Two-stage least squares based iterative estimation algorithm for CARARMA system modeling

Applied Mathematical Modelling

Volumn 37, Issue 7, 2013, Pages 4798-4808

  Ding, Feng ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Iterative identification; Least squares; Parameter estimation; Recursive identification

Indexed keywords

AUTO-REGRESSIVE; AUTOREGRESSIVE MOVING AVERAGE; ESTIMATION THEORY; ITERATIVE ALGORITHM; ITERATIVE ESTIMATION; ITERATIVE IDENTIFICATION; LEAST SQUARE; NOISE MODELS; PARAMETER VECTORS; RECURSIVE IDENTIFICATION; SYSTEM MODELING; SYSTEM MODELS;

ALGORITHMS; ESTIMATION; IDENTIFICATION (CONTROL SYSTEMS); PARAMETER ESTIMATION;

ITERATIVE METHODS;

EID: 84872619148     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2012.10.014     Document Type: Article

References (59)

1. 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.
2. Yu B., Shi Y., Huang H. l-2 and l-infnity filtering for multirate systems using lifted models. Circ. Syst. Signal Process. 2008, 27(5):699-711.
3. Zhang Y., Cui G.M. Bias compensation methods for stochastic systems with colored noise. Appl. Math. Model. 2011, 35(4):1709-1716.
4. F. Ding, T. Chen, Hierarchical identification of lifted state-space models for general dual-rate systems, in: IEEE Transactions on Circuits and Systems - I: Regular Papers, 52, 6, 2005, pp. 1179-1187.
5. 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.
6. Dehghan M., Hajarian M. An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices. Appl. Math. Model. 2010, 34(3):639-654.
7. Dehghan M., Hajarian M. Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 2011, 35(7):3285-3300.
8. Ding F. Transformations between some special matrices. Comput. Math. Appl. 2010, 59(8):2676-2695.
9. TD=F. Appl. Math. Comput. 2010, 217(5):2191-2199.
10. Xiao Y.S., Ding F., et al. On consistency of recursive least squares identification algorithms for controlled auto-regression models. Appl. Math. Model. 2008, 32(11):2207-2215.
11. Ding F., Xiao Y.S. A finite-data-window least squares algorithm with a forgetting factor for dynamical modeling. Appl. Math. Comput. 2007, 186(1):184-192.
12. Xie L., Yang H.Z., et al. Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theory Appl. 2010, 4(5):784-794.
13. Wang D.Q., Ding F. Input-output data filtering based recursive least squares parameter estimation for CARARMA systems. Digit. Signal Process. 2010, 20(4):991-999.
14. Ding F., Chen T., Qiu L. Bias compensation based recursive least squares identification algorithm for MISO systems. IEEE Trans. Circ. Syst. II Exp. Briefs 2006, 53(5):349-353.
15. Zhang Y. Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods. Math. Comput. Model. 2011, 53(9-10):1810-1819.
16. Xiao Y.S., Yue N. Parameter estimation for nonlinear dynamical adjustment models. Math. Comput. Model. 2011, 54(5-6):1561-1568.
17. Wang W., Li J.H., Ding R.F. Maximum likelihood parameter estimation algorithm for controlled autoregressive models. Int. J. Comput. Math. 2011, 88(16):3458-3467.
18. Shi Y., Chen T. Optimal design of multi-channel transmultiplexers with stopband energy and passband magnitude constraints. IEEE Trans. Circ. Syst. II Analog Digit. Signal Process. 2003, 50(9):659-662.
19. Shi Y., Ding F., Chen T. Multirate crosstalk identification in xDSL systems. IEEE Trans. Commun. 2006, 54(10):1878-1886.
20. Shi Y., Ding F., Chen T. 2-Norm based recursive design of transmultiplexers with designable filter length. Circ. Syst. Signal Process. 2006, 25(4):447-462.
21. F. Ding, T. Chen, Performance bounds of the forgetting factor least squares algorithm for time-varying systems with finite measurement data, in: IEEE Transactions on Circuits and Systems-I: Regular Papers, 52, 3, 2005, pp. 555-566.
22. Ding J., Ding F. Bias compensation based parameter estimation for output error moving average systems. Int. J. Adapt. Control Signal Process 2011, 25(12):1100-1111.
23. Ding J., Ding F., et al. Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Automat. Control 2011, 56(11):2677-2683.
24. Ding F., Liu X.P., Shi Y. Convergence analysis of estimation algorithms for dual-rate stachatic systems. Appl. Math. Comput. 2006, 176(1):245-261.
