experiment

12. Thanks Q&A