The Lie Algebraic Structure of a Class of Finite Dimensional Nonlinear Filters

摘要

We present an example of the application of Lie algebraic techniques to nonlinear estimation problems. The method relates the computation of the (unnormalized) conditional density and the computation of statistics with finite dimensional estimators. The general method is explained; for a particular example, the structures of the Lie algebras associated with the unnormalized conditional density equation and the finite dimensionally computable conditional moment equations are analyzed in detail. The relationship between these Lie algebras is studied, and the implications of these results are discussed. (Author)