Stochastic Filtering in Manifolds

Abstract

A nonlinear filtering problem is formulated where the state evolves in a compact Riemannian manifold and the observations evolve in a noncompact Riemannian symmetric space. Absolute continuity methods are used to obtain an expression for the conditional probability. A stochastic equation is obtained for the unnormalized conditional probability density. This equation is described in the bundle of orthonormal frames.