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Variational Bayesian-Based Iterative Algorithm for ARX Models with Random Missing Outputs

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Abstract

In this paper, a variational Bayesian (VB)-based iterative algorithm for ARX models with random missing outputs is proposed. The distributions of missing outputs can be estimated in the VB-E step, and the distributions of unknown parameters can be estimated in the VB-M step by the estimated missing outputs and the available outputs. Compared with the expectation–maximization-based iterative algorithm, this algorithm computes the latent variable and the parameter distributions at each iteration. Therefore, it is more accurate. The simulation results demonstrate the advantages of the proposed algorithm.

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References

  1. J. Chen, Several gradient parameter estimation algorithms for dual-rate sampled systems. J. Frankl. Inst. 351(1), 543–554 (2014)

    Article  MATH  Google Scholar 

  2. J. Chen, J. Li, Y.J. Liu, Gradient iterative algorithm for dual-rate nonlinear systems based on a novel particle filter. J. Frankl. Inst. 354(11), 4425–4437 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. F. Ding, X.M. Liu, X.Y. Ma, Kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition. J. Comput. Appl. Math. 301, 135–143 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Ding, F.F. Wang, T. Hayat, A. Alsaedi, Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique. IET Control Theory Appl. 11(3), 390–400 (2017)

    Article  MathSciNet  Google Scholar 

  5. F. Ding, F.F. Wang, L. Xu, M.H. Wu, Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering. J. Frankl. Inst. 354(3), 1321–1339 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Ding, X.H. Wang, Hierarchical stochastic gradient algorithm and its performance analysis for a class of bilinear-in-parameter systems. Circuits Syst. Signal Process. 36(4), 1393–1405 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Ding, X.H. Wang, L. Mao, L. Xu, Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering. Digit. Signal Process. 62, 211–223 (2017)

    Article  Google Scholar 

  8. F. Ding, L. Xu, Q.M. Zhu, Performance analysis of the generalised projection identification for time-varying systems. IET Control Theory Appl. 10(18), 2506–2514 (2016)

    Article  MathSciNet  Google Scholar 

  9. J. Ding, J.X. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33(5), 1439–1449 (2014)

    Article  Google Scholar 

  10. V.Z. Filipovic, Consistency of the robust recursive Hammerstein model identification algorithm. J. Frankl. Inst. 352(5), 1932–1945 (2015)

    Article  MathSciNet  Google Scholar 

  11. L.J. Guo, Y.J. Wang, C. Wang, A recursive least squares algorithm for pseudo-linear ARMA systems using the auxiliary model and the filtering technique. Circuits Syst. Signal Process. 35(7), 2655–2667 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Ji, F. Ding, Multiperiodicity and exponential attractivity of neural networks with mixed delays. Circuits Syst. Signal Process. 36(6), 2558–2573 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. Y. Ji, X.M. Liu, Unified synchronization criteria for hybrid switching-impulsive dynamical networks. Circuits Syst. Signal Process. 34(5), 1499–1517 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. Q.B. Jin, Z. Wang, X.P. Liu, Auxiliary model-based interval-varying multi-innovation least squares identification for multivariable OE-like systems with scarce measurements. J. Process Control 35, 154–168 (2015)

    Article  Google Scholar 

  15. D. Li, S. Shah, T. Chen, Analysis of dual-rate inferential control systems. Automatica 38(6), 1053–1059 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  16. H. Li, Y. Shi, W. Yan, Distributed receding horizon control of constrained nonlinear vehicle formations with guaranteed \(\gamma \)-gain stability. Automatica 68, 148–154 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. H. Li, W. Yan, Y. Shi, Continuous-time model predictive control of under-actuated spacecraft with bounded control torques. Automatica 75, 144–153 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. J.H. Li, W.X. Zheng, J.P. Gu, L. Hua, Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements. J. Frankl. Inst. 354(1), 316–331 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. M.H. Li, X.M. Liu, F. Ding, The gradient based iterative estimation algorithms for bilinear systems with autoregressive noise. Circuits Syst. Signal Process. (2017). doi:10.1007/s00034-017-0527-4

