Two-stage least squares based iterative identification algorithm for controlled autoregressive moving average (CARMA) systems

Computers and Mathematics with Applications

Volumn 63, Issue 5, 2012, Pages 975-984

  Yao, Guoyu ^a   Ding, Ruifeng ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Iterative algorithm; Least squares; Parameter estimation; Two stage identification

Indexed keywords

COMPUTATIONAL EFFICIENCY; COVARIANCE MATRIX; GAUSSIAN NOISE (ELECTRONIC); PARAMETER ESTIMATION;

AUTOREGRESSIVE MOVING AVERAGE; COVARIANCE MATRICES; IDENTIFICATION ALGORITHMS; ITERATIVE ALGORITHM; ITERATIVE IDENTIFICATION; LEAST SQUARE; TWO STAGE LEAST SQUARES; TWO-STAGE IDENTIFICATION;

ITERATIVE METHODS;

EID: 84865661437     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.12.002     Document Type: Article

References (80)

1. M. Dehghan, M. Hajarian, Matrix equations over (R,S)-symmetric and (R,S)-skew symmetric matrices, Computers & Mathematics with Applications 59 (11) (2010) 3583-3594
2. M. Dehghan, M. Hajarian, An iterative algorithm for solving a pair of matrix equations AYB=E, CYD=F over generalized centro-symmetric matrices, Computers & Mathematics with Applications 56 (12) (2008) 3246-3260
3. M. Dehghan, M. Hajarian, An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices, Applied Mathematical Modelling 34 (3) (2010) 639-654
4. M. Dehghan, M. Hajarian, Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1 + A2X2B2 = C, Mathematical and Computer Modelling 49 (9-10) (2009) 1937-1959
5. L. Xie, J. Ding, F. Ding, Gradient based iterative solutions for general linear matrix equations, Computers & Mathematics with Applications 58 (7) (2009) 1441-1448
6. J. Ding, Y.J. Liu, F. Ding, Iterative solutions to matrix equations of form AiXBi = Fi, Computers & Mathematics with Applications 59 (11) (2010) 3500-3507
7. F. Ding, T. Chen, Gradient based iterative algorithms for solving a class of matrix equations, IEEE Transactions on Automatic Control 50 (8) (2005) 1216-1221 (Pubitemid 41410122)
8. L. Xie, J. Ding, F. Ding, Gradient based iterative solutions for general linear matrix equations, Computers and Mathematics with Applications 58 (7) (2009) 1441-1448
9. A.G. Wu, B. Li, Y. Yang, G.R. Duan, Finite iterative solutions to coupled Sylvester-conjugate matrix equations, Applied Mathematical Modelling 35 (3) (2011) 1065-1080
10. Y. Shi, H. Fang, Kalman filter based identification for systems with randomly missing measurements in a network environment, International Journal of Control 83 (3) (2010) 538-551
11. Y. Shi, H. Fang, M. Yan, Kalman filter based adaptive control for networked systems with unknown parameters and randomly missing outputs, International Journal of Robust and Nonlinear Control 19 (18) (2009) 1976-1992. (special issue on control with limited information (part II)
12. B. Yu, Y. Shi, H. Huang, l-2 and l-infnity filtering for multirate systems using lifted models, Circuits, Systems, and Signal Processing 27 (5) (2008) 699-711
13. H. Fang, J. Wu, Y. Shi, Genetic adaptive state estimation with missing input/output data, Proceedings of the Institution of Mechanical Engineers-Part I: Journal of Systems and Control Engineering 224 (5) (2010) 611-617
14. Y. Shi, F. Ding, T. Chen, 2-norm based recursive design of transmultiplexers with designable filter length, Circuits, Systems and Signal Processing 25 (4) (2006) 447-462 (Pubitemid 44480296)
15. Y.S. Xiao, Y. Zhang, J. Ding, J.Y. Dai, The residual based interactive least squares algorithms and simulation studies, Computers & Mathematics with Applications 58 (6) (2009) 1190-1197
16. L.Y. Wang, L. Xie, X.F. Wang, The residual based interactive stochastic gradient algorithms for controlled moving average models, Applied Mathematics and Computation 211 (2) (2009) 442-449
17. F. Ding, T. Chen, L. Qiu, Bias compensation based recursive least squares identification algorithm for MISO systems, IEEE Transactions on Circuits and Systems - II: Express Briefs 53 (5) (2006) 349-353 (Pubitemid 43786576)
18. F. Ding, Y. Shi, T. Chen, Performance analysis of estimation algorithms of non-stationary ARMA processes, IEEE Transactions on Signal Processing 54 (3) (2006) 1041-1053 (Pubitemid 43280579)
19. F. Ding, P.X. Liu, G.L. Liu, Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital Signal Processing 20 (3) (2010) 664-677
20. D.Q. Wang, G.W. Yang, R.F. Ding, Gradient-based iterative parameter estimation for Box-Jenkins systems, Computers & Mathematics with Applications 60 (5) (2010) 1200-1208
21. Y.J. Liu, D.Q. Wang, F. Ding, Least squares based iterative identification for identifying Box-Jenkins models with finite measurement date, Digital Signal Processing 20 (5) (2010) 1458-1467
22. F. Ding, T. Chen, Identification of Hammerstein nonlinear ARMAX systems, Automatica 41 (9) (2005) 1479-1489 (Pubitemid 41000116)
