Optimal joint probabilistic data association filter avoiding coalescence in close proximity

This paper deals with an estimation problem where a known number of objects in close proximity are observed but the measurement originations are uncertain. It is well known that joint probabilistic data association filters (JPDAF) are effective in handing uncertain measurement originations with clutter, but they are prone to estimation coalescence, particularly when close neighboring objects share measurements. This paper proposes a Coalescence Avoiding Optimal JPDAF (C-JPDAF) that minimizes the weighted sum of the posterior uncertainty and a measure of similarity between estimated probability densities. The proposed approach has simpler structures than other coalescence avoiding approaches based on pruning, while exhibiting excellent filtering performance for objects in close proximity with crossing tracks. These are illustrated by a numerical example of two satellites on crossing orbits around the Earth.