1. Discussion for SAMSI Tracking session, 8 th 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 Tracking - Grand Challenges High dimensionality - Many simultaneous objects: n Unpredictable manoeuvres n Unknown intentionality/grouping n Following terrain constraints n High clutter levels, spatially varying clutter, low detection probabilities Networks of sensors n Multiple modalities, different platforms, non- coregistered, moving n Differing computational resources at local/central nodes, different degrees of algorithmic control n Variable communication bandwidths /constraints – data intermittent, unreliable. Source: SFO Flight Tracks http://live.airportnetwork.com/sfo/

3. Particle filter solutions n 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 n e.g. group object tracking: –Need to model interactions between members of same group. –Need to determine group membership (dynamic cluster modelling) n The state-space is high-dimensional and hierarchically structured

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

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

7. Group Tracking n 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, … n This group information can be used to improve detection and tracking. Can also help to learn higher level behavioural aspects and intentionality. n 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]. n 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. Initial state prior State dynamics Group dynamics Likelihood

11. Group variable G

12. Inference objective

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

14. State Space Model: Optimal Filtering:

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

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

20. Stochastic models for groups n Require dynamical models that adequately capture the correlated behaviour of group objects n We base this on simple behavioural properties of individuals relative to other members of their group (attractive/repulsive forces) n 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 n We require a powerful scheme that is sequential and able to sample a high- dimensional, structured state-space n 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

52. Conclusions and Future Directions

55. Acknowledgements n Funding support from QinetiQ UK and the UK governments Data and Information Fusion Defence Technology Centre (DIF-DTC)