A novel formulation of the Bayes recursion for single-cluster filtering

In this paper we address the problem of tracking several moving targets with a sensor whose location and orientation are uncertain. This is a generalization of the well-known problem of feature-based simultaneous localization and mapping (SLAM). It is also a generalization of multitarget tracking (MTT) in general, and related to sensor bias estimation. We address such problems from the perspective of finite set statistics (FISST) and point process theory, and develop general expressions for the posterior multiobject density, as represented by probability-generating functionals (p.g.fl.'s). We discuss how this general solution relates to approximative solutions previously suggested in the literature, and we also discuss how the p.g.fl. should be defined for such problems. To the best of our knowledge, this is the first paper to outline a FISST-based treatment of explicit data association for SLAM and related problems.