Multiple‐Model Trajectory PMBM Filter for Tracking Manoeuvring Extended Targets

ABSTRACT This paper addresses the challenging problem of tracking multiple manoeuvring extended targets in cluttered environments by introducing the Multiple Model Extended Target Trajectory Poisson Multi‐Bernoulli Mixture (MM‐ET‐TPMBM) filter. The proposed framework integrates the Jump Markov System (JMS) for motion mode switching with the trajectory random finite set (RFS) formalism, enabling simultaneous estimation of target trajectories, kinematic states, spatial extents and dynamic models within a unified Bayesian recursion. We derive closed‐form prediction and update equations and present a computationally efficient implementation using gamma Gaussian inverse Wishart (GGIW) distributions for extended target representation. Comprehensive Monte Carlo simulations demonstrate that the MM‐ET‐TPMBM filter significantly outperforms existing methods, reducing the generalised optimal sub‐pattern assignment (GOSPA) error by up to 53% and cardinality error by up to 71% while maintaining robust trajectory continuity and accurate model identification. The filter's principled approach and computational tractability make it suitable for demanding applications in autonomous navigation, surveillance and defence systems.