Bayesian filtering for dynamic spatial point processes

Speaker: Daniel Clark (Heriot-Watt University)

Abstract

Stochastic filtering is a fundamental concept in the theory of estimation of dynamic systems. In its discrete-time formulation, the stochastic filter can be described by the Chapman-Kolmogorov equation, which models the evolution of a posterior distribution over time, and Bayes rule, to update the posterior based on new observations. The optimal solution to the multi-object filtering can be found through a direct generalisation of the Bayes filter to multi-object systems using point process theory. This solution, derived by Ron Mahler has led to mathematically principled and tractable multi-target tracking algorithms that now have been deployed in a number of industrial applications for autonomous robotics navigation and radar surveillance. This talk will present the theoretical foundation for these results and discuss new developments in this field.