Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. (English) Zbl 1255.93147

Li, Junhong; Ding, Feng; Yang, Guowei

Math. Comput. Modelling 55, No. 3-4, 442-450 (2012).

Summary: According to the maximum likelihood principle, a maximum likelihood least squares identification method is presented for input nonlinear finite impulse response moving average (IN-FIR-MA) systems (e.g., Hammerstein FIR-MA systems). The simulation results indicate that the proposed algorithm is effective.

MSC:

93E12	Identification in stochastic control theory
62F10	Point estimation

Keywords:

least squares; parameter estimation; recursive identification; maximum likelihood; Hammerstein model; nonlinear system

References:

[1]	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
[2]	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
[3]	Zhang, Y.; Cui, G.M., Bias compensation methods for stochastic systems with colored noise, Applied mathematical modelling, 35, 4, 1709-1716, (2011) · Zbl 1217.93163
[4]	Zhang, Y., Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods, Mathematical and computer modelling, 53, 9-10, 1810-1819, (2011) · Zbl 1219.93141
[5]	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
[6]	Shi, Y.; Fang, H., Kalman filter based identification for systems with randomly missing measurements in a network environment, International journal of control, 83, 3, 538-551, (2010) · Zbl 1222.93228
[7]	Sun, X.F.; Rosin, P.L.; Martin, R.R., Fast rule identification and neighborhood selection for cellular automata, IEEE transactions on systems, man and cybernetics-part B: cybernetics, 41, 3, 749-760, (2011)
[8]	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
[9]	Rizogiannis, C.; Kofidis, E.; Papadias, C.B.; Theodoridis, S., Semi-blind maximum-likelihood joint channel/data estimation for correlated channels in multiuser MIMO networks, Signal processing, 90, 4, 1209-1224, (2010) · Zbl 1197.94116
[10]	Krummenauer, R.; Cazarotto, M.; Lopes, A.; Larzabal, P.; Forster, P., Improving the threshold performance of maximum likelihood estimation of direction of arrival, Signal processing, 90, 5, 1582-1590, (2010) · Zbl 1194.94101
[11]	Ljung, L., System identification: theory for the user, (1999), Prentice-Hall Englewood Cliffs, NJ
[12]	Myung, I.J., Tutorial on maximum likelihood estimation, Journal of mathematical psychology, 47, 1, 90-100, (2003) · Zbl 1023.62112
[13]	Ding, F.; Chen, T., Identification of Hammerstein nonlinear ARMAX systems, Automatica, 41, 9, 1479-1489, (2005) · Zbl 1086.93063
[14]	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
[15]	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
[16]	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
[17]	Ding, F.; Liu, X.P.; Liu, G., Identification methods for Hammerstein nonlinear systems, Digital signal processing, 21, 2, 215-238, (2011)
[18]	Ahmadi, M.; Mojallali, H., Identification of multiple-input single-output Hammerstein models using bezier curves and Bernstein polynomials, Applied mathematical modelling, 35, 4, 1969-1982, (2011) · Zbl 1217.93171
[19]	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
[20]	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
[21]	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
[22]	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
[23]	Dehghan, M.; Hajarian, M., Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation \(A_1 X_1 B_1 + A_2 X_2 B_2 = C\), Mathematical and computer modelling, 49, 9-10, 1937-1959, (2009) · Zbl 1171.15310
[24]	Dehghan, M.; Hajarian, M., An efficient algorithm for solving general coupled matrix equations and its application, Mathematical and computer modelling, 51, 9-10, 1118-1134, (2010) · Zbl 1208.65054
[25]	Bao, B.; Xu, Y.Q.; Sheng, J.; Ding, R.F., Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data, Mathematical and computer modelling, 53, 9-10, 1664-1669, (2011) · Zbl 1219.62133
[26]	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)
[27]	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
[28]	Ding, F.; Chen, T., Iterative least squares solutions of coupled Sylvester matrix equations, Systems & control letters, 54, 2, 95-107, (2005) · Zbl 1129.65306
[29]	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
[30]	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
[31]	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
[32]	Ding, F., Transformations between some special matrices, Computers & mathematics with applications, 59, 8, 2676-2695, (2010) · Zbl 1193.15028
[33]	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
[34]	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
[35]	Wang, W.; Li, J.H.; Ding, R.F., Maximum likelihood identification algorithm for controlled autoregressive autoregressive models, International journal of computer mathematics, (2011) · Zbl 1248.93161
[36]	Wang, W.; Ding, F.; Dai, J.Y., Maximum likelihood least squares identification for systems with autoregressive moving average noise, Applied mathematical modelling, 36, x, (2012) · Zbl 1242.62105
[37]	Ding, F.; Chen, T., Performance analysis of multi-innovation gradient type identification methods, Automatica, 43, 1, 1-14, (2007) · Zbl 1140.93488
[38]	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
[39]	Han, L.L.; Ding, F., Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital signal processing, 19, 4, 545-554, (2009)
[40]	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
[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., Multi-innovation least squares identification for system modeling, IEEE transactions on systems, man, and cybernetics, part B: cybernetics, 40, 3, 767-778, (2010)
[43]	Ding, F., Several multi-innovation identification methods, Digital signal processing, 20, 4, 1027-1039, (2010)
[44]	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)
[45]	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
[46]	Ding, F.; Chen, T., Least squares based self-tuning control of dual-rate systems, International journal of adaptive control and signal processing, 18, 8, 697-714, (2004) · Zbl 1055.93044
[47]	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
[48]	Ding, F.; Chen, T., Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE transactions on automatic control, 50, 9, 1436-1441, (2005) · Zbl 1365.93480
[49]	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
[50]	Ding, F.; Chen, T., A gradient based adaptive control algorithm for dual-rate systems, Asian journal of control, 8, 4, 314-323, (2006)
[51]	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, (2007) · Zbl 1126.93034
[52]	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
[53]	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)
[54]	Ding, F.; Liu, G.; Liu, X.P., Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE transaction on automatic control, 55, 8, 1976-1981, (2010) · Zbl 1368.93121
[55]	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
[56]	Ding, F.; Liu, G.; Liu, X.P., Parameter estimation with scarce measurements, Automatica, 47, 8, 1646-1655, (2011) · Zbl 1232.62043