Integral-transform derivations of exact closed-form multitarget trackers

The generalized labeled multi-Bernoulli (GLMB) filter, introduced by B.-T. Vo and B.-N. Vo in 2013, is an exact closed-form solution of the multitarget recursive Bayes filter, based on the theory of labeled random finite sets (labeled RFS's). Vo and Vo's derivation was rather long and involved. The purpose of this paper is twofold. First, to provide a more streamlined derivation of the GLMB filter using probability generating functional (p.g.fl.) methods. Second, to use p.g.fl. methods to derive another tractable, exact closed-form multitarget tracker, the “labeled multi-Bernoulli mixture (LMBM) filter.” This filter may be of some utility, since LMB mixtures are computationally simpler than GLMB distributions.