Laplace Particle Filter on Lie Groups Applied to Angles-Only Navigation

Particle Filters are an active field of study to address highly nonlinear estimation problems, especially when coupled with optimisation methods (e.g. with the Laplace Particle Filter). Moreover, recent studies revealed the advantage of Kalman filtering on Lie groups. This paper introduces an improved version of the Laplace Particle Filter by deriving a formulation on Lie Groups. The core idea is to harness probability density functions on Lie groups to cope with the state intrinsic geometric constraints and nonlinear nature. In addition, the Lie Group Laplace Particle Filter (LG-LPF) leverages an optimisation algorithm fully defined on Lie Groups. Numerical results on a nonlinear and angles-only navigation scenario demonstrate a significant enhancement in terms of estimation accuracy and robustness.