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Iterative Parameter Estimation for a Class of Multivariable Systems Based on the Hierarchical Identification Principle and the Gradient Search

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Abstract

For a multivariable controlled autoregressive system with autoregressive noises, its corresponding identification model contains a parameter matrix and a parameter vector. This paper presents the hierarchical gradient-based iterative (HGI) algorithm to interactively estimate the parameter matrix and the parameter vector by using the hierarchical identification principle and the gradient search. The simulation results show that the HGI algorithm is effective.

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References

  1. J. Chen, Y. Zhang, R.F. Ding, Auxiliary model based multi-innovation algorithms for multivariable nonlinear systems. Math. Comput. Model. 52(9–10), 1428–1434 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. F. Ding, Several multi-innovation identification methods. Digit. Signal Process. 20(4), 1027–1039 (2010)

    Article  Google Scholar 

  3. F. Ding, Transformations between some special matrices. Comput. Math. Appl. 59(8), 2676–2695 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Ding, T. Chen, Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans. Autom. Control 50(8), 1216–1221 (2005)

    Article  MathSciNet  Google Scholar 

  5. F. Ding, T. Chen, Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41(2), 315–325 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Ding, T. Chen, Hierarchical identification of lifted state-space models for general dual-rate systems. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(6), 1179–1187 (2005)

    Article  MathSciNet  Google Scholar 

  7. F. Ding, T. Chen, Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Autom. Control 50(3), 397–402 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Ding, T. Chen, Iterative least squares solutions of coupled Sylvester matrix equations. Syst. Control Lett. 54(2), 95–107 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Ding, T. Chen, On iterative solutions of general coupled matrix equations. SIAM J. Control Optim. 44(6), 2269–2284 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Ding, T. Chen, Performance analysis of multi-innovation gradient type identification methods. Automatica 43(1), 1–14 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. F. Ding, P.X. Liu, J. Ding, Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Appl. Math. Comput. 197(1), 41–50 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Ding, X.P. Liu, H.Z. Yang, Parameter identification and intersample output estimation for dual-rate systems. IEEE Trans. Syst. Man Cybern., Part A, Syst. Hum. 38(4), 966–975 (2008)

    Article  Google Scholar 

  14. F. Ding, X.P. Liu, G. Liu, Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises. Signal Process. 89(10), 1883–1890 (2009)

    Article  MATH  Google Scholar 

  15. F. Ding, L. Qiu, T. Chen, Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica 45(2), 324–332 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. J. Ding, L.L. Han, X.M. Chen, Time series AR modeling with missing observations based on the polynomial transformation. Math. Comput. Model. 51(5–6), 527–536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Ding, Y.J. Liu, F. Ding, Iterative solutions to matrix equations of form AiXBi=Fi. Comput. Math. Appl. 59(11), 3500–3507 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. F. Ding, G. Liu, X.P. Liu, Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Autom. Control 55(8), 1976–1981 (2010)

    Article  MathSciNet  Google Scholar 

  19. F. Ding, P.X. Liu, G. Liu, Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit. Signal Process. 20(3), 664–677 (2010)

    Article  Google Scholar 

  20. F. Ding, G. Liu, X.P. Liu, Parameter estimation with scarce measurements. Automatica 47(8), 1646–1655 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  22. 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 

  23. H.Z. Fang, Y. Shi, J.G. Yi, On stable simultaneous input and state estimation for discrete-time linear systems. Int. J. Adapt. Control Signal Process. 25(8), 671–686 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. S.V. Halunga, N. Vizireanu, Performance evaluation for conventional and MMSE multiuser detection algorithms in imperfect reception conditions. Digit. Signal Process. 20(1), 166–178 (2010)

    Article  Google Scholar 

  25. S.V. Halunga, N. Vizireanu, O. Fratu, Imperfect cross-correlation and amplitude balance effects on conventional multiuser decoder with turbo encoding. Digit. Signal Process. 20(1), 191–200 (2010)

    Article  Google Scholar 

  26. L.L. Han, F. Ding, Identification for multirate multi-input systems using the multi-innovation identification theory. Comput. Math. Appl. 57(9), 1438–1449 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. L.L. Han, F. Ding, Multi-innovation stochastic gradient algorithms for multi-input multi-output systems. Digit. Signal Process. 19(4), 545–554 (2009)

    Article  MathSciNet  Google Scholar 

  28. L.L. Han, J. Sheng, F. Ding, Y. Shi, Auxiliary model identification method for multirate multi-input systems based on least squares. Math. Comput. Model. 50(7–8), 1100–1106 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. H.Q. Han, L. Xie, F. Ding, X.G. Liu, 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 

  30. B. Jiang, P. Shi, Z.H. Mao, Sliding mode observer-based fault estimation for nonlinear networked control systems. Circuits Syst. Signal Process. 30(1), 1–16 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. 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  MathSciNet  MATH  Google Scholar 

