Discussion for SAMSI Tracking session,Discussion for SAMSI Tracking session,8 8thth September 2008 September 2008Simon GodsillSimon GodsillSignal Processing and Communications Lab.Signal Processing and Communications Lab.University of CambridgeUniversity of Cambridgewww-sigproc.eng.cam.ac.uk/sjgwww-sigproc.eng.cam.ac.uk/sjgTexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA Tracking - Grand ChallengesHigh dimensionality - Many simultaneous objects:High dimensionality - Many simultaneous objects: n nUnpredictable manoeuvresUnpredictable manoeuvresn nUnknown intentionality/groupingUnknown intentionality/groupingn nFollowing terrain constraintsFollowing terrain constraintsn nHigh clutter levels, spatially varying clutter, low High clutter levels, spatially varying clutter, low detection probabilitiesdetection probabilitiesNetworks of sensorsNetworks of sensorsn nMultiple modalities, different platforms, non-Multiple modalities, different platforms, non-coregistered, movingcoregistered, movingn nDiffering computational resources at Differing computational resources at local/central nodes, different degrees of local/central nodes, different degrees of algorithmic controlalgorithmic controln nVariable communication bandwidths Variable communication bandwidths /constraints data intermittent, unreliable/constraints data intermittent, unreliable. . Source: SFO Flight Tracks :/live.airportnetwork/sfo/ Particle filter solutionsn nProblems with dimensionality - currently handle with approximations spatial independence: multiple filters spatial independence: multiple filters low-dimensional subspaces for filter low-dimensional subspaces for filter (Vaswani)(Vaswani)Approximations to point process intensity Approximations to point process intensity functions in RFS formulations (Vo) not functions in RFS formulations (Vo) not easy to generalise models, howevereasy to generalise models, howeverChallenge structured, high-dimensional state-spacesn ne.g. group object tracking:Need to model interactions between Need to model interactions between members of same group. members of same group. Need to determine group membership Need to determine group membership (dynamic cluster modelling) (dynamic cluster modelling) n n The state-space is high-dimensional and hierarchically structuredPossible algorithmsn nMCMC is good at handling such structured high-dimensional state-spaces: IS is not.n nSee Septier et al. poster this eveningOverviewn nThe Group Tracking ProblemThe Group Tracking Problemn nMonte Carlo Filtering for high-dimensional problemsMonte Carlo Filtering for high-dimensional problemsn nStochastic models for groupsStochastic models for groupsn nInference algorithmInference algorithmn nResultsResultsn nFuture directionsFuture directionsGroup Trackingn nFor many surveillance applications, targets of interest tend to travel in For many surveillance applications, targets of interest tend to travel in a group - groups of aircraft in a tight formation, a convoy of vehicles a group - groups of aircraft in a tight formation, a convoy of vehicles moving along a road, groups of football fans, moving along a road, groups of football fans, n nThis group information can be used to improve detection and tracking. This group information can be used to improve detection and tracking. Can also help to learn higher level behavioural aspects and Can also help to learn higher level behavioural aspects and intentionality.intentionality.n nSome tracking algorithms do exist for group tracking. However Some tracking algorithms do exist for group tracking. However implementation problems resulting from the splitting and merging of implementation problems resulting from the splitting and merging of groups have hindered progress in this area see e.g. Blackman and groups have hindered progress in this area see e.g. Blackman and Popoli 99.Popoli 99.n nThis work develops a group models and algorithms for joint inference This work develops a group models and algorithms for joint inference of targets states as well as their group structures both may be of targets states as well as their group structures both may be dynamic over time (splitting/merging, breakaway)dynamic over time (splitting/merging, breakaway)Standard multi-target problem:Dynamic group-based problem:Initial state priorState dynamicsGroup dynamicsLikelihoodGroup variable GInference objectiveBayesian Object Trackingn nOptimally track target(s) based on:Optimally track target(s) based on: Dynamic models of behaviour:Dynamic models of behaviour: Sensor (observation) models:Sensor (observation) models:Hidden state (position/velocity)Measurements (range, bearing, )State Space Model:Optimal Filtering:Monte Carlo FiltersGordon, Salmond and Smith (1993), Kitagawa (1996), Isard and Blake (1996), )Probabilistic updating of states:t=0Approx with sequential update of Monte Carlo particle clouds: Stochastic models for groupsn nRequire dynamical models that ad