Approximate identification of linear stochastic systems

A novel method for estimating models for stochastic linear systems is described. The essential idea of the method is to convert the usual nonlinear estimation problem into a problem that is linear in the parameters by use of a generalized expansion in terms of a stable operator. The method leads to a simple estimation scheme based on weighted least squares. A recursive scheme for successively adding terms to the expansion is described, and a stopping criterion is suggested. Novel features of the method include a method for quantifying the errors resulting from the truncation of this expansion. This has been used to develop a method for deciding on the order of the expansion. Examples illustrate the utility of the procedure