Particle filtering and the Laplace method for target tracking

International audienceThe deterministic Laplace method is combined with particle filtering for the state estimation in nonlinear state-space models. Multidimensional Laplace approximations of the posterior moments are embedded in a particle filter. These approximations are used to design an affine transformation taking into account the observation. This transformation is applied to the particle sample in order to improve particle approximation. The resulting algorithm is called the Laplace particle filter (LPF). It is tested by simulation and exhibits good performance on three tracking problems: bearings-only target tracking, ballistic target tracking during atmospheric reentry, and neural decoding for motion analysis