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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

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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/

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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

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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

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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

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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

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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…)

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Standard multi-target problem:

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Dynamic group-based problem:

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Initial state prior State dynamics Group dynamics Likelihood

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Group variable G

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Inference objective

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

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State Space Model: Optimal Filtering:

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

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Approx with sequential update of Monte Carlo particle `clouds:

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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

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TexPoint Display

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

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State variables

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Bayesian Inference

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Bayesian filtering recursions

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State Transition Probabilities

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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

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Empirical distribution from t-1

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Conclusions and Future Directions

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

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