Particle Filters for Infinite (or Large) Dimensional State Spaces-Part 2

We study particle filtering algorithms for tracking on infinite (in practice, large) dimensional state spaces. Particle filtering (Monte Carlo sampling) from a large dimensional system noise distribution is computationally expensive. But, in most large dim tracking applications, it is fair to assume that "most of the state change" occurs in a small dimensional basis and the basis itself may be slowly time varying (approximated as piecewise constant). We have proposed a PF algorithm with basis change detection and re-estimation steps that uses this idea. The implicit assumptions in defining this algorithm are very strong. We study here the implications of weaker assumptions and how to handle them. We propose to use a simple modification of the asymptotically stable adaptive particle filter to handle errors in estimating the basis dimension