Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems

Mathematical and Computer Modelling

Volumn 55, Issue 3-4, 2012, Pages 442-450

  Li, Junhong ^a,b   Ding, Feng ^a,b   Yang, Guowei ^c  

^a JIANGNAN UNIVERSITY   (China)

^b NANTONG UNIVERSITY   (China)

^c NANCHANG HANGKONG UNIVERSITY   (China)

Author keywords

Hammerstein model; Least squares; Maximum likelihood; Nonlinear system; Parameter estimation; Recursive identification

Indexed keywords

HAMMERSTEIN MODEL; LEAST SQUARE; LEAST SQUARES IDENTIFICATION; MAXIMUM LIKELIHOOD PRINCIPLE; MOVING AVERAGES; NONLINEAR FINITE IMPULSE RESPONSE; RECURSIVE IDENTIFICATION;

ALGORITHMS; IMPULSE RESPONSE; LEAST SQUARES APPROXIMATIONS; MAXIMUM LIKELIHOOD; NONLINEAR SYSTEMS; PARAMETER ESTIMATION;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 80755154802     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.08.023     Document Type: Article

References (56)

1. Ding F., Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Transactions on Automatic Control 2005, 50(3):397-402.
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 2009, 50(7-8):1100-1106.
3. Zhang Y., Cui G.M. Bias compensation methods for stochastic systems with colored noise. Applied Mathematical Modelling 2011, 35(4):1709-1716.
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 2011, 53(9-10):1810-1819.
5. Cao Y.N., Liu Z.Q. Signal frequency and parameter estimation for power systems using the hierarchical identification principle. Mathematical and Computer Modelling 2010, 52(5-6):854-861.
6. Shi Y., Fang H. Kalman filter based identification for systems with randomly missing measurements in a network environment. International Journal of Control 2010, 83(3):538-551.
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 2011, 41(3):749-760.
8. Liu Y.J., Sheng J., Ding R.F. Convergence of stochastic estimation gradient algorithm for multivariable ARX-like systems. Computers & Mathematics with Applications 2010, 59(8):2615-2627.
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 2010, 90(4):1209-1224.
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 2010, 90(5):1582-1590.
11. Ljung L. System Identification: Theory for the User 1999, Prentice-Hall, Englewood Cliffs, NJ. 2nd ed.
12. Myung I.J. Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology 2003, 47(1):90-100.
13. Ding F., Chen T. Identification of Hammerstein nonlinear ARMAX systems. Automatica 2005, 41(9):1479-1489.
14. Chen J., Zhang Y., Ding R.F. Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Mathematical and Computer Modelling 2010, 52(9-10):1428-1434.
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 2010, 59(9):3092-3098.
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 2010, 52(1-2):309-317.
17. Ding F., Liu X.P., Liu G. Identification methods for Hammerstein nonlinear systems. Digital Signal Processing 2011, 21(2):215-238.
18. Ahmadi M., Mojallali H. Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials. Applied Mathematical Modelling 2011, 35(4):1969-1982.
19. Wang D.Q., Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Computers & Mathematics with Applications 2008, 56(12):3157-3164.
20. Ding F., Shi Y., Chen T. Gradient based identification algorithms for nonlinear Hammerstein ARMAX models. Nonlinear Dynamics 2006, 45(1-2):31-43.
21. Ding F., Shi Y., Chen T. Auxiliary model-based least-squares identification methods for Hammerstein output-error systems. Systems & Control Letters 2007, 56(5):373-380.
22. Wang D.Q., Ding F. Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Processing 2011, 91(5):1182-1189.
23. 2=C. Mathematical and Computer Modelling 2009, 49(9-10):1937-1959.
24. Dehghan M., Hajarian M. An efficient algorithm for solving general coupled matrix equations and its application. Mathematical and Computer Modelling 2010, 51(9-10):1118-1134.
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 2011, 53(9-10):1664-1669.
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 2010, 20(3):664-677.
27. Ding F., Chen T. Gradient based iterative algorithms for solving a class of matrix equations. IEEE Transactions on Automatic Control 2005, 50(8):1216-1221.
28. Ding F., Chen T. Iterative least squares solutions of coupled Sylvester matrix equations. Systems & Control Letters 2005, 54(2):95-107.
29. Ding F., Chen T. On iterative solutions of general coupled matrix equations. SIAM Journal on Control and Optimization 2006, 44(6):2269-2284.
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 2008, 197(1):41-50.
31. Xie L., Ding J., Ding F. Gradient based iterative solutions for general linear matrix equations. Computers & Mathematics with Applications 2009, 58(7):1441-1448.
32. Ding F. Transformations between some special matrices. Computers & Mathematics with Applications 2010, 59(8):2676-2695.
33. Ding J., Liu Y.J., Ding F. Iterative solutions to matrix equations of form AiXBi=Fi. Computers & Mathematics with Applications 2010, 59(11):3500-3507.
34. TD=F. Applied Mathematics and Computation 2010, 217(5):2191-2199.
35. Wang W., Li J.H., Ding R.F. Maximum likelihood identification algorithm for controlled autoregressive autoregressive models. International Journal of Computer Mathematics 2011, 10.1080/00207160.2011.598514.
36. Wang W., Ding F., Dai J.Y. Maximum likelihood least squares identification for systems with autoregressive moving average noise. Applied Mathematical Modelling 2012, 36(x). 10.1016/j.apm.2011.07.083.
37. Ding F., Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica 2007, 43(1):1-14.
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 2009, 215(4):1477-1483.
39. Han L.L., Ding F. Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digital Signal Processing 2009, 19(4):545-554.
40. Ding F., Liu P.X., Liu G. Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Processing 2009, 89(10):1883-1890.
41. Zhang J.B., Ding F., Shi Y. Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Systems & Control Letters 2009, 58(1):69-75.
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 2010, 40(3):767-778.
43. Ding F. Several multi-innovation identification methods. Digital Signal Processing 2010, 20(4):1027-1039.
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 2010, 20(3):750-762.
45. Ding F., Chen T. Identification of dual-rate systems based on finite impulse response models. International Journal of Adaptive Control and Signal Processing 2004, 18(7):589-598.
46. Ding F., Chen T. Least squares based self-tuning control of dual-rate systems. International Journal of Adaptive Control and Signal Processing 2004, 18(8):697-714.
47. Ding F., Chen T. Combined parameter and output estimating of dual-rate systems using an auxiliary model. Automatica 2004, 40(10):1739-1748.
48. Ding F., Chen T. Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Transactions on Automatic Control 2005, 50(9):1436-1441.
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 2005, 52(6):1179-1187.
50. Ding F., Chen T. A gradient based adaptive control algorithm for dual-rate systems. Asian Journal of Control 2006, 8(4):314-323.
51. Ding F., Chen T., Iwai Z. Adaptive digital control of Hammerstein nonlinear systems with limited output sampling. SIAM Journal on Control and Optimization 2007, 45(6):2257-2276.
52. Ding F., Qiu L., Chen T. Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 2009, 45(2):324-332.
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 2009, 223(4):445-454.
54. Ding F., Liu G., Liu X.P. Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Transaction on Automatic Control 2010, 55(8):1976-1981.
55. Ding F., Ding J. Least squares parameter estimation with irregularly missing data. International Journal of Adaptive Control and Signal Processing 2010, 24(7):540-553.
56. Ding F., Liu G., Liu X.P. Parameter estimation with scarce measurements. Automatica 2011, 47(8):1646-1655.