23. H.Q. Han, L. Xie, F. Ding, X.G. Liu, Hierarchical least-squares based iterative identification for multivariable systems with moving average noises, Automatica 51 (9-10) (2010) 1213-1220
24. Z.N. Zhang, F. Ding, X.G. Liu, Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems, Computers & Mathematics with Applications 61 (3) (2011) 672-682
25. B. Bao, Y.Q. Xu, J. Sheng, R.F. Ding, Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data, Mathematical and Computer Modelling 53 (9-10) (2011) 1664-1669
26. F. Ding, Y.J. Liu, B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering (2011), in press (doi:10.1177/0959651811409491
27. E.W. Bai, An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems, Automatica 34 (3) (1998) 333-338
28. K. Li, J.X. Peng, E. Bai, A two-stage algorithm for identification of nonlinear dynamic systems, Automatica 42 (7) (2006) 1189-1197 (Pubitemid 43767490)
29. S.H. Hwang, S.T. Lai, Use of two-stage least-squares algorithms for identification of continuous systems with time delay based on pulse responses, Automatica 40 (9) (2004) 1561-1568
30. Z.H. Cao, Rounding error analysis of two-stage iterative methods for large linear systems, Applied Mathematics and Computation 139 (2-3) (2003) 371-381
31. H.H. Duan, J. Jia, R.F. Ding, Two-stage recursive least squares parameter estimation algorithm for output error models, Mathematical and Computer Modelling 55 (x) (2012) doi:10.1016/j.mcm.2011.09.039
32. D.Q. Wang, F. Ding, Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems, Computers & Mathematics with Applications 56 (12) (2008) 3157-3164
33. J. Chen, Y. Zhang, R.F. Ding, Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems, Mathematical and Computer Modelling 52 (9-10) (2010) 1428-1434
34. D.Q. Wang, Least squares-based recursive and iterative estimation for output error moving average (OEMA) systems using data filtering, IET Control Theory and Applications 5 (14) (2011) 1648-1657
35. D.Q. Wang, F. Ding, Input-output data filtering based recursive least squares parameter estimation for CARARMA systems, Digital Signal Processing 20 (4) (2010) 991-999
36. L.L. Han, F. Ding, Parameter estimation for multirate multi-input systems using auxiliary model and multi-innovation, Journal of Systems Engineering and Electronics 21 (6) (2010) 1079-1083
37. L.L. Han, F. Ding, Identification for multirate multi-input systems using the multi-innovation identification theory, Computers & Mathematics with Applications 57 (9) (2009) 1438-1449
38. F. Ding, T. Chen, Combined parameter and output estimation of dual-rate systems using an auxiliary model, Automatica 40 (10) (2004) 1739-1748
39. F. Ding, T. Chen, Identification of dual-rate systems based on finite impulse response models, International Journal of Adaptive Control and Signal Processing 18 (7) (2004) 589-598
40. F. Ding, T. Chen, Least squares based self-tuning control of dual-rate systems, International Journal of Adaptive Control and Signal Processing 18 (8) (2004) 697-714
41. F. Ding, T. Chen, Parameter estimation of dual-rate stochastic systems by using an output error method, IEEE Transactions on Automatic Control 50 (9) (2005) 1436-1441 (Pubitemid 41388188)
42. Y.J. Liu, J. Sheng, R.F. Ding, Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems, Computers & Mathematics with Applications 59 (8) (2010) 2615-2627
43. F. Ding, T. Chen, Performance analysis of multi-innovation gradient type identification methods, Automatica 43 (1) (2007) 1-14 (Pubitemid 44792035)
44. Y.J. Liu, Y.S. Xiao, X.L. Zhao, Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model, Applied Mathematics and Computation 215 (4) (2009) 1477-1483
45. F. Ding, P.X. Liu, G. Liu, Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal Processing 89 (10) (2009) 1883-1890
46. J.B. Zhang, F. Ding, Y. Shi, Self-tuning control based on multi-innovation stochastic gradient parameter estimation, Systems & Control Letters 58 (1) (2009) 69-75
47. F. Ding, P.X. Liu, G. Liu, Multi-innovation least squares identification for system modeling, IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 40 (3) (2010) 767-778
48. F. Ding, Several multi-innovation identification methods, Digital Signal Processing 20 (4) (2010) 1027-1039
49. D.Q. Wang, F. Ding, Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems, Digital Signal Processing 20 (3) (2010) 750-762
50. L. Xie, H.Z. Yang, F. Ding, Modeling and identification for non-uniformly periodically sampled-data systems, IET Control Theory & Applications 4 (5) (2010) 784-794
51. L.L. Han, F. Ding, Multi-innovation stochastic gradient algorithms for multi-input multi-output systems, Digital Signal Processing 19 (4) (2009) 545-554
