Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models

Applied Mathematical Modelling

Volumn 36, Issue 8, 2012, Pages 3454-3463

  Zhuang, Linfan ^a   Pan, Feng ^a   Ding, Feng ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Least squares; Parameter estimation; Recursive identification; State estimation; State space model

Indexed keywords

ESTIMATED PARAMETER; HIERARCHICAL IDENTIFICATION PRINCIPLE; INFORMATION VECTOR; INPUT-OUTPUT DATA; LEAST SQUARE; LEAST SQUARES ALGORITHM; NEW PARAMETERS; NOISE TERMS; PARAMETER AND STATE ESTIMATION; RECURSIVE IDENTIFICATION; SINGLE INPUT SINGLE OUTPUT; SINGLE INPUT SINGLE OUTPUT SYSTEMS; STATE SPACE MODEL; SYSTEM STATE; UNKNOWN NOISE; UNKNOWN STATE;

ALGORITHMS; LINEAR SYSTEMS; STATE ESTIMATION; STATE SPACE METHODS;

PARAMETER ESTIMATION;

EID: 84859818704     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2011.10.028     Document Type: Article

References (59)

1. Singh V. Stability of discrete-time systems joined with a saturation operator on the state-space: Generalized form of Liu-Michel's criterion. Automatica 2011, 47(3):634-637.
2. Yan M., Shi Y. Robust discrete-time sliding mode control for uncertain systems with time-varying state delay. IET Control Theor. Appl. 2008, 2(8):662-674.
3. Han L.L., Sheng J., Ding F., Shi Y. Auxiliary model identification method for multirate multi-input systems based on least squares. Math. Comput. Modell. 2009, 50(7-8):1100-1106.
4. Shi Y., Yu B. Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Automat. Control 2009, 54(7):1668-1674.
5. Shi Y., Fang H. Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 2010, 83(3):538-551.
6. Xiao Y.S., Ding F., Zhou Y., Li M., Dai J.Y. On consistency of recursive least squares identification algorithms for controlled auto-regression models. Appl. Math. Modell. 2008, 32(11):2207-2215.
7. Zhang Y., Cui G.M. Bias compensation methods for stochastic systems with colored noise. Appl. Math. Modell. 2011, 35(4):1709-1716.
8. Wang L.Y., Xie L., Wang X.F. The residual based interactive stochastic gradient algorithms for controlled moving average models. Appl. Math. Comput. 2009, 211(2):442-449.
9. Xiao Y.S., Zhang Y., Ding J., Dai J.Y. The residual based interactive least squares algorithms and simulation studies. Comput. Math. Appl. 2009, 58(6):1190-1197.
10. Viberg M. Subspace-based methods for the identification of linear time-invariant systems. Automatica 1995, 31(12):1835-1851.
11. Lovera M., Gustafsson T., Verhaegen M. Recursive subspace identification of linear and non-linear Wiener state-space models. Automatica 2000, 36(11):1639-1650.
12. Ding F., Chen T. Hierarchical identification of lifted stated-space models for general dual-rate systems. IEEE Trans. Circ. Syst. I: Regular Papers 2005, 52(6):1179-1187.
13. 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.
14. Li D., Shah S.L., Chen T. Identification of fast-rate models from multirate data. Int. J. Control Automat. Syst. 2001, 74(7):680-689.
15. Ljung L. System Identification: Theory for the User 1999, Prentice-hall, Englewood Cliffs, NJ. second ed.
16. Ding F., Chen T. Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 2005, 41(2):315-325.
17. Zhang Y. Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods. Math. Comput. Modell. 2011, 53(9-10):1810-1819.
18. Ding J., Ding F. Bias compensation based parameter estimation for output error moving average systems. Int. J. Adapt. Control Signal Process. 2011, 10.1002/acs.1266.
19. Agero J.C., Yuz J.I., Goodwin G.C., Delgado R.A. On the equivalence of time and frequency domain maximum likelihood estimation. Automatica 2010, 46(2):260-270.
20. Söderström T., Hong M., Schoukens J., Pintelon R. Accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors-in-variables and output error identification. Automatica 2010, 46(4):721-727.
21. Wang W., Li J.H., Ding R.F. Maximum likelihood identification algorithm for controlled autoregressive autoregressive models. Int. J. Comput. Math. 2011, 88(16):3458-3467.
22. Wang W., Ding F., Dai J.Y. Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Modell. 2012, 36(x). 10.1016/j.apm.2011.07.083.
23. 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. Modell. 2012, 55(x). 10.1016/j.mcm.2011.08.023.
24. Han H.Q., Xie L., Ding F., Liu X.G. Hierarchical least squares based iterative identification for multivariable systems with moving average noises. Math. Comput. Modell. 2010, 51(9-10):1213-1220.
25. Zhang Z.N., Ding F., Liu X.G. Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Comput. Math. Appl. 2011, 61(3):672-682.
26. Xiang L.L., Xie L.B., Liao Y.W., Ding RF. Hierarchical least squares algorithms for single-input multiple-output systems based on the auxiliary model. Math. Comput. Modell. 2010, 52(5-6):918-924.
