Marginal marginalised particle filter

This paper deals with filters that combine the analytical Kalman filtering and the Monte Carlo simulation based particle filtering. Since the particles are related to the state trajectories from the initial time up to the current time rather than to the state at the last time only, these filters cannot be directly used in fusion of probability densities of the last state. Therefore, marginalisation of the outdated parts of the state trajectories is proposed in the paper. In order to obtain a reproducible probability density, at least theoretically, the Gaussian sum description of random variables is also newly considered in the problem formulation.