Two stochastic approximation procedures for identifying linear systems

A Kiefer-Wolfowitz procedure for identifying a Finite Memory, Time Discrete, Linear System is developed. The procedure is shown to reduce to a Robbins-Monro method. Two algorithms are presented to sequentially identify the linear system. The first one is derived directly from the Kiefer-Wolfowitz procedure and is shown to develop a bias which depends on the input measurement error noise variance. The second algorithm is a modification of the first assuming that the input noise variance is known exactly. For this algorithm the system can be identified correctly in the limit as time increases indefinitely.