Monte Carlo Tracking on the Riemannian Manifold of Multivariate Normal Distributions

In this contribution, a general scheme of particle filtering on Riemannian manifolds is proposed. In addition to the nonlinear dynamics, the system state is constrained to lie on a Riemannian manifold M, which dimension is much lower than the whole embedding space dimension. The Riemannian manifold formulation of the state space model avoids the curse of dimensionality from which suffers most of the particle filter methods. Furthermore, this formulation is the only natural tool when the embedding Euclidean space cannot be defined (the state space is defined in an abstract geometric way) or when the constraints are not easily handled (space of positive definite matrices).