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IMA Journal of Mathematical Control and Information 1985 2(1):25-36; doi:10.1093/imamci/2.1.25
© 1985 by Institute of Mathematics and its Applications
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Nonlinear Filtering in Rieznnnnifln Manifolds

S. K. NG and P. E. CAINES

Department of Electrical Engineering, McGill University Montreal, P.Q. Canada

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.


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