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Recursive Extended Least Squares Parameter Estimation for Wiener Nonlinear Systems with Moving Average Noises

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Abstract

Many control algorithms are based on the mathematical models of dynamic systems. System identification is used to determine the structures and parameters of dynamic systems. Some identification algorithms (e.g., the least squares algorithm) can be applied to estimate the parameters of linear regressive systems or linear-parameter systems with white noise disturbances. This paper derives two recursive extended least squares parameter estimation algorithms for Wiener nonlinear systems with moving average noises based on over-parameterization models. The simulation results indicate that the proposed algorithms are effective.

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References

  1. M. Dehghan, M. Hajarian, Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations. Appl. Math. Lett. 24(4), 444–449 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Dehghan, M. Hajarian, Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations. Appl. Math. Model. 35(7), 3285–3300 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Dehghan, M. Hajarian, SSHI methods for solving general linear matrix equations. Eng. Comput. 28(8), 1028–1043 (2011)

    Article  Google Scholar 

  4. M. Dehghan, M. Hajarian, Fourth-order variants of Newton’s method without second derivatives for solving non-linear equations. Eng. Comput. 29(4), 356–365 (2012)

    Article  Google Scholar 

  5. M. Dehghan, M. Hajarian, Iterative algorithms for the generalized centro-symmetric and central anti-symmetric solutions of general coupled matrix equations. Eng. Comput. 29(5), 528–560 (2012)

    Article  Google Scholar 

  6. F. Ding, System Identification—New Theory and Methods (Science Press, Beijing, 2013)

    Google Scholar 

  7. F. Ding, Decomposition based fast least squares algorithm for output error systems. Signal Process. 93(5), 1235–1242 (2013)

    Article  Google Scholar 

  8. F. Ding, Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Model. 37(4), 1694–1704 (2013)

    Article  MathSciNet  Google Scholar 

  9. F. Ding, Two-stage least squares based iterative estimation algorithm for CARARMA system modeling. Appl. Math. Model. 37(7), 4798–4808 (2013)

    Article  MathSciNet  Google Scholar 

  10. F. Ding, Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7(1), 68–79 (2013)

    Article  MathSciNet  Google Scholar 

  11. F. Ding, T. Chen, Identification of Hammerstein nonlinear ARMAX systems. Automatica 41(9), 1479–1489 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Ding, F. Ding, Bias compensation based parameter estimation for output error moving average systems. Int. J. Adapt. Control Signal Process. 25(12), 1100–1111 (2011)

    Article  MATH  Google Scholar 

  13. F. Ding, Y. Gu, Performance analysis of the auxiliary model based least squares identification algorithm for one-step state delay systems. Int. J. Comput. Math. 89(15), 2019–2028 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  14. F. Ding, Y. Gu, Performance analysis of the auxiliary model-based stochastic gradient parameter estimation algorithm for state space systems with one-step state delay. Circuits Syst. Signal Process. 32(2), 585–599 (2013)

    Article  MathSciNet  Google Scholar 

  15. J. Ding, Y. Shi et al., A modified stochastic gradient based parameter estimation algorithm for dual-rate sampled-data systems. Digit. Signal Process. 20(4), 1238–1249 (2010)

    Article  Google Scholar 

  16. J. Ding, F. Ding et al., Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans. Autom. Control 56(11), 2677–2683 (2011)

    Article  Google Scholar 

  17. F. Ding, X.P. Liu, G. Liu, Identification methods for Hammerstein nonlinear systems. Digit. Signal Process. 21(2), 215–238 (2011)

    Article  Google Scholar 

  18. F. Ding, Y.J. Liu, B. Bao, 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)

    Article  Google Scholar 

  19. F. Ding, X.G. Liu, J. Chu, 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)

    Article  MathSciNet  Google Scholar 

  20. F. Ding, J.X. Ma, Y.S. Xiao, Newton iterative identification for a class of output nonlinear systems with moving average noises. Nonlinear Dyn. 74(1–2), 21–30 (2013)

    Article  MathSciNet  Google Scholar 

  21. W. Fan, Identification of a class of Wiener nonlinear systems (I). Master’s Degree Thesis, Jiangnan University, Wuxi, China, 2008

  22. Y. Gu, X.L. Lu, R.F. Ding, Parameter and state estimation algorithm for a state space model with a one-unit state delay. Circuits Syst. Signal Process. 32(5), 2267–2280 (2013)

    Article  MathSciNet  Google Scholar 

  23. H.Q. Han, L. Xie et al., Hierarchical least squares based iterative identification for multivariable systems with moving average noises. Math. Comput. Model. 51(9–10), 1213–1220 (2010)

    Article  MATH  Google Scholar 

  24. Y.B. Hu, Iterative and recursive least squares estimation algorithms for moving average systems. Simul. Model. Pract. Theory 34, 12–19 (2013)

    Article  Google Scholar 

  25. J.H. Li, Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91–96 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  26. J.H. Li, F. Ding, 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)

