First-moment filters for spatial independent cluster processes

摘要

A group target is a collection of individual targets which are, for example, part of a convoy of articulated vehicles or a crowd of football supporters and can be represented mathematically as a spatial cluster process. The process of detecting, tracking and identifying group targets requires the estimation of the evolution of such a dynamic spatial cluster process in time based on a sequence of partial observation sets. A suitable generalisation of the Bayes filter for this system would provide us with an optimal (but computationally intractable) estimate of a multi-group multi-object state based on measurements received up to the current time-step. In this paper, we derive the first-moment approximation of the multi-group multi-target Bayes filter, inspired by the first-moment multi-object Bayes filter derived by Mahler. Such approximations are Bayes optimal and provide estimates for the number of clusters (groups) and their positions in the group state-space, as well as estimates for the number of cluster components (object targets) and their positions in target state-space.