Particle Filtering on the Stiefel Manifold with Optimal Transport

Abstract

Estimating the state of a stochastic differential equation (SDE) evolving in a Stiefel manifold occurs in many applications in science and engineering. This problem has been handled by particle filtering. However, many existing schemes share common shortcomings: estimated states fail to satisfy geometric constraints in the sampling step and the conventional particle filter suffers from particle depletion in the resampling step. Here we overcome these issues by managing the geometry with a numerical Ito-Cayley scheme and ensuring particle diversity with optimal transport. We give simulations to illustrate the new algorithm.