27. Wang D.Q., Yang G.W., Ding R.F. Gradient-based iterative parameter estimation for Box-Jenkins systems. Comput. Math. Appl. 2010, 60(5):1200-1208.
28. Liu Y.J., Sheng J., Ding R.F. Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems. Comput. Math. Appl. 2010, 59(8):2615-2627.
29. Chen J., Zhang Y., Ding R.F. Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Math. Comput. Modell. 2010, 52(9-10):1428-1434.
30. Wang D.Q., Ding F. Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Comput. Math. Appl. 2008, 56(12):3157-3164.
31. Li J.H., Ding R.F., Yang Y. Iterative parameter identification methods for nonlinear functions. Appl. Math. Modell. 2012, 26(x). 10.1016/j.apm.2011.09.057.
32. Ding F., Liu P.X., Liu G. Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digital Signal Process. 2010, 20(3):664-677.
33. Ding F., Liu P.X., Liu G. Identification methods for Hammerstein nonlinear systems. Digital Signal Process. 2011, 21(2):215-238.
34. Ding J., Ding F., Liu X.P., Liu G. Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Automat. Control 2011, 56(x). 10.1109/TAC.2011.2158137.
35. Xie L., Yang H.Z., Ding F. Recursive least squares parameter estimation for non-uniformly sampled systems based on the data filtering. Math. Comput. Modell. 2011, 54(1-2):315-324.
36. Chen L., Li J.H., Ding R.F. Identification of the second-order systems based on the step response. Math. Comput. Modell. 2011, 53(5-6):1074-1083.
37. Ding J., Han L.L., Chen X.M. Time series AR modeling with missing observations based on the polynomial transformation. Math. Comput. Modell. 2010, 51(5-6):527-536.
38. Ding F., Shi Y., Chen T. Auxiliary model based least-squares identification methods for Hammerstein output-error systems. Syst. Control Lett. 2007, 56(5):373-380.
39. Mercère G., Bako L. Parameterization and identification of multivariable state-space systems: A canonical approach. Automatica 2011, 47(8):1547-1555.
40. Ding F., Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica 2007, 43(1):1-14.
41. Han L.L., Ding F. Identification for multirate multi-input systems using the multi-innovation identification theory. Comput. Math. Appl. 2009, 57(9):1438-1449.
42. Liu Y.J., Xiao Y.S., Zhao X.L. Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 2009, 215(4):1477-1483.
43. Han L.L., Ding F. Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digital Signal Process. 2009, 19(4):545-554.
44. Ding F., Liu P.X., Liu G. Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 2009, 89(10):1883-1890.
45. Zhang J.B., Ding F., Shi Y. Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Syst. Control Lett. 2009, 58(1):69-75.
46. Xie L., Yang H.Z., Ding F. Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theor. Appl. 2010, 4(5):784-794.
47. Ding F., X Liu P., Liu G. Multi-innovation least squares identification for system modeling. IEEE Trans. Syst. Man Cybernet., Part B: Cybernet. 2010, 40(3):767-778.
48. Ding F. Several multi-innovation identification methods. Digital Signal Process. 2010, 20(4):1027-1039.
49. Wang D.Q., Ding F. Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems. Digital Signal Process. 2010, 20(3):750-762.
50. Liu Y.J., Xie L., Ding F. An auxiliary model based recursive least squares parameter estimation algorithm for non-uniformly sampled multirate systems. Proc. Institut. Mech. Engineers, Part I: J. Syst. Control Eng. 2009, 223(4):445-454.
51. Ding F., Liu G., Liu X.P. Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Automat. Control 2010, 55(8):1976-1981.
52. Ding F., Ding J. Least squares parameter estimation with irregularly missing data. Int. J. Adapt. Control Signal Process. 2010, 24(7):540-553.
53. Ding F., Liu G., Liu X.P. Parameter estimation with scarce measurements. Automatica 2011, 47(8):1646-1655.
54. Ding F., Chen T. Identification of dual-rate systems based on finite impulse response models. Int. J. Adapt. Control Signal Process. 2004, 18(7):589-598.
55. Ding F., Chen T. Least squares based self-tuning control of dual-rate systems. Int. J. Adapt. Control Signal Process. 2004, 18(8):697-714.
56. Ding F., Chen T. Combined parameter and output estimating of dual-rate systems using an auxiliary model. Automatica 2004, 40(10):1739-1748.
57. Ding F., Chen T. Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Trans. Automat. Control 2005, 50(9):1436-1441.
58. Ding F., Chen T. A gradient based adaptive control algorithm for dual-rate systems. Asian J. Control 2006, 8(4):314-323.
59. Ding F., Chen T., Iwai Z. Adaptive digital control of Hammerstein nonlinear systems with limited output sampling. SIAM J. Control Optimizat. 2007, 45(6):2257-2276.