## IMA Postdoc Seminar (April 7, 2009)

**Speaker:** Vasileios Maroulas (IMA)

**Title:** Sequential Monte Carlo Multi-Object Second Moment
Approximation: An Application to Ecology

**Abstract:**
In recent years, scientists have tagged and tracked, via Argos (a satellite-based system which
collects data from mobile platforms worldwide), various species in order to discover how
wildlife behaves. A plethora of these species moves in groups and a sudden change in motion
of the individual might happen, causing rapid modification of the number of tracking objects.
Consequently, it is understood that a multi-object framework is crucial, tracking not only the
trajectories of the entire group, but also the number of individual species belonging to it. In
the past, several studies approached the multi-object tracking problem by monitoring each
individual of the group and reporting recursively the number of targets, thus resulting in
a rise of the algorithm's computational cost. Furthermore, it has been assumed that the
motions of targets are statistically independent and the number of tracking objects fixed.

The approach of this talk is quite different, providing an analogue of the single-object
Bayes filtering methods. The key strategy is to conceptually view the collection of individual
targets as a set-valued state, and the collection of individual observations as a set-valued
observation, adopting random finite set (RFS) theory as a unified approach to multi-target
tracking. Modeling set-valued states and set-valued observations through RFS theory allows the
problem of dynamically estimating multiple objects in the presence of clutter and association
uncertainty to be cast in a Bayesian filtering framework. On the other hand, the multi-object
Bayes filtering density is computationally intractable, hence, a second moment approximation,
called cardinalized probability hypothesis density (CPHD), is proposed to overpass its
computational complexity. The CPHD propagates at each time step, not only the position estimates
of the objects, but also the distribution of the number of targets in the scene. Furthermore,
multi-target sequential Monte Carlo techniques have been implemented to a simulated data set,
resembling possible trajectories of a wildlife group, and accurate performance of the CPHD has
been verified.