Joint multi-Bernoulli RFS for two-target scenario

In this paper, we propose a new class of random finite set (RFS), which is the union of a group of Bernoulli RFSs with unknown level of correlation, whose statistics are considered jointly. The proposed RFS is referred to as joint multi-Bernoulli (JMB) RFS defined by a set of parameters. As a preliminary study, this paper provides the derivations of set density, set marginal density of JMB RFS family, and the resultant tracking filter for a two-target scenario based on finite-set statistics (FISST). Note that the theoretically sound way of computing the set marginal density is not well defined in current FISST. The JMB RFS family offers a parameterized and generalized set density which bridges the gap between set density and vector density. Hence, the JMB RFS family inherits several advantages of vector density, such as analyzing the correlation between states, extracting the statistics of partial states from global statistics conveniently, and embedding the target identities implicitly. The corresponding tracking filter has an accurate update equations with no need to specify measurement model, and can be further improved by utilizing the advantages of JMB RFS family. The aforementioned advantages are clearly highlighted by the numerical results.