×

Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. (English) Zbl 1217.15022

Summary: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided.

MSC:

15A24 Matrix equations and identities
15A29 Inverse problems in linear algebra
65F30 Other matrix algorithms (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aihara, S.I.; Bagchi, A., Parameter estimation of term structures modeled by stochastic hyperbolic systems, International journal of innovative computing, information and control, 6, 1, 171-182, (2010)
[2] Aihara, S.I.; Bagchi, A.; Saha, S., On parameter estimation of stochastic volatility models from stock data using particle filter-application to AEX index, International journal of innovative computing, information and control, 5, 1, 17-28, (2009)
[3] Dong, J.; Wei, X.P.; Zhang, Q.; Zhao, L.S., Speech enhancement algorithm based on higher-order cumulants parameter estimation, International journal of innovative computing, information and control, 5, 9, 2725-2734, (2009)
[4] Qu, Q.; Jin, M.L., Parameter estimation of a quadratic FM signal based on FRFT, ICIC express letters, 3, 3A, 385-390, (2009)
[5] 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
[6] Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009)
[7] Ding, F.; Chen, T.; Iwai, Z., Adaptive digital control of Hammerstein nonlinear systems with limited output sampling, SIAM journal on control and optimization, 45, 6, 2257-2276, (2006) · Zbl 1126.93034
[8] Wang, D.Q.; Ding, F., Input – output data filtering based recursive least squares identification for CARARMA systems, Digital signal processing, 20, 4, 991-999, (2010)
[9] 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
[10] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[11] Ding, F., Several multi-innovation identification methods, Digital signal processing, 20, 4, 1027-1039, (2010)
[12] Wang, D.Q.; Ding, F., Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems, Digital signal processing, 20, 3, 750-762, (2010)
[13] 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
[14] 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
[15] Xie, L.; Liu, Y.J.; Yang, H.Z.; Ding, F., Modeling and identification for non-uniformly periodically sampled-data systems, IET control theory & applications, 4, 5, 784-794, (2010)
[16] Ding, F.; Liu, P.X.; Liu, G., Multi-innovation least squares identification for linear and pseudo-linear regression models, IEEE transactions on systems, man, and cybernetics, part B: cybernetics, 40, 3, 767-778, (2010)
[17] Liu, Y.J.; Yu, L.; Ding, F., Multi-innovation extended stochastic gradient algorithm and its performance analysis, Circuits, systems and signal processing, 29, 4, 649-667, (2010) · Zbl 1196.94026
[18] Dehghan, M.; Hajarian, M., An iterative algorithm for solving a pair of matrix equations AY B=E, CY D=F over generalized centro-symmetric matrices, Computers & mathematics with applications, 56, 12, 3246-3260, (2008) · Zbl 1165.15301
[19] Dehghan, M.; Hajarian, M., An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation, Applied mathematics and computation, 202, 2, 571-588, (2008) · Zbl 1154.65023
[20] Golub, G.H.; Van Loan, C.F., Matrix computations, (1996), Johns Hopkins University Press Baltimore, MD · Zbl 0865.65009
[21] Ding, F.; Chen, T., On iterative solutions of general coupled matrix equations, SIAM journal on control and optimization, 44, 6, 2269-2284, (2006) · Zbl 1115.65035
[22] Ding, F.; Liu, P.X.; Ding, J., Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Applied mathematics and computation, 197, 1, 41-50, (2008) · Zbl 1143.65035
[23] Ding, F.; Chen, T., Iterative least squares solutions of coupled Sylvester matrix equations, Systems & control letters, 54, 2, 95-107, (2005) · Zbl 1129.65306
[24] Ding, F.; Chen, T., Gradient based iterative algorithms for solving a class of matrix equations, IEEE transactions on automatic control, 50, 8, 1216-1221, (2005) · Zbl 1365.65083
[25] Xie, L.; Ding, J.; Ding, F., Gradient based iterative solutions for general linear matrix equations, Computers & mathematics with applications, 58, 7, 1441-1448, (2009) · Zbl 1189.65083
[26] Ding, F., Transformations between some special matrices, Computers & mathematics with applications, 59, 8, 2676-2695, (2010) · Zbl 1193.15028
[27] Ding, J.; Liu, Y.J.; Ding, F., Iterative solutions to matrix equations of form aixbi=fi, Computers & mathematics with applications, 59, 11, 3500-3507, (2010) · Zbl 1197.15009
[28] Xie, L.; Liu, Y.J.; Yang, H.Z., Gradient based and least squares based iterative algorithms for matrix equations AXB+CX^{T}D=F, Applied mathematics and computation, 217, 5, 2191-2199, (2010) · Zbl 1210.65097
