A technique for the identification of linear systems

An iterative technique is proposed to identify a linear system from samples of its input and output in the presence of noise by minimizing the mean-square error between system and model outputs. The model chosen has a transfer function which is a ratio of polynomials in z-1. Although the regression equations for the optimal set of coefficients are highly nonlinear and intractable, it is shown that the problem can be reduced to the repeated solution of a related linear problem. Computer simulation of a number of typical discrete systems is used to demonstrate the considerable improvement over the Kalman estimate which can be obtained in a few iterations. The procedure is found to be effective at signal-to-noise ratios less than unity, and with as few as 200 samples of the input and output records.