Identification of transfer function model in consideration of III‐conditioning

Often in the identification of the transfer function of a discrete‐time system, the least‐squares estimation does not work well if the system has a pole near z =1, even if the input signal is white sequence. This is because the output correlation function has a small decay, making the corresponding normal equation ill conditioned. This paper proposes an identification method to ameliorate the ill condition of the correlation matrix for such a system. In the proposed method, the identification model is rewritten so that the difference of the output signal is represented explicitly, providing a matrix transformation for the parameters to be identified. The method prepares, for the n‐th order system, n identification models with the highest order L being from 0 to (n‐1). The least‐squares estimation is performed for the identification models, and the values of the evaluation functions obtained by the estimations are compared. Then the estimation minimizing the evaluation function is adopted; L determined by the proposed method is related closely to the number of poles near z =1, which is the cause of the ill condition. This situation is examined by computer simulations.