TY - JOUR

T1 - Identification of transfer function model in consideration of III‐conditioning

AU - Adachi, Shuichi

AU - Izumisawa, Tooru

AU - Sano, Akira

PY - 1988/8

Y1 - 1988/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0024057261&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024057261&partnerID=8YFLogxK

U2 - 10.1002/ecja.4410710803

DO - 10.1002/ecja.4410710803

M3 - Article

AN - SCOPUS:0024057261

VL - 71

SP - 25

EP - 35

JO - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

JF - Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)

SN - 8756-6621

IS - 8

ER -