Nonlinear filtering problems with finite dimensional matrix estimation algebras

Matrix estimation algebras are Lie algebras that arise naturally in the nonlinear filtering problem for systems with random structure. These are systems that have finitely many modes of operation, where transitions from one mode to another are governed by a finite-state Markov process. Necessary conditions for finite dimensionality of matrix estimation algebras have been given. Finite dimensional filter realizations have been constructed for some of the cases for which the matrix estimation algebra is finite dimensional.