25. Ding F. Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 2012, 10.1016/j.apm.2012.04.039.
26. Ding F., Chen T., Iwai Z. Adaptive digital control of Hammerstein nonlinear systems with limited output sampling. SIAM J. Control Optimiz. 2007, 45(6):2257-2276.
27. Shi Y., Yu B. Robust mixed H2/Hinfinity control of networked control systems with random time delays in both forward and backward communication links. Automatica 2011, 47(4):754-760.
28. Ding F., Shi Y., Chen T. Gradient-based identification methods for Hammerstein nonlinear ARMAX models. Nonlinear Dynam. 2006, 45(1-2):31-43.
29. Xiao Y.S., Wang D.Q., et al. The residual based ESG algorithm and its performance analysis. J. Franklin Inst. Eng. Appl. Math. 2010, 347(2):426-437.
30. Ding F., Yang H.Z., Liu F. Performance analysis of stochastic gradient algorithms under weak conditions. Sci. Chin. Ser. F Info. Sci. 2008, 51(9):1269-1280.
31. 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.
32. 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.
33. Ding F., Chen T. Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Automat. Control 2005, 50(3):397-402.
34. 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.
35. Ding F., Chen T. Performance analysis of multi-innovation gradient type identification methods. Automatica 2007, 43(1):1-14.
36. Ding F., Chen H.B., Li M. Multi-innovation least squares identification methods based on the auxiliary model for MISO systems. Appl. Math. Comput. 2007, 187(2):658-668.
37. 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.
38. Ding F. Several multi-innovation identification methods. Digit. Signal Process. 2010, 20(4):1027-1039.
39. Ding F., Liu G., Liu X.P. Parameter estimation with scarce measurements. Automatica 2011, 47(8):1646-1655.
40. 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.
41. Ding F., Liu X.P., Liu G. Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 2009, 89(10):1883-1890.
42. 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. 2012, 226(1):43-55.
43. Ding F., Liu X.P., Liu G. Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 2011, 21(1):1-24.
44. Wang D.Q., Ding F. Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 2011, 91(5):1182-1189.
45. Li J.H., Ding R.F., Yang Y. Iterative parameter identification methods for nonlinear functions. Appl. Math. Model. 2012, 26(6):2739-2750.
46. 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. 2011, 62(11):4170-4177.
47. Wang W., Ding F., Dai J.Y. Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 2012, 36(5):1842-1853.
48. 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. 2012, 55(3-4):442-450.
49. Ding F., Liu X.P., Liu G. Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 2010, 20(3):664-677.
50. 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.
51. Xiao Y.S., Zhang Y., et al. The residual based interactive least squares algorithms and simulation studies. Comput. Math. Appl. 2009, 58(6):1190-1197.
52. Yao G.Y., Ding R.F. Two-stage least squares based iterative identification algorithm for controlled autoregressive moving average (CARMA) systems. Comput. Math. Appl. 2012, 63(5):975-984.
53. Duan H.H., Jia J., Ding R.F. Two-stage recursive least squares parameter estimation algorithm for output error models. Math. Comput. Model. 2012, 55(3-4):1151-1159.
54. Ding F. System Identification - New Theory and Methods 2012, Science Press, Beijing.
55. Xiao Y.S., Chen H.B., et al. Identification of multi-input systems based on the correlation techniques. Int. J. Syst. Sci. 2011, 42(1):139-147.
56. Ding J., Ding F. The residual based extended least squares identification method for dual-rate systems. Comput. Math. Appl. 2008, 56(6):1479-1487.
57. Ding J., Han L.L., Chen X.M. Time series AR modeling with missing observations based on the polynomial transformation. Math. Comput. Model. 2010, 51(5-6):527-536.
58. Zhuang L.F., Pan F., et al. Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models. Appl. Math. Model. 2012, 36(8):3454-3463.
59. Wang D.Q. Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 2011, 5(14):1648-1657.