An engineer's guide to particle filtering on matrix Lie groups

Abstract

In many important engineering applications the state dynamics of a system are modelled by Stochastic Differential Equations (SDEs) evolving in non-Euclidean spaces such as matrix Lie groups. Due to the advances in computing power, the problem of state estimation can be efficiently addressed by the particle filtering method. This requires dealing with both the geometry and the stochastics of the problem. However, the very few papers that properly deal with either are in the mathematics literature and not accessible. The engineering literature is also small but plagued with problems. With this in mind, we give a direct accessible derivation of the particle filter algorithm for state estimation in matrix Lie groups. We do not rely on differential geometry or advanced stochastic calculus. Simulation examples are provided.