A General Pairwise-Markov GLMB Filter

The generalized labeled multi-Bernoulli (GLMB) filter is the first general and exact-closed-form approximation of the labeled multitarget recursive Bayes filter. It is, like almost all single-target tracking and multi-target tracking algorithms, based on hidden Markov Models (HMMs). Unfortunately, HMM assumptions are physically unrealistic for many target tracking applications. For this reason, Pieczynski's generalization of the HMM, the pairwise-Markov model (PMM), has attracted interest in the target-tracking community. This paper answers in the affirmative the following question: Is there a theoretically rigorous PMM generalization of the GLMB filter? The update equation for this generalization is similar in form to the measurement-update equation for the GLMB filter, and the derivation of the former is closely patterned after a cleaner probability generating functional (PGFL) derivation of the latter.