Parameter Estimation for Observed Diffusions in Manifolds
S. K. Ng, Peter E. Caines, H. F. CHEN · IMA Journal of Mathematical Control and Information · 1984
Following the procedure described by Elworthy (1982) and Ikeda & Watanabe (1981) we construct the solution of stochastic differential equations (SDEs) in manifolds. We take such SDEs to describe parametrized completely observed stochastic systems and manifold-valued state processes. The likelihood function for the system parameter is computed by two methods: the first applies to the case of parallelizable manifolds; the second applies to the general case, here the solution of the system SDE is constructed in the orthonormal frame bundle of the manifold. Two examples are given.