Gaussian trajectory PMBM filter with nonlinear measurements based on posterior linearisation

This paper presents a Gaussian implementation of the Poisson multi-Bernoulli mixture (PMBM) filter for sets of trajectories with non-linear/non-Gaussian measurements. In this filter, the single-trajectory densities are Gaussian and their updates are performed using the iterated posterior linearisation technique, applied on the current target state. With this approach, we first compute the posterior distribution of the current target state by iteratively refining the linear approximation of the measurement, and the resulting mean square error of the linearisation, based on our current guess of the posterior distribution. After obtaining a Gaussian approximation of the current target state, the distribution of the past states of the trajectory can be obtained in closed form. Via numerical simulations, we compare different algorithms to approximate the single-trajectory posteriors and normalising constants for trajectory PMBM and trajectory Poisson multi-Bernoulli filters.