Bayesian Multiple Target Filtering Using Random Finite Sets

The random finite set (RFS) approach, introduced by Mahler as finite set statistics (FISST), is an elegant Bayesian formulation of multitarget filtering based on RFS theory. This chapter describes the RFS approach to multitarget tracking. It focuses on RFS-based algorithms such as the probability hypothesis density (PHD), and cardinalized PHD (CPHD) filters. The chapter also focuses on the recent developments such as the multitarget multi-Bernoulli (MeMBer) filters. An overview of the developments in the RFS approach and the PHD/CPHD filters is also given. The chapter examines the fundamental notion of miss distance or estimation error for multiple targets. It evaluates the PHD/CPHD filters and their Gaussian mixture implementations. Finally, the chapter outlines the MeMBer filter as another approximation approach to the multitarget filtering problem.