Discussion for SAMSI Tracking session, 8 th September 2008

1. Discussion for SAMSI Tracking session,8th September 2008 Simon Godsill Signal Processing and Communications Lab. University of Cambridge www-sigproc.eng.cam.ac.uk/~sjg TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA

2. Tracking - Grand Challenges High dimensionality - Many simultaneous objects: • Unpredictable manoeuvres • Unknown intentionality/grouping • Following terrain constraints • High clutter levels, spatially varying clutter, low detection probabilities Networks of sensors • Multiple modalities, different platforms, non-coregistered, moving • Differing computational resources at local/central nodes, different degrees of algorithmic control • Variable communication bandwidths /constraints – data intermittent, unreliable. Source: SFO Flight Tracks http://live.airportnetwork.com/sfo/

3. Particle filter solutions • Problems with dimensionality - currently handle with approximations • spatial independence: multiple filters • low-dimensional subspaces for filter (Vaswani) • Approximations to point process intensity functions in RFS formulations (Vo) – not easy to generalise models, however

4. Challenge – structured, high-dimensional state-spaces • e.g. group object tracking: • Need to model interactions between members of same group. • Need to determine group membership (dynamic cluster modelling) • The state-space is high-dimensional and hierarchically structured

5. Possible algorithms • MCMC is good at handling such structured high-dimensional state-spaces: IS is not. • See Septier et al. poster this evening

6. Overview • The Group Tracking Problem • Monte Carlo Filtering for high-dimensional problems • Stochastic models for groups • Inference algorithm • Results • Future directions

7. Group Tracking • For many surveillance applications, targets of interest tend to travel in a group- groups of aircraft in a tight formation, a convoy of vehicles moving along a road, groups of football fans, … • This group information can be used to improve detection and tracking. Can also help to learn higher level behavioural aspects and intentionality. • Some tracking algorithms do exist for group tracking. However implementation problems resulting from the splitting and merging of groups have hindered progress in this area [see e.g. Blackman and Popoli 99]. • This work develops a group models and algorithms for joint inference of targets’ states as well as their group structures– both may be dynamic over time (splitting/merging, breakaway…)

8. Standard multi-target problem:

9. Dynamic group-based problem:

10. State dynamics Group dynamics Likelihood Initial state prior

11. Group variable G

12. Inference objective

13. Hidden state (position/velocity…) Measurements (range, bearing, …) Bayesian Object Tracking • Optimally track target(s) based on: • Dynamic models of behaviour: • Sensor (observation) models:

14. Optimal Filtering: State Space Model:

15. Gordon, Salmond and Smith (1993), Kitagawa (1996), Isard and Blake (1996), …) Monte Carlo Filters Probabilistic updating of states: t=0

19. Approx with sequential update of Monte Carlo particle `clouds’:

20. Stochastic models for groups • Require dynamical models that adequately capture the correlated behaviour of group objects • We base this on simple behavioural properties of individuals relative to other members of their group (attractive/repulsive forces) • Some similarities to flocking models in animal behaviour analysis

26. TexPoint Display

28. Also include a repulsion mechanism for close targets which discourages collisions.

31. State variables

32. Bayesian Inference

33. Bayesian filtering recursions

34. State Transition Probabilities

35. Inference Algorithm • We require a powerful scheme that is sequential and able to sample a high-dimensional, structured state-space • We adopt a sequential MCMC scheme that samples from the joint states at t and t-1, based on the empirical filtering distribution at time t-1

36. Empirical distribution from t-1