On the moment dynamics of discrete measures

In this paper, we provide a systematic account on the use of elementary symmetric polynomials as a specification of both states and outputs of a group of agents in a multitarget tracking setup. In particular, this includes a generalization of so-called symmetric measurement equations, which were previously introduced in multitarget tracking for special cases. Furthermore, we show that the dynamics of these symmetric polynomials are governed by linear tensor systems, which are typically studied in the context of the Carleman embedding, as well as polynomial systems.