SAMSI Discussion Session Random Sets/ Point Processes in Multi-Object Tracking: Vo Dr Daniel Clark EECE Department Heriot-Watt University UK

observation produced by targets target motion state space observation space 5 targets 3 targets X k-1 XkXk Number of states and their values are (random) variables Need to estimate the number of target states and their state vectors online Multi-object filtering with point processes Multi-object filtering with point processes

state space vk vk v k-1 PHD filter v k-1 (x k-1 |Z 1:k-1 )v k (x k |Z 1:k ) v k|k-1 (x k |Z 1:k-1 ) PHD prediction PHD update Multi-object Bayes filter p k-1 (X k-1 |Z 1:k-1 ) p k (X k |Z 1:k ) p k|k-1 (X k |Z 1:k-1 ) prediction update PHD filters PHD filters

PHD: assumes that the prior intensity is Poisson MeMBer: assumes multi-Bernoulli i.e. each target is assumed to be Bernoulli with probability of target existence PHD/CPHD filters propagate an intensity function of a point process Approximation Strategies Approximation Strategies

How do we estimate single/ multiple target states from a multi-modal particle density? - Clustering algorithms such as k-means and EM can be unreliable Problems: Problems:

Complexity: -How does the complexity/ reliability of the approach scale with the number of targets? -Poisson PP: mean=var Problems: Problems:

SMC implementations for filtering propagate intensity functions not probability densities -Usual convergence properties of SMC algorithms of probability distributions needs modifying. -Non Feynman-Kac model. Problems: Problems:

How do we obtain tracks/ trajectories of individual targets? - Possible solutions – include track id in the state / find greatest intersection of particles Problems: Problems: