Nonlinear Filtering in Rieznnnnifln Manifolds

A general formulation of the nonlinear filtering problem in Riemanman manifolds is given by use of the strong solutions of the stochastic differential equations for the state and observation processes in the orthonormal frame bundles of the state and observation process manifolds, respectively. A general Bayes formula for the conditional expectation of smooth functions of the state process is given. This is used to give a direct derivation of the Zakai equation for the general problem under consideration. An example is presented.