[29] Ding, F.; Liu, P.X.; Liu, G., Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital signal processing, 20, 3, 664-677, (2010)
[30] Liu, Y.J.; Wang, D.Q.; Ding, F., Least-squares based iterative algorithms for identifying box-Jenkins models with finite measurement data, Digital signal processing, 20, 5, 1458-1467, (2010)
[31] Wang, D.Q.; Yang, G.W.; Ding, R.F., Gradient-based iterative parameter estimation for box – jenkins systems, Computers & mathematics with applications, 60, 5, 1200-1208, (2010) · Zbl 1201.94046
[32] 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
[33] Cao, Y.N.; Liu, Z.Q., Signal frequency and parameter estimation for power systems using the hierarchical identification principle, Mathematical and computer modelling, 52, 5-6, 854-861, (2010) · Zbl 1202.94116
[34] Nazarenko, O.M.; Filchenko, D.V., Parametric identification of state-space dynamic systems: a time-domain perspective, International journal of innovative computing, information and control, 4, 7, 1553-1566, (2008)
[35] Cho, H.C.; Lee, K.S.; Fadali, M.S., Online learning algorithm of dynamic Bayesian networks for nonstationary signal processing, International journal of innovative computing, information and control, 5, 4, 1027-1042, (2009)
[36] Ding, F.; Chen, T., Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica, 41, 2, 315-325, (2005) · Zbl 1073.93012
[37] 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
[38] Xiang, L.L.; Xie, L.B.; Liao, Y.W.; Ding, R.F., Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model, Mathematical and computer modelling, 52, 5-6, 918-924, (2010) · Zbl 1202.93085
[39] Han, H.Q.; Xie, L.; Ding, F.; Liu, X.G., Hierarchical least squares based iterative identification for multivariable systems with moving average noises, Mathematical and computer modelling, 51, 9-10, 1213-1220, (2010) · Zbl 1198.93216
[40] Liu, X.G.; Qian, J., Modeling, control and optimization of ideal internal thermally coupled distillation columns, Chemical engineering & technology, 23, 3, 235-241, (2000)
[41] Shi, J.; Liu, X.G., Melt index prediction by weighted least squares support vector machines, Journal of applied polymer science, 101, 1, 285-289, (2005)
[42] Zhao, C.Y.; Liu, X.G.; Ding, F., Melt index prediction based on adaptive particle swarm optimization algorithm-optimized radial basis function neural networks, Chemical engineering & technology, 33, 11, 1909-1916, (2010)
[43] Ding, F.; Chen, T., Hierarchical identification of lifted state-space models for general dual-rate systems, IEEE transactions on circuits and systems-I: regular papers, 52, 6, 1179-1187, (2005) · Zbl 1374.93342
[44] Ding, J.; Shi, Y.; Wang, H.G.; Ding, F., A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems, Digital signal processing, 20, 4, 1238-1249, (2010)
[45] Ding, F.; Liu, P.X.; Yang, H.Z., Parameter identification and intersample output estimation for dual-rate systems, IEEE transactions on systems, man, and cybernetics, part A: systems and humans, 38, 4, 966-975, (2008)
[46] Ding, F.; Qiu, L.; Chen, T., Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica, 45, 2, 324-332, (2009) · Zbl 1158.93365
[47] Liu, Y.J.; Xie, L.; Ding, F., An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems, Proceedings of the institution of mechanical engineers, part I: journal of systems and control engineering, 223, 4, 445-454, (2009)
[48] Ding, F.; Liu, G.; Liu, X.P., Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE transactions on automatic control, 55, 8, 1976-1981, (2010) · Zbl 1368.93121
[49] Ding, F.; Ding, J., Least squares parameter estimation with irregularly missing data, International journal of adaptive control and signal processing, 24, 7, 540-553, (2010) · Zbl 1200.93130
[50] Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063
[51] 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
[52] 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
[53] Wang, D.Q.; Chu, Y.Y.; Ding, F., Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems, Computers & mathematics with applications, 59, 9, 3092-3098, (2010) · Zbl 1193.93170
[54] Wang, D.Q.; Chu, Y.Y.; Yang, G.W.; Ding, F., Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems, Mathematical and computer modelling, 52, 1-2, 309-317, (2010) · Zbl 1201.93134
[55] Ding, F.; Liu, P.X.; Liu, G., Identification methods for Hammerstein nonlinear systems, Digital signal processing, (2010)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.