Maximum likelihood Newton recursive and the Newton iterative estimation algorithms for Hammerstein CARAR systems

Nonlinear Dynamics

Volumn 75, Issue 1-2, 2014, Pages 235-245

  Li, Junhong ^a,b   Ding, Feng ^b   Hua, Liang ^a  

^a NANTONG UNIVERSITY   (China)

^b JIANGNAN UNIVERSITY   (China)

Author keywords

Hammerstein models; Maximum likelihood; Newton iterative algorithm; Newton recursive algorithm; Parameter estimation

Indexed keywords

AUTO-REGRESSIVE; HAMMERSTEIN MODEL; IDENTIFICATION PROBLEM; ITERATIVE ALGORITHM; ITERATIVE ESTIMATION; MAXIMUM LIKELIHOOD PRINCIPLE; NEWTON OPTIMIZATIONS; RECURSIVE ALGORITHMS;

ALGORITHMS; MAXIMUM LIKELIHOOD; PARAMETER ESTIMATION;

ITERATIVE METHODS;

EID: 84891559805     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-1061-y     Document Type: Article

References (42)

1. Kolodziej, R.K.; Joseph Mook, D.: Model determination for nonlinear state-based system identification. Nonlinear Dyn. 63(4), 735-753 (2011)
2. Hu, P.P.; Ding, F.: Multistage least squares based iterative estimation for feedback nonlinear systems with moving average noises using the hierarchical identification principle. Nonlinear Dyn. 73(1-2), 583-592 (2013)
3. Chen, J.; Zhang, Y.; Ding, R.F.: Gradient-based parameter estimation for input nonlinear systems with ARMA noises based on the auxiliary model. Nonlinear Dyn. 72(4), 865-871 (2013)
4. Sun, J.L.; Liu, X.G.: A novel APSO-aided maximum likelihood identification method for Hammerstein systems. Nonlinear Dyn. 73(1-2), 449-462 (2013)
5. Vörös, J.: Modeling and identification of systems with backlash. Automatica 46(2), 369-374 (2010)
6. Vörös, J.: Recursive identification of systems with noninvertible output nonlinearities. Informatica 21(1), 139-148 (2010)
7. Ding, F.: Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694-1704 (2013)
8. Vörös, J.: Iterative algorithm for parameter identification of Hammerstein systems with two-Segment nonlinearities. IEEE Trans. Autom. Control 44(11), 2145-2149 (1999)
9. Wang, D.Q.; Chu, Y.Y.; Yang, G.W.; et al.: Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems. Math. Comput. Model. 52(1-2), 309-317 (2010)
10. Ding, F.; Liu, X.G.; Chu, J.: Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle. IET Control Theory Appl. 7(2), 176-184 (2013)
11. Zhang, Y.; Cui, G.M.: Bias compensation methods for stochastic systems with colored noise. Appl. Math. Model. 35(4), 1709-1716 (2011)
12. Ding, F.: Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798-4808 (2013)
13. Ding, F.: Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235-1242 (2013)
14. Ding, F.; Liu, Y.J.; Bao, B.: Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng.; Part I, J. Syst. Control Eng. 226(1), 43-55 (2012)
15. Shi, Y.; Fang, H.Z.: Kalman filter-based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538-551 (2010)
16. i. Comput. Math. Appl. 59(11), 3500-3507 (2010)
17. Dehghan, M.; Hajarian, M.: Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 35(7), 3285-3300 (2011)
18. Shi, J.; Liu, X.G.: Melt index prediction by weighted least squares support vector machines. J. Appl. Polym. Sci. 101(1), 285-289 (2006)
19. Jiang, H.Q.; Yan, Z.B.; Liu, X.G.: Melt index prediction using optimized least squares support vector machines based on hybrid particle swarm optimization algorithm. Neurocomputing 119, 469-477 (2013)
20. Zhang, M.; Liu, X.G.: Melt index prediction by fuzzy functions and weighted least squares support vector machines optimized by particle swarm optimization. Chem. Eng. Technol. 36(9), 1577-1584 (2013)
21. Liu, X.G.; Lu, J.: Least squares based iterative identification for a class of multirate systems. Automatica 46(3), 549-554 (2010)
22. Wang, D.Q.: Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648-1657 (2011)
23. Ding, F.: Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7(1), 68-79 (2013)
24. Liu, Y.J.; Wang, D.Q.; et al.: Least squares based iterative algorithms for identifying box - Jenkins models with finite measurement data. Digit. Signal Process. 20(5), 1458-1467 (2010)
25. Ding, F.; Liu, X.P.; Liu, G.: Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 20(3), 664-677 (2010)
26. Li, J.H.; Ding, R.F.; Yang, Y.: Iterative parameter identification methods for nonlinear functions. Appl. Math. Model. 36(6), 2739-2750 (2012)
27. Li, J.H.; Ding, R.: Parameter estimation methods for nonlinear systems. Appl. Math. Comput. 219(9), 4278-4287 (2013)
28. Hagenblad, A.; Ljung, L.; Wills, A.: Maximum likelihood identification of Wiener models. Automatica 44(11), 2697-2705 (2008)
29. Vanbeylen, L.; Pintelon, R.; Schoukens, J.: Blind maximum-likelihood identification of Wiener systems. IEEE Trans. Signal Process. 57(8), 3017-3029 (2009)
30. Wang, W.; Ding, F.; Dai, J.Y.: Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 36(5), 1842-1853 (2012)
31. Schön, T.B.; Wills, A.; Ninness, B.: System identification of nonlinear state-space models. Automatica 47(1), 39-49 (2011)
32. Pence, B.L.; Fathy, H.K.; Stein, J.L.: Recursive maximum likelihood parameter estimation for state space systems using polynomial chaos theory. Automatica 47(11), 2420-2424 (2011)
33. Li, J.H.; Ding, F.: Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique. Comput. Math. Appl. 62(11), 4170-4177 (2011)
34. Li, J.H.; Ding, F.; Yang, G.W.: Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 55(3-4), 442-450 (2012)
35. Vanbeylen, L.; Pintelon, R.; Schoukens, J.: Blind maximum likelihood identification of Hammerstein systems. Automatica 44(12), 3139-3146 (2008)
36. Vanbeylen, L.; Pintelon, R.; Schoukens, J.: Blind maximum-likelihood identification of Wiener systems. IEEE Trans. Signal Process. 57(8), 3017-3029 (2009)
37. Dehghan, M.; Hajarian, M.: Fourth-order variants of Newton's method without second derivatives for solving non-linear equations. Eng. Comput. 29(4), 356-365 (2012)
38. Ding, F.; Liu, X.P.; Liu, G.: Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215-238 (2011)
39. Li, J.H.: Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91-96 (2013)
40. Ljung, L.; Söerström, T.: Theory and Practice of Recursive Identification. MIT Press, Cambridge (1983)
41. Ding, F.; Ma, J.X.; Xiao, Y.S.: Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn. 74(1-2), 21-30 (2013)
42. Wang, Z.Y.; Shen, Y.X.; Ji, Z.C.; Ding, R.: Filtering based recursive least squares algorithm for Hammerstein FIR-MA systems. Nonlinear Dyn. 73(1-2), 1045-1054 (2013)