Algebraic Structure and Finite Dimensional Nonlinear Estimation,
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Optimal recursive state estimators have been derived for very general classes of nonlinear stochastic systems. The optimal estimator requires, in general, an infinite dimensional computation to generate the conditional mean of the system state given the past observations. This computation involves either the solution of a stochastic partial differential equations for the conditional density or an infinite set of coupled ordinary stochastic differential equations for the conditional moments. However, the class of linear stochastic systems with linear observations and white Gaussian plant and observation noises has a particularly appealing structure, because the optimal state estimator consists of a finite dimensional linear system -- the Kalman-Bucy filter. In this paper the authors exploit the algebraic structure of certain other classes of systems, in order to prove that the optimal estimators for these systems are finite dimensional.
- Statistics and Probability