Discussion for SAMSI Tracking session, 8 th September 2008 Simon Godsill Signal Processing and Communications Lab. University of Cambridge sjg.

Discussion for SAMSI Tracking Discussion for SAMSI Tracking session,session,

88thth September 2008 September 2008

Simon GodsillSimon Godsill

Signal Processing and Communications Signal Processing and Communications Lab.Lab.

University of CambridgeUniversity of Cambridge

www-sigproc.eng.cam.ac.uk/~sjgwww-sigproc.eng.cam.ac.uk/~sjg

Tracking - Grand Tracking - Grand ChallengesChallenges

High dimensionality - Many simultaneous High dimensionality - Many simultaneous objects:objects:

Unpredictable manoeuvresUnpredictable manoeuvres Unknown intentionality/groupingUnknown intentionality/grouping Following terrain constraintsFollowing terrain constraints High clutter levels, spatially varying clutter, High clutter levels, spatially varying clutter,

low detection probabilitieslow detection probabilities

Networks of sensorsNetworks of sensors

Multiple modalities, different platforms, non-Multiple modalities, different platforms, non-coregistered, movingcoregistered, moving

Differing computational resources at Differing computational resources at local/central nodes, different degrees of local/central nodes, different degrees of algorithmic controlalgorithmic control

Variable communication bandwidths Variable communication bandwidths /constraints – data intermittent, unreliable/constraints – data intermittent, unreliable. .

Source: SFO Flight Tracks http://live.airportnetwork.com/sfo/

Particle filter solutionsParticle filter solutions

Problems with dimensionality - Problems with dimensionality - currently handle with approximations currently handle with approximations – spatial independence: multiple filtersspatial 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, however

Challenge – structured, Challenge – structured, high-dimensional state-high-dimensional state-

spacesspaces

e.g. group object tracking:e.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) The state-space is high-dimensional The state-space is high-dimensional

and hierarchically structuredand hierarchically structured

Possible algorithmsPossible algorithms

MCMC is good at handling such MCMC is good at handling such structured high-dimensional state-structured high-dimensional state-spaces: IS is not.spaces: IS is not.

See Septier et al. poster this eveningSee Septier et al. poster this evening

OverviewOverview

The Group Tracking ProblemThe Group Tracking Problem Monte Carlo Filtering for high-dimensional Monte Carlo Filtering for high-dimensional

problemsproblems Stochastic models for groupsStochastic models for groups Inference algorithmInference algorithm ResultsResults Future directionsFuture directions

Group TrackingGroup Tracking For many surveillance applications, targets of interest tend to For many surveillance applications, targets of interest tend to

travel in a group - groups of aircraft in a tight formation, a travel in a group - groups of aircraft in a tight formation, a convoy of vehicles moving along a road, groups of football fans, convoy of vehicles moving along a road, groups of football fans, ……

This group information can be used to improve detection and This group information can be used to improve detection and tracking. Can also help to learn higher level behavioural aspects tracking. Can also help to learn higher level behavioural aspects and intentionality.and intentionality.

Some tracking algorithms do exist for group tracking. However Some tracking algorithms do exist for group tracking. However implementation problems resulting from the splitting and implementation problems resulting from the splitting and merging of groups have hindered progress in this area [see e.g. merging of groups have hindered progress in this area [see e.g. Blackman and Popoli 99].Blackman and Popoli 99].

This work develops a group models and algorithms for joint This work develops a group models and algorithms for joint inference of targets’ states as well as their group structures – inference of targets’ states as well as their group structures – both may be dynamic over time (splitting/merging, both may be dynamic over time (splitting/merging, breakaway…)breakaway…)

Standard multi-target problem:Standard multi-target problem:

Dynamic group-based Dynamic group-based problem:problem:

Initial state prior

State dynamics

Group dynamics

Likelihood

Group variable GGroup variable G

Inference objectiveInference objective

Bayesian Object TrackingBayesian Object Tracking Optimally 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 FiltersMonte Carlo Filters

Gordon, Salmond and Smith (1993), Kitagawa (1996), Isard and Blake (1996), …)

Probabilistic updating of states:

t=0

Approx with sequential update of Monte

Carlo particle `clouds’:

Stochastic models for Stochastic models for groupsgroups

Require dynamical models that adequately capture the Require dynamical models that adequately capture the correlated behaviour of group objectscorrelated behaviour of group objects

We base this on simple behavioural properties of We base this on simple behavioural properties of individuals relative to other members of their group individuals relative to other members of their group (attractive/repulsive forces)(attractive/repulsive forces)

Some similarities to flocking models in animal behaviour Some similarities to flocking models in animal behaviour analysisanalysis

TexPoint Display

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

State variablesState variables

Bayesian InferenceBayesian Inference

Bayesian filtering Bayesian filtering recursionsrecursions

State Transition State Transition ProbabilitiesProbabilities

Inference AlgorithmInference Algorithm

We require a powerful scheme that is We require a powerful scheme that is sequential and able to sample a high-sequential and able to sample a high-dimensional, structured state-spacedimensional, structured state-space

We adopt a sequential MCMC scheme We adopt a sequential MCMC scheme that samples from the joint states at t that samples from the joint states at t and t-1, based on the empirical and t-1, based on the empirical filtering distribution at time t-1 filtering distribution at time t-1

Empirical distribution from t-1

Conclusions and Future Conclusions and Future DirectionsDirections

AcknowledgementsAcknowledgements

Funding support from QinetiQ UK and the UK Funding support from QinetiQ UK and the UK government’s Data and Information Fusion government’s Data and Information Fusion Defence Technology Centre (DIF-DTC)Defence Technology Centre (DIF-DTC)