Improved Kalman-Particle Kernel Filter on Lie Groups Applied to Angles-Only UAV Navigation

Kalman-Particle Kernel Filter (KPKF) is a sub-class of Particle Filter (PF) that uses Gaussian kernels as particles, which enables a local Kalman update for each measurement in addition to the usual weight update. Besides, recent research about filtering on Lie groups brought powerful theoretical results, and showed the superiority of this approach. Hence, this paper extends the Euclidean KPKF to a new formulation on Lie groups and introduces substantial improvements based on Lie groups Kalman filters theory and Laplace Particle Filters on Lie groups (LG-LPF) for improved resampling. The proposed algorithm is tested on an angles-only UAV navigation scenario with challenging initial errors. It shows superior robustness and accuracy compared to Lie group Extended Kalman Filter (LG-EKF), with near-to optimal performance, even with a limited amount of particles.