Filtrage non lineaire avec observation sur une variete

Abstract

This paper concerns a filtering problem where the observation process is, conditioned on the state, a diffusion taking values in a manifold. Such problems arise naturally in phase demodulation, spherical mechanics and other physical situations where the state variables are constrained. We show that the natural filtration of the observation coincides with that of another process taking values in Euclidean space R, thus reducing the problem to a classical one. The equations satisfied by the conditional law are derived

Keywords:

• Filtering equations
• manifolds
• rotational processes
• innovation theorem