    Article  MATH  MathSciNet  Google Scholar 

  27. H. Li, Y. Shi, Robust H-infty filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains. Automatica 48(1), 159–166 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  28. J.H. Li, R.F. Ding, Y. Yang, Iterative parameter identification methods for nonlinear functions. Appl. Math. Model. 36(6), 2739–2750 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  29. J.H. Li, F. Ding, G.W. Yang, Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems. Math. Comput. Model. 55(3–4), 442–450 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  30. Y.J. Liu, Y.S. Xiao, X.L. Zhao, Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model. Appl. Math. Comput. 215(4), 1477–1483 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  31. Y.J. Liu, J. Sheng, R.F. Ding, Convergence of stochastic gradient algorithm for multivariable ARX-like systems. Comput. Math. Appl. 59(8), 2615–2627 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  32. Y.J. Liu, F. Ding, Y. Shi, Least squares estimation for a class of non-uniformly sampled systems based on the hierarchical identification principle. Circuits Syst. Signal Process. 31(6), 1985–2000 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  33. M.M. Liu, Y.S. Xiao, R.F. Ding, Iterative identification algorithm for Wiener nonlinear systems using the Newton method. Appl. Math. Model. 37(9), 6584–6591 (2013)

    Article  MathSciNet  Google Scholar 

  34. J.X. Ma, F. Ding, Recursive relations of the cost functions for the least squares algorithms for multivariable systems. Circuits Syst. Signal Process. 32(1), 83–101 (2013)

    Article  MathSciNet  Google Scholar 

  35. B. Shen, Z.D. Wang et al., H-infinity filtering for uncertain time-varying systems with multiple randomly occurred nonlinearities and successive packet dropouts. Int. J. Robust Nonlinear Control 21(14), 1693–1709 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  36. B. Shen, Z.D. Wang et al., Sampled-data H-infinity filtering for stochastic genetic regulatory networks. Int. J. Robust Nonlinear Control 21(15), 1759–1777 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  37. Y. Shi, T. Chen, Optimal design of multi-channel transmultiplexers with stopband energy and passband magnitude constraints. IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process. 50(9), 659–662 (2003)

    Article  Google Scholar 

  38. Y. Shi, H. Fang, Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control 83(3), 538–551 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  39. Y. Shi, B. Yu, Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control 54(7), 1668–1674 (2009)

    Article  MathSciNet  Google Scholar 

  40. Y. Shi, B. Yu, Robust mixed H-2/H-infinity control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754–760 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  41. R.M. Udrea, D.N. Vizireanu, S. Ciochina, An improved spectral subtraction method for speech enhancement using a perceptual weighting filter. Digit. Signal Process. 18(4), 581–587 (2008)

    Article  Google Scholar 

  42. R.M. Udrea, D.N. Vizireanu, S. Ciochina, S. Halunga, Nonlinear spectral subtraction method for colored noise reduction using multi-band Bark scale. Signal Process. 88(5), 1299–1303 (2008)

    Article  MATH  Google Scholar 

  43. D.N. Vizireanu, S.V. Halunga, Simple, fast and accurate eight points amplitude estimation method of sinusoidal signals for DSP based instrumentation. J. Instrum. 7(4), P04001 (2012)

    Article  Google Scholar 

  44. D.Q. Wang, 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)

    Article  MathSciNet  Google Scholar 

  45. D.Q. Wang, F. Ding, Extended stochastic gradient identification algorithms for Hammerstein-Wiener ARMAX systems. Comput. Math. Appl. 56(12), 3157–3164 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  46. D.Q. Wang, F. Ding, Least squares based and gradient based iterative identification for Wiener nonlinear systems. Signal Process. 91(5), 1182–1189 (2011)

    Article  MATH  Google Scholar 

  47. D.Q. Wang, F. Ding, Hierarchical least squares estimation algorithm for Hammerstein-Wiener systems. IEEE Signal Process. Lett. 19(12), 825–828 (2012)

    Article  Google Scholar 

  48. D.Q. Wang, R. Ding, X.Z. Dong, Iterative parameter estimation for a class of multivariable systems based on the hierarchical identification principle and the gradient search. Circuits Syst. Signal Process. 31(6), 2167–2177 (2012)

    Article  MathSciNet  Google Scholar 

  49. W.L. Xiong, J.X. Ma, R.F. Ding, An iterative numerical algorithm for modeling a class of Wiener nonlinear systems. Appl. Math. Lett. 26(4), 487–493 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  50. Y. Zhang, Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods. Math. Comput. Model. 53(9–10), 1810–1819 (2011)

    Article  MATH  Google Scholar 

  51. Y. Zhang, G.M. Cui, Bias compensation methods for stochastic systems with colored noise. Appl. Math. Model. 35(4), 1709–1716 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  52. J.B. Zhang, F. Ding, Y. Shi, Self-tuning control based on multi-innovation stochastic gradient parameter estimation. Syst. Control Lett. 58(1), 69–75 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  53. Z.N. Zhang, F. Ding, X.G. Liu, Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems. Comput. Math. Appl. 61(3), 672–682 (2011)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 51204149), the Fundamental Research Funds for the Central Universities (No. 2-9-2012-45), and the Open Project Fund of the Key Laboratory on Deep GeoDrilling Technology of the Ministry of Land and Resources (No. NLSD201213).

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  1. Key Laboratory on Deep GeoDrilling Technology of the Ministry of Land and Resources, China University of Geosciences, Beijing, 100083, PR China

    Yuanbiao Hu, Baolin Liu, Qin Zhou & Chun Yang

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  1. Yuanbiao Hu
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Correspondence to Yuanbiao Hu.

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Hu, Y., Liu, B., Zhou, Q. et al. Recursive Extended Least Squares Parameter Estimation for Wiener Nonlinear Systems with Moving Average Noises. Circuits Syst Signal Process 33, 655–664 (2014). https://doi.org/10.1007/s00034-013-9652-x

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  • DOI: https://doi.org/10.1007/s00034-013-9652-x

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