An efficient algorithm for stochastic system identification with noisy input

This paper considers the problem of identifying linear systems, where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances. It is noticed that the applicability of the bias-eliminated least-squares (BELS) method depends fully upon a prefilter designed with its order equal to the system order plus one. An efficient method is developed in this paper which can perform consistent parameter estimation without utilizing such a prefilter. The developed method is characterized by attractive features: direct use of the observed data without prefiltering; no need to evaluate autocorrelation functions for the input noise; no need to identify a high-order augmented system; and provision of a direct BELS estimate of the system parameters without parameter extraction