Monte Carlo filtering on Lie groups

We propose a nonlinear filter for estimating the trajectory of a random walk on a matrix Lie group with constant computational complexity. It is based on a finite-dimensional approximation of the conditional distribution of the state-given past measurements-via a set of fair samples, which are updated at each step and proven to be consistent with the updated conditional distribution. The algorithm proposed, like other Monte Carlo methods, can in principle track arbitrary distributions evolving on arbitrarily large state spaces. However, several issues concerning sample impoverishment need to be taken into account when designing practical working systems.