A generalized expression of multi-target probability density in the framework of FISST

In this paper, we propose a generalized expression of multi-target probability density in the framework of finite-set statistics (FISST). It differs from the existing expression in that it is completely defined by a set of parameters. The parameterized expression offers three important advantages. Firstly, the statistics of any subset of an random finite set (RFS) can be conveniently extracted by directly computing the marginal distribution of the proposed parameterized probability density. Note that the theoretically sound way of computing the marginal distribution of an RFS probability density is not well defined in current FISST. Secondly, it inherits advantages of the vector notation based density in that the identities of target states are implicitly embedded with no need to augment target state with an extra label. Thirdly, it is a generalized expression capable to describe the statistics of almost all kinds of RFSs and doesn´t need to assume a specified measurement model for the development of target tracking filter. As a preliminary study, this paper provides both the derivations of the proposed expression and the resultant tracking filter for a two-target scenario. The aforementioned advantages are clearly highlighted by the numerical results.