On the Bayes filtering equations of finite set statistics

In multi-target tracking, not only the locations of the targets vary with time, the number of targets also varies with time due to targets appearing and disappearing in the scene. The random finite set approach offers a natural and elegant means to model multiple targets and measurements received by the sensors. This framework has culminated in novel multi-target tracking algorithms developed using the tools of finite set statistics (FISST). FISST concepts are not conventional probabilistic concepts and their relationships to conventional probability are not clear. In particular, the validity of the FISST Bayes filter has not been established. This paper presents some connections between FISST and standard probability theory. Moreover, a measure theoretic treatment of the multi-object filtering problem is given to establish the validity of the FISST Bayes filter.