52. Y.J. Liu, L. Yu, F. Ding, Multi-innovation extended stochastic gradient algorithm and its performance analysis, Circuits, Systems and Signal Processing 29 (4) (2010) 649-667
53. F. Ding, T. Chen, Hierarchical gradient-based identification of multivariable discrete-time systems, Automatica 41 (2) (2005) 315-325 (Pubitemid 41536582)
54. F. Ding, T. Chen, Hierarchical least squares identification methods for multivariable systems, IEEE Transactions on Automatic Control 50 (3) (2005) 397-402 (Pubitemid 40448592)
55. F. Ding, T. Chen, Hierarchical identification of lifted state-space models for general dual-rate systems, IEEE Transactions on Circuits and Systems - I: Regular Papers 52 (6) (2005) 1179-1187 (Pubitemid 40970287)
56. F. Ding, T. Chen, A gradient based adaptive control algorithm for dual-rate systems, Asian Journal of Control 8 (4) (2006) 314-323
57. F. Ding, T. Chen, Z. Iwai, Adaptive digital control of Hammerstein nonlinear systems with limited output sampling, SIAM Journal on Control and Optimization 45 (6) (2007) 2257-2276 (Pubitemid 350171715)
58. F. Ding, L. Qiu, T. Chen, Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems, Automatica 45 (2) (2009) 324-332
59. Y.J. Liu, L. Xie, F. Ding, 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) (2009) 445-454
60. F. Ding, G. Liu, X.P. Liu, Partially coupled stochastic gradient identification methods for non-uniformly sampled systems, IEEE Transactions on Automatic Control 55 (8) (2010) 1976-1981
61. F. Ding, J. Ding, Least squares parameter estimation with irregularly missing data, International Journal of Adaptive Control and Signal Processing 24 (7) (2010) 540-553
62. F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements, Automatica 47 (8) (2011) 1646-1655
63. L. Xie, H.Z. Yang, F. Ding, Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering, Mathematical and Computer Modelling 54 (1-2) (2011) 315-324
64. J. Chen, F. Ding, Modified stochastic gradient algorithms with fast convergence rates, Journal of Vibration and Control 17 (9) (2011) 1281-1286
65. J. Ding, Y. Shi, H.G. Wang, F. Ding, A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems, Digital Signal Processing 20 (4) (2010) 1238-1249
66. F. Ding, P.X. Liu, H.Z. Yang, Parameter identification and intersample output estimation for dual-rate systems, IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 38 (4) (2008) 966-975
67. F. Ding, H.Z. Yang, F. Liu, Performance analysis of stochastic gradient algorithms under weak conditions, Science in China Series F: Information Sciences 51 (9) (2008) 1269-1280
68. F. Ding, T. Chen, Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data, IEEE Transactions on Circuits and Systems - I: Regular Papers 52 (3) (2005) 555-566 (Pubitemid 40466884)
69. W. Wang, F. Ding, J.Y. Dai, Maximum likelihood least squares identification for systems with autoregressive moving average noise, Applied Mathematical Modelling 36 (x) (2012) doi:10.1016/j.apm.2011.07.083
70. J. Ding, F. Ding, X.P. Liu, G. Liu, Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data, IEEE Transactions on Automatic Control 56 (11) (2011) 2677-2683
71. J. Ding, F. Ding, Bias compensation based parameter estimation for output error moving average systems, International Journal of Adaptive Control and Signal Processing 25 (12) (2011) 1100-1111
72. L.F. Zhuang, F. Pan, F. Ding, Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models, Applied Mathematical Modelling 26 (x) (2012) doi:10.1016/j.apm.2011.10. 028
73. J.H. Li, F. Ding, Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique, Computers & Mathematics with Applications 62 (11) (2011) 4170-4177
74. F. Ding, P.X. Liu, G. Liu, Identification methods for Hammerstein nonlinear systems, Digital Signal Processing 21 (2) (2011) 215-238
75. D.Q. Wang, Y.Y. Chu, F. Ding, Auxiliary model-based RELS and MI-ELS algorithms for Hammerstein OEMA systems, Computers & Mathematics with Applications 59 (9) (2010) 3092-3098
76. D.Q. Wang, Y.Y. Chu, G.W. Yang, F. Ding, Auxiliary model-based recursive generalized least squares parameter estimation for Hammerstein OEAR systems, Mathematical and Computer Modelling 52 (1-2) (2010) 309-317
77. D.Q. Wang, F. Ding, Least squares based and gradient based iterative identification for Wiener nonlinear systems, Signal Processing 91 (5) (2011) 1182-1189
78. F. Ding, Y. Shi, T. Chen, Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Systems & Control Letters 56 (5) (2007) 373-380 (Pubitemid 46435731)
79. F. Ding, Y. Shi, T. Chen, Gradient-based identification methods for Hammerstein nonlinear ARMAX models, Nonlinear Dynamics 45 (1-2) (2006) 31-43 (Pubitemid 44048446)
80. D.Q. Wang, F. Ding, Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems, Computers & Mathematics with Applications 56 (12) (2008) 3157-3164.