    MathSciNet  MATH  Google Scholar 

  20. M.H. Li, X.M. Liu, F. Ding, Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems. Nonlinear Dyn. 89(1), 197–211 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  21. Y. Liu, E.W. Bai, Iterative identification of Hammerstein systems. Automatica 43(2), 346–354 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Y.J. Lu, B. Huang, S. Khatibisepehr, A variational Bayesian approach to robust identification of switched ARX models. IEEE Trans. Cybern. 99, 1–14 (2015)

    Article  Google Scholar 

  23. G. Mercère, L. Bako, Parameterization and identification of multivariable state-space systems: a canonical approach. Automatica 47(8), 1547–1555 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Pan, X. Jiang, X.K. Wan, W. Ding, A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems. Int. J. Control Autom. Syst. 15(3), 1189–1197 (2017)

    Article  Google Scholar 

  25. J. Vörös, Modeling and identification of systems with backlash. Automatica 46(2), 369–374 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. X.K. Wan, Y. Li, C. Xia, M.H. Wu, J. Liang, N. Wang, A T-wave alternans assessment method based on least squares curve fitting technique. Measurement 86, 93–100 (2016)

    Article  Google Scholar 

  27. D.Q. Wang, L. Mao, F. Ding, Recasted models based hierarchical extended stochastic gradient method for MIMO nonlinear systems. IET Control Theory Appl. 11(4), 476–485 (2017)

    Article  MathSciNet  Google Scholar 

  28. D.Q. Wang, Z. Zhang, J.Y. Yuan, Maximum likelihood estimation method for dual-rate Hammerstein systems. Int. J. Control Autom. Syst. 15, 698–705 (2017)

    Article  Google Scholar 

  29. Y.J. Wang, F. Ding, The filtering based iterative identification for multivariable systems. IET Control Theory Appl. 10(8), 894–902 (2016)

    Article  MathSciNet  Google Scholar 

  30. W.L. Xiong, X.Q. Yang, B. Huang, B.G. Xu, Multiple-based linear parameter varying time-delay system identification with missing output data using an expectation-maximization algorithm. Ind. Eng. Chem. Res. 53, 11074–11083 (2014)

    Article  Google Scholar 

  31. W.L. Xiong, X.Q. Yang, K. Liang, B.G. Xu, EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data. Nonlinear Dyn. 80(1), 329–339 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  32. L. Xu, F. Ding, Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling. Circuits Syst. Signal Process. 36(4), 1735–1753 (2017)

    Article  MATH  Google Scholar 

  33. L. Xu, F. Ding, The parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle. IET Signal Process. 11(2), 228–237 (2017)

    Article  Google Scholar 

  34. L. Xu, F. Ding, Y. Gu, A. Alsaedi, T. Hayat, A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay. Signal Process. 140, 97–103 (2017)

    Article  Google Scholar 

  35. X. Yin, J. Liu, Distributed moving horizon state estimation of two-time-scale nonlinear systems. Automatica 79, 152–161 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  36. Y.J. Zhao, A. Fatehi, B. Huang, Robust estimation of ARX models with time varying time delays using variational Bayesian approach. IEEE Trans. Cybern. (2017). doi:10.1109/TCYB.2016.2646059

    Google Scholar 

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Authors and Affiliations

  1. School of Science, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Jing Chen

  2. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, People’s Republic of China

    Yanjun Liu

Authors
  1. Jing Chen
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  2. Yanjun Liu
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Correspondence to Jing Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61403165, 61374126), the Natural Science Foundation of Jiangsu Province (No. BK20131109) and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (No. 16KJB120006).

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Chen, J., Liu, Y. Variational Bayesian-Based Iterative Algorithm for ARX Models with Random Missing Outputs. Circuits Syst Signal Process 37, 1594–1608 (2018). https://doi.org/10.1007/s00034-017-0612-8

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  • DOI: https://doi.org/10.1007/s00034-017-0612-8

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