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Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering. (English) Zbl 1225.62120

Summary: By using an estimated noise transfer function to filter the input-output data, two identification models are obtained for the non-uniformly sampled Box-Jenkins system, one containing the parameters of the system model, and the other containing the parameters of the noise model. Then we apply the recursive least squares method to identify the parameters of these two models, by replacing the unmeasurable terms in the information vectors with their estimates. Thus a filtering based recursive least squares algorithm is finally derived. The given illustrative example indicates that the proposed algorithm can generate more accurate parameter estimates compared with the auxiliary model based recursive generalized extended least squares algorithm.

MSC:

62M09 Non-Markovian processes: estimation
62M20 Inference from stochastic processes and prediction
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[1] Lewis, S.J.; Raval, A.; Angus, J.E., Bayesian Monte Carlo estimation for profile hidden Markov models, Mathematical and computer modelling, 47, 11-12, 1198-1216, (2008) · Zbl 1145.62313
[2] Figueroa, J.L.; Biagiola, S.I.; Agamennoni, O.E., An approach for identification of uncertain Wiener systems, Mathematical and computer modelling, 48, 1-2, 305-315, (2008) · Zbl 1145.93432
[3] Pektas, B., Modelling and computer simulation of the identification problem related to the sludge concentration in a settler, Mathematical and computer modelling, 49, 5-6, 843-855, (2009) · Zbl 1165.76368
[4] 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)
[5] Ding, F.; Liu, P.X.; Liu, G.J., Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital signal processing, 20, 3, 664-677, (2010)
[6] Han, H.Q.; Xie, L.; Liu, X.G.; Ding, F., 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
[7] 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
[8] Xie, L.; Liu, Y.J.; Yang, H.Z., Gradient based and least squares based iterative algorithms for matrix equations \(A X B + C X^{\operatorname{T}} D = F\), Applied mathematics and computation, 217, 5, 2191-2199, (2010) · Zbl 1210.65097
[9] Ding, F., Transformations between some special matrices, Computers & mathematics with applications, 59, 8, 2676-2695, (2010) · Zbl 1193.15028
[10] Ding, F.; Chen, T.; Xiao, D.Y., State-space modeling and hierarchical identification for general dual-rate stochastic systems, Acta automatica sinica, 30, 5, 652-663, (2004)
[11] 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
[12] Li, D.; Shah, S.L.; Chen, T., Analysis of dual-rate inferential control systems, Automatica, 38, 6, 1053-1059, (2002) · Zbl 1038.93033
[13] Salt, J.L.; Albertos, P., Model-based multirate controllers design, IEEE transactions on control systems technology, 13, 6, 988-997, (2005)
[14] Wang, X.R.; Huang, B.; Chen, T., Multirate minimum variance control design and control performance assessment: a data-driven subspace approach, IEEE transactions on control systems technology, 15, 1, 65-74, (2007)
[15] Zhu, Y.; Telkamp, H., System identification using slow and inregular output samples, Journal of process control, 19, 1, 58-67, (2009) · Zbl 1198.93223
[16] Ding, F.; Chen, T.; Xiao, D.Y., Identification of non-uniformly periodically sampled multirate systems, Acta electronica sinica, 32, 9, 1414-1420, (2004)
[17] 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
[18] Xie, L.; Yang, H.Z., Gradient based iterative identification for non-uniform sampling output error systems, Journal of vibration and control, 17, 3, 471-478, (2011) · Zbl 1271.93046
[19] 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 & control engineering, 223, 4, 445-454, (2009)
[20] Jiang, H.X.; Wang, J.H.; Ding, F., Least-squares-iterative identification of a class of non-uniformly sampled-data systems, Systems engineering and electronics, 30, 8, 1535-1539, (2008) · Zbl 1174.93623
[21] L. Xie, H.Z. Yang, F. Ding, Filtering based recursive least squares identification for non-uniformly sampled systems, in: 2010 Chinese Control and Decision Conference, Xuzhou, China, 2010, pp. 1123-1128.
[22] Xie, L.; Liu, Y.J.; Yang, H.Z.; Ding, F., Modelling and identification for non-uniformly periodically sampled-data systems, IET control theory & applications, 4, 5, 784-794, (2010)
[23] Li, W.H.; Han, Z.; Shah, S.L., Subspace identification for FDI in systems with non-uniformly sampled multirate data, Automatica, 42, 4, 619-627, (2006) · Zbl 1102.93013
[24] Li, W.H.; Shah, S.L.; Xiao, D.Y., Kalman filters in non-uniformly sampled multirate systems: for FDI and beyond, Automatica, 44, 1, 199-208, (2008) · Zbl 1138.93056
[25] Sheng, J.; Chen, T.; Shah, S.L., Generalized predictive control for non-uniformly sampled systems, Journal of process control, 12, 8, 875-885, (2002)
[26] 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)
[27] 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
[28] 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)
[29] Liu, Y.J.; Sheng, J.; Ding, R.F., Convergence of stochastic estimation gradient algorithm for multivariable ARX-like systems, Computers & mathematics with applications, 59, 8, 2615-2627, (2010) · Zbl 1193.60057
[30] 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
[31] Ding, F.; Liu, P.X.; Liu, G., Identification methods for Hammerstein nonlinear systems, Digital signal processing, 21, 2, 215-238, (2011)
[32] Chen, J.; Zhang, Y.; Ding, R.F., Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems, Mathematical and computer modelling, 52, 9-10, 1428-1434, (2010) · Zbl 1205.93142
[33] 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
[34] 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
[35] Ding, F.; Shi, Y.; Chen, T., Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems & control letters, 56, 5, 373-380, (2007) · Zbl 1130.93055
[36] Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[37] Ding, F., Several multi-innovation identification methods, Digital signal processing, 20, 4, 1027-1039, (2010)
[38] 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)
[39] 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
[40] Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009)
[41] 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
[42] 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
[43] 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
[44] Ding, F.; Liu, P.X.; Liu, G., Multi-innovation least squares identification for system modeling, IEEE transactions on systems, man, and cybernetics, part B: cybernetics, 40, 3, 767-778, (2010)
[45] 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
[46] 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)
[47] 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
[48] Wang, D.Q.; Ding, F., Least squares based and gradient based iterative identification for Wiener nonlinear systems, Signal processing, 91, 5, 1182-1189, (2011) · Zbl 1219.94052
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