Estimation Algebra Research Articles

Optimal filter realization for a class of nonlinear systems with finite-dimensional estimation algebra

A close relationship between the dimension of the estimation algebra and the existence of a finite-dimensional filter of a particular type has been established by several researchers. However, a general procedure for constructing the filter realization has not been developed. In this paper a realization is presented for a special class of nonlinear systems with finite-dimensional estimation algebra. The filter consists of two dynamic processes, one which is data independent and one which is data dependent

New classes of finite-dimensional nonlinear filters

We derive sufficient conditions for the estimation algebras of two special classes of nonlinear estimation systems to be finite dimensional. By carrying out the Brockett—Wei—Norman program new classes of finite-dimensional filters are obtained. These systems can be regarded respectively as extensions of the Kalman—Bucy filters and the Benes filters.

Current algebras and the identification problem

In this paper, we investigate the identification problem of linear system theory from the viewpoint of nonlinear filtering. Following the work of Brockett and Mitter, one associates in a natural way a certain (infinite dimensional) Lie algebra of differential operators known as the estimation algebra of the problem. For the identification problem the estimation algebra is a subalgebra of a current algebra. In this paper we study questions of representation and integrability of current algebras as they impinge upon the identification problem. A Wei-Norman type procedure for the associated Cauchy problem is developed which reveals a sequence of functionals of the observations that play the role of joint sufficient statistics for the identification problem.

The invariane group of the Zakai equation

In this paper the stochastic filter is studied as an infinite dimentional control system on the space of all densities. The Volterra series representation of the corresponding input-output map is then shown to be globally convergent, and the coordinate changes on the space of all densities that preserve the ‘estimation algebra’ structure are characterized.

Nonlinear filtering problems with finite dimensional estimation algebras

Nonlinear filtering problems with finite dimensional estimation algebras