Multiple model trajectory poisson multi-bernoulli mixtures filter for tracking multiple maneuvering objects

Multi-object tracking (MOT) in cluttered and dynamic environments remains challenging, especially for maneuvering objects. While trajectory-based random finite set (RFS) filters provide principled solutions for trajectory estimation, they typically rely on a single motion model, limiting their adaptability. To address this gap, we propose the Multiple-Model Trajectory Poisson Multi-Bernoulli Mixture (MM-TPMBM) filter, which integrates jump Markov system (JMS) dynamics within the trajectory RFS framework. The filter enables closed-form Bayesian recursion for joint trajectory estimation and motion model switching. We derive its prediction and update equations, implement it using Gaussian mixtures for computational efficiency, and evaluate performance against benchmark filters (MM-PMBM, TPMBM, δ-GLMB) via Monte Carlo simulations. Results demonstrate that the MM-TPMBM filter achieves superior accuracy in trajectory estimation, localization, and cardinality, reducing the generalized optimal sub-pattern assignment (GOSPA) error by up to 24% and cardinality error by up to 52% compared to state-of-the-art methods, validating its robustness in complex tracking scenarios.