Particle Filtering on the Euclidean Group

We address general filtering problems on the Euclidean group SE(3). We first generalize, to stochastic nonlinear systems evolving on SE(3)9 the particle filter of Liu and West (2001) for simultaneously estimating the state and covariance. The filter is constructed in a coordinate-invariant way, and explicitly takes into account the geometry of SE(3) and P(n)9 the space of symmetric positive definite matrices. An experimental case study involving vision-based robot end-effector pose estimation is also presented.