Abstract

Abstract: The last decade has witnessed exciting developments in multi-object state estimation with the introduction of stochastic geometry to the field. Stochastic geometry-the marriage between geometry and probability-is a mathematical discipline that deals with random spatial patterns. The history of stochastic geometry traces back to the problem of Buffon’s needle and has long been used by statisticians in many diverse applications including astronomy, particle physics, biology, sampling theory, stereology, etc. Since 2003, Mahler’s seminal work on the random finite set approach to multi-object filtering, which culminated in the probability hypothesis density (PHD) filter, has continued to attract substantial interests from academia and industry alike. This seminar presents an overview of the random finite set paradigm to dynamic state estimation and outlines recent developments beyond the PHD filters as well as applications in areas such as sensor scheduling, computer vision, and field robotics.