×

Auxiliary model-based RELS and MI-ELS algorithm for Hammerstein OEMA systems. (English) Zbl 1193.93170

Summary: This paper considers the identification problem for Hammerstein output error moving average (OEMA) systems. An auxiliary model-based recursive extended least-squares (RELS) algorithm and an auxiliary model-based multi-innovation extended least-squares (MI-ELS) algorithm are presented using the multi-innovation identification theory. The basic idea is to express the system output as a linear combination of the parameters by using the key-term separation principle and auxiliary model method. The proposed algorithms can give highly accurate parameter estimates. The simulation results show the effectiveness of the proposed algorithms.

MSC:

93E10 Estimation and detection in stochastic control theory
62F10 Point estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Shi, Y.; Fang, H.; Yan, M., Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs, Control with Limited Information (Part II). Control with Limited Information (Part II), International Journal of Robust and Nonlinear Control, 19, 18, 1976-1992 (2009), (special issue) · Zbl 1192.93118
[2] Shi, Y.; Ding, F.; Chen, T., Multirate crosstalk identification in xDSL systems, IEEE Transactions on Communications, 54, 10, 1878-1886 (2006)
[3] Shi, Y.; Ding, F.; Chen, T., 2-norm based recursive design of transmultiplexers with designable filter length, Circuits, Systems, and Signal Processing, 25, 4, 447-462 (2006) · Zbl 1130.94312
[4] Han, L. L.; Ding, F., Identification for multirate multi-input systems using the multi-innovation identification theory, Computers & Mathematics with Applications, 57, 9, 1438-1449 (2009) · Zbl 1186.93076
[5] Han, L. L.; Sheng, J.; Ding, F.; Shi, Y., Auxiliary model identification method for multirate multi-input systems based on least squares, Mathematical and Computer Modelling, 50, 7-8, 1100-1106 (2009) · Zbl 1185.93139
[6] Xiao, Y. S.; Zhang, Y.; Ding, J.; Dai, J. Y., The residual based interactive least squares algorithms and simulation studies, Computers & Mathematics with Applications, 58, 6, 1190-1197 (2009) · Zbl 1189.62149
[7] Xiao, Y. S.; Ding, F.; Zhou, Y.; Li, M.; Dai, J. Y., On consistency of recursive least squares identification algorithms for controlled auto-regression models, Applied Mathematical Modelling, 32, 11, 2207-2215 (2008) · Zbl 1156.93411
[8] Ding, F.; Shi, Y.; Chen, T., Performance analysis of estimation algorithms of non-stationary ARMA processes, IEEE Transactions on Signal Processing, 54, 3, 1041-1053 (2006) · Zbl 1373.94569
[9] Ding, J.; Ding, F., The residual based extended least squares identification method for dual-rate systems, Computers & Mathematics with Applications, 56, 6, 1479-1487 (2008) · Zbl 1155.93435
[10] Ding, F.; Chen, T., Hierarchical least squares identification methods for multivariable systems, IEEE Transactions on Automatic Control, 50, 3, 397-402 (2005) · Zbl 1365.93551
[11] Ding, F.; Chen, T., Combined parameter and output estimating of dual-rate systems using an auxiliary model, Automatica, 40, 10, 1739-1748 (2004) · Zbl 1162.93376
[12] Ding, F.; Chen, T., Identification of dual-rate systems based on finite impulse response models, International Journal of Adaptive Control and Signal Processing, 18, 7, 589-598 (2004) · Zbl 1055.93018
[13] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489 (2005) · Zbl 1086.93063
[14] Ding, F.; Shi, Y.; Chen, T., Gradient based identification algorithms for nonlinear Hammerstein ARMAX models, Nonlinear Dynamics, 45, 1-2, 31-43 (2006) · Zbl 1134.93321
[15] Ding, F.; Shi, Y.; Chen, T., Auxiliary model-based least-squares identification methods for Hammerstein output-error systems, Systems and Letters, 56, 5, 373-380 (2007) · Zbl 1130.93055
[16] Ding, F.; Liu, P. X.; Liu, G., Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal Processing, 89, 10, 1883-1890 (2009) · Zbl 1178.94137
[17] Liu, Y. J.; Xiao, Y. S.; Zhao, X. L., Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model, Applied Mathematics and Computation, 215, 4, 1477-1483 (2009) · Zbl 1177.65095
[18] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14 (2007) · Zbl 1140.93488
[19] Zhang, J. B.; Ding, F.; Shi, Y., Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems & Control Letters, 58, 1, 69-75 (2009) · Zbl 1154.93040
[20] Han, L. L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital Signal Processing, 19, 4, 545-554 (2009)
[21] Vörös, J., Iterative algorithm for parameter identification of Hammerstein systems with two-Segment nonlinearities, IEEE Transactions on Automatic Control, 44, 11, 2145-22149 (1999) · Zbl 1136.93446
[22] Vörös, J., Identification of Hammerstein systems with time-varying piecewise-linear characteristics, IEEE Transactions on Circuits and Systems—II: Express Briefs, 52, 12, 865-869 (2005)
[23] Vörös, J., Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones, IEEE Transactions on Automatic Control, 48, 12, 2203-2206 (2003) · Zbl 1364.93172
[24] Wang, D. Q.; Ding, F., Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems, Computers & Mathematics with Applications, 56, 12, 3157-3164 (2008) · Zbl 1165.65308
[25] Cerone, V.; Regruto, D., Parameter bounds for discrete-time Hammerstein models with bounded output errors, IEEE Transactions on Automatic Control, 48, 10, 1855-1860 (2003) · Zbl 1364.93417
[26] Goodwin, G. C.; Sin, K. S., Adaptive Filtering, Prediction and Control (1984), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0653.93001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.