  32. S. Li, L.M. Song, T.S. Qiu, Steady-state and tracking analysis of fractional lower-order constant modulus algorithm. Circuits Syst. Signal Process. 30(6), 1275–1288 (2011)

    Article  MATH  Google Scholar 

  33. 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  MathSciNet  Google Scholar 

  34. 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  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  36. Y.J. Liu, D.Q. Wang, F. Ding, Least-squares based iterative algorithms for identifying Box–Jenkins models with finite measurement data. Digit. Signal Process. 20(5), 1458–1467 (2010)

    Article  Google Scholar 

  37. Y.J. Liu, L. Yu, F. Ding, Multi-innovation extended stochastic gradient algorithm and its performance analysis. Circuits Syst. Signal Process. 29(4), 649–667 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  38. Y. Liu, R. Ranganathan, M.T. Hunter, W.B. Mikhael, Complex adaptive LMS algorithm employing the conjugate gradient principle for channel estimation and equalization. Circuits Syst. Signal Process. (2012). doi:10.1007/s00034-011-9368-8

    MathSciNet  Google Scholar 

  39. M. Mansouri, H. Snoussi, C. Richard, Channel estimation and multiple target tracking in wireless sensor networks based on quantised proximity sensors. IET Wirel. Sens. Syst. 1(1), 7–14 (2011)

    Article  Google Scholar 

  40. A.A. Nasir, H. Mehrpouyan, S.D. Blostein, S. Durrani, R.A. Kennedy, Timing and carrier synchronization with channel estimation in multi-relay cooperative networks. IEEE Trans. Signal Process. 60(2), 793–811 (2012)

    Article  MathSciNet  Google Scholar 

  41. S.S. Ram, V.V. Veeravalli, A. Nedic, Distributed and recursive parameter estimation in parametrized linear state-space models. IEEE Trans. Autom. Control 55(2), 488–492 (2010)

    Article  MathSciNet  Google Scholar 

  42. X.Z. Shen, G. Meng, MIMO instantaneous blind identification based on second-order temporal structure and steepest-descent method. Circuits Syst. Signal Process. 30(3), 515–525 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. Y. Shi, F. Ding, T.W. Chen, Multirate crosstalk identification in xDSL systems. IEEE Trans. Commun. 54(10), 1878–1886 (2006)

    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, Performance analysis of the auxiliary models based multi-innovation stochastic gradient estimation algorithm for output error systems. Digit. Signal Process. 20(3), 750–762 (2010)

    Article  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. L.Y. Wang, L. Xie, X.F. Wang, The residual based interactive stochastic gradient algorithms for controlled moving average models. Appl. Math. Comput. 211(2), 442–449 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  48. D.Q. Wang, G.W. Yang, R.F. Ding, Gradient-based iterative parameter estimation for Box-Jenkins systems. Comput. Math. Appl. 60(5), 1200–1208 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  49. W. Wang, F. Ding, J.Y. Dai, Maximum likelihood least squares identification for systems with autoregressive moving average noise. Appl. Math. Model. 36(5), 1842–1853 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  50. Y.S. Xiao, Y. Zhang, J. Ding, J.Y. Dai, The residual based interactive least squares algorithms and simulation studies. Comput. Math. Appl. 58(6), 1190–1197 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  51. L. Xie, J. Ding, F. Ding, Gradient based iterative solutions for general linear matrix equations. Comput. Math. Appl. 58(7), 1441–1448 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  52. L. Xie, Y.J. Liu, H.Z. Yang, Gradient based and least squares based iterative algorithms for matrix equations AXB+CXTD=F. Appl. Math. Comput. 217(5), 2191–2199 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  53. L. Xie, H.Z. Yang, F. Ding, Modeling and identification for non-uniformly periodically sampled-data systems. IET Control Theory Appl. 4(5), 784–794 (2010)

    Article  MathSciNet  Google Scholar 

  54. J.I. Yuz, J. Alfaro, J.C. Agüero, G.C. Goodwin, Identification of continuous-time state-space models from non-uniform fast-sampled data. IET Control Theory Appl. 5(7), 842–855 (2011)

    Article  MathSciNet  Google Scholar 

  55. 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  MathSciNet  MATH  Google Scholar 

  56. 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  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61104001), the Shandong Provincial Natural Science Foundation (ZR2010FM024), the Postdoctoral Innovation Program Foundation of Shandong Province of China (201002002), and the 111 Project (B12018).

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Authors and Affiliations

  1. College of Automation Engineering, Qingdao University, Qingdao, 266071, PR China

    Dongqing Wang & Xinzhuang Dong

  2. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, PR China

    Rui Ding

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  1. Dongqing Wang
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Correspondence to Dongqing Wang.

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Wang, D., Ding, R. & Dong, X. Iterative Parameter Estimation for a Class of Multivariable Systems Based on the Hierarchical Identification Principle and the Gradient Search. Circuits Syst Signal Process 31, 2167–2177 (2012). https://doi.org/10.1007/s00034-012-9425-y

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