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(m 3 )

7. Non-ideal sensing OccamTrack’s performance is poor. 0 - target is s.w. outside R i 1 - target is s.w inside R 0

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