SECOND-ORDER POLYNOMIAL ESTIMATION FOR DISTRIBUTED PARAMETER SYSTEMS WITH UNCERTAIN OBSERVATIONS

摘要

In this paper we consider a kind of discrete-time distributed parameter system with uncertain observations where the uncertain is modeled by independent Bernoulli random variables. Our aim is to study the least mean squared error second-order polynomial filtering problem in these systems. We have obtained the recursive algorithm for determining the second-order polynomial filter. The practical resolution of this infinite dimensional filtering algorithm is also presented; for it, we expand the estimators into eigenfuction series and apply the separation of variables method. The approximation of the series by a finite number of terms will reduce the infinite dimensional algorithm to one finite dimensional and this provides us an approximate solution to the second-order polynomial estimation problem.