<title>Search for tractable Bayesian multitarget filters</title>

Abstract

In the book Mathematics of Data Fusion as well as in earlier papers and the recent monograph An Introduction to Multisource-Multitarget Statistics and Its Applications, I have proposed a unified Bayesian approach to multisource-multitarget fusion, detection, tracking, and identification based on a multitarget generalization of the Bayesian recursive nonlinear filtering equations. The foundation for this approach is finite-set statistics, a systematic generalization of standard engineer's statistical calculus to the multisensor-multitarget realm. I showed, in particular, how true multitarget likelihood functions can be constructed using this calculus. In this paper I show that true multitarget Markov motion models can be constructed in much the same manner. If such an approach is to ever become practical, however, computationally tractable approximate filters will have to be devised. This paper elaborates an approach suggested in Mathematics of Data Fusion: para-Gaussian densities-i.e., multitarget analogs of Gaussian distributions that result in closed-form integrations when inserted into the multitarget Bayesian recursive nonlinear equations. I propose an approximate multitarget filter based on the para-Gaussian concept that shows some promise of leading to computational tractibility.