Stable identification scheme for linear discrete-time systems

This paper is concerned with the problem of identifying parameters in stochastic systems described by single-input single-output linear discrete-time equations. A stable estimation error system is developed by using the extended Kalman filter technique and the concept of strictly positive real transfer function. The identifier corresponding to the estimation error system is constructed, and the convergence of parameter estimates to the exact values is proved under some bounded conditions. It is shown that the recursive maximum likelihood identifier and the recursive extended least squares identifier are obtained by neglecting the correction terms in the proposed identifier. Numerical examples for a fourth-order system are presented to illustrate the effectiveness of the proposed method.