Sequential Monte Carlo PHD and CPHD Filters for Generic Observation Model

This paper extends the widely used probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters to non-standard observation models (NSOMs), such as pixelized track-before-detect and superpositional sensor models. Classical (C)PHD filters are computationally attractive but are derived under the standard point-object observation model. Existing (C)PHD variants for specific NSOMs typically rely on simplified assumptions, such as independent object-generated observations, to obtain closed-form solutions. These assumptions can fail in practical scenarios, such as closely spaced or merged-observation objects, resulting in severe performance degradation. To address this issue, we adapt (C)PHD filtering to the generic observation model (GOM), where the update step directly uses a generic multi-object likelihood. The Bayesian posterior under the GOM is projected back onto the Poisson and independently and identically distributed cluster families via Kullback-Leibler divergence minimization, yielding the proposed GOM-PHD and GOM-CPHD filters. We further show that the proposed filters reduce to existing (C)PHD variants under specific model assumptions and analyze the posterior-projection error. Furthermore, we develop a fast sequential Monte Carlo implementation of the proposed filters that avoids the combinatorial explosion, reduces the number of likelihood evaluations, and includes its convergence analysis. Finally, simulation results, including one diagnostic posterior-projection analysis scenario and two NSOM tracking scenarios, show regimes in which the posterior-projection error is smaller than the error induced by a mismatched likelihood and that the proposed filters improve tracking accuracy over representative NSOM-specific baselines with lower computational cost than labeled random finite set GOM baselines.