Generalized Laplace Particle Filter on Lie Groups Applied to Ambiguous Doppler Navigation

Particle filters are suited to solve nonlinear and non-Gaussian estimation problems which find numerous applications in autonomous systems navigation. Previous works on Laplace Particle Filter on Lie groups (LG-LPF) demonstrated its robustness and accuracy on challenging navigation scenarios compared to classic particle filters. Nevertheless, LG-LPF is applicable when the prior probability density and the likelihood have a predominant mode, which narrows the scope of applications of this method. Thus, this paper proposes a generalized strategy to use LG-LPF while keeping its benefits. The core idea is to compute an accurate multimodal importance function based on local optimizations and resample the particles accordingly. This approach is compared to a Laplace Particle Filter (LPF) designed in the Euclidean space, on a UAV navigation scenario with ambiguous Doppler measurements. The Lie group approach shows improved accuracy and robustness in every case, even with a reduced number of particles.