190
Views
5
CrossRef citations to date
0
Altmetric
Articles

Maximum likelihood based identification methods for rational models

, ORCID Icon, &
Pages 2579-2591 | Received 21 Sep 2017, Accepted 18 Sep 2019, Published online: 01 Oct 2019

References

  • AlMutawa, J. (2015). Robust maximum likelihood estimation for stochastic state space model with observation outliers. International Journal of Systems Science, 47(11), 2733–2744.
  • Bates, D. M., & Watts, D. G. (2007). Nonlinear regression analysis and its applications. Hoboken, NJ: John Wiley & Sons.
  • Billings, S. A., & Mao, K. Z. (1998). Structure detection for nonlinear rational models using genetic algorithms. International Journal of Systems Science, 29(3), 223–231.
  • Billings, S. A., & Zhu, Q. M. (1991). Rational model identification using extended least squares algorithm. International Journal of Control, 54(3), 529–546.
  • Calafiore, G., & Ghaoui, L. E. (2001). Robust maximum likelihood estimation in the linear model. Automatica, 37(4), 573–580.
  • Cao, Y., Ma, L. C., Xiao, S., Zhang, X., & Xu, W. (2017). Standard analysis for transfer delay in CTCS-3. Chinese Journal of Electronics, 26(5), 1057–1063.
  • Chen, F. Y., & Ding, F. (2016). The filtering based maximum likelihood recursive least squares estimation for multiple-input single-output systems. Applied Mathematical Modelling, 40(3), 2106–2118.
  • Chen, J., Ding, F., Liu, Y. J., & Zhu, Q. M. (2018). Multi-step-length gradient iterative algorithm for equation-error type models. Systems & Control Letters, 115, 15–21.
  • Chen, F. Y., Ding, F., & Sheng, J. (2015). Maximum likelihood based recursive parameter estimation for controlled autoregressive ARMA systems using the data filtering technique. Journal of the Franklin Institute, 352(12), 5882–5896.
  • Chen, M. T., Ding, F., Xu, L., Hayat, T., & Alsaedi, A. (2017). Iterative identification algorithms for bilinear-in-parameter systems with autoregressive moving average noise. Journal of the Franklin Institute, 354(17), 7885–7898.
  • Chen, J., Huang, B., Ding, F., & Gu, Y. (2018). Variational Bayesian approach for ARX systems with missing observations and varying time-delays. Automatica, 94, 194–204.
  • Chen, J., Liu, Y. J., Ding, F., & Zhu, Q. M. (2018). Gradient based particle filter algorithm for an ARX model with nonlinear communication output. IEEE Transactions on Systems, Man and Cybernetics: Systems, 99, 1–10. doi:10.1109/TSMC.2018.2810277
  • David, B., & Bastin, G. (2002). Parameter estimation in nonlinear systems with auto and crosscorrelated noise. Automatica, 38(1), 81–90.
  • Degroot, M. H., & Schervish, M. J. (2011). Probability and statistics (4th ed.). Boston: Pearson.
  • Ding, F., Chen, H. B., Xu, L., Dai, J., Li, Q., & Hayat, T. (2018). A hierarchical least squares identification algorithm for Hammerstein nonlinear systems using the key term separation. Journal of the Franklin Institute, 355(8), 3737–3752.
  • Ding, F., & Wang, X. H. (2017). Hierarchical stochastic gradient algorithm and its performance analysis for a class of bilinear-in-parameter systems. Circuits, Systems and Signal Processing, 36(4), 1393–1405.
  • Ding, F., Wang, Y. J., Dai, J. Y., Li, Q., & Chen, Q. (2017). A recursive least squares parameter estimation algorithm for output nonlinear autoregressive systems using the input–output data filtering. Journal of the Franklin Institute, 354(15), 6938–6955.
  • Ding, F., Xu, L., Alsaadi, F. E., & Hayat, T. (2018). Iterative parameter identification for pseudo-linear systems with ARMA noise using the filtering technique. IET Control Theory and Applications, 12(7), 892–899.
  • Du, T., & Guo, L. (2016). Unbiased information filtering for systems with missing measurement based on disturbance estimation. Journal of the Franklin Institute, 353(4), 936–954.
  • Hegde, A., & Tang, J. (2016). Identifying parametric variation in second-order system from frequency response measurement. Journal of Vibration and Control, 24(5), 879–891.
  • Kennedy, J. (1997). The particle swarm: Social adaptation of knowledge. Proceedings of IEEE international conference on evolutionary computation (pp. 303–308).
  • Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. Proceedings of IEEE international conference on neural networks IV (pp. 1942–1948).
  • Li, P., Dargaville, R., Cao, Y., Li, D. Y., & Xia, J. (2018). Storage aided system property enhancing and hybrid robust smoothing for large-scale PV systems. IEEE Transactions on Smart Grid, 8(6), 2871–2879.
  • Li, P., & Xie, G. (2018). Multi-objective sizing optimization for island microgrids using triangular aggregation model and Levy–Harmony algorithm. IEEE Transactions on Industrial Informatics, 14(8), 3495–3505. doi:10.1109/TII.2017.2778079
  • Lin, L. W., & Ren, X. M. (2017). Decomposition-based recursive least-squares parameter estimation algorithm for Wiener–Hammerstein systems with dead-zone nonlinearity. International Journal of Systems Science, 48(11), 2405–2417.
  • Lin, Y., & Zhang, W. (2018). Necessary/sufficient conditions for Pareto optimum in cooperative difference game. Optimal Control, Applications and Methods, 39(2), 1043–1060.
  • Liu, F. (2018). Continuity and approximate differentiability of multisublinear fractional maximal functions. Mathematical Inequalities & Applications, 21(1), 25–40.
  • Liu, X., & Lu, J. (2010). Least squares based iterative identification for a class of multirate systems. Automatica, 46(3), 549–554.
  • Liu, F., Xue, Q. Y., & Yabuta, K. (2018). Rough maximal singular integral and maximal operators supported by subvarieties on Triebel–Lizorkin spaces. Nonlinear Analysis, 171, 41–72.
  • Ma, P., Ding, F., & Zhu, Q. M. (2018). Decomposition-based recursive least squares identification methods for multivariate pseudolinear systems using the multi-innovation. International Journal of Systems Science, 49(5), 920–928.
  • Ma, L., & Liu, X. (2015). A nonlinear recursive instrumental variables identification method of Hammerstein ARMAX system. Nonlinear Dynamics, 79(2), 1601–1613.
  • Ma, L., & Liu, X. (2016). Recursive maximum likelihood method for the identification of Hammerstein ARMAX system. Applied Mathematical Modelling, 40(13–14), 6523–6535.
  • Ma, L., & Liu, X. (2017). A novel APSO-aided weighted LSSVM method for nonlinear Hammerstein system identification. Journal of the Franklin Institute, 354(4), 1892–1906.
  • Mu, B. Q., Bai, E. W., Zheng, W. X., & Zhu, Q. (2017). A globally consistent nonlinear least squares estimator for identification of nonlinear rational systems. Automatica, 77, 322–335.
  • Shi, Y., & Eberhart, R. C. (1998). A modified particle swarm optimizer. Proceedings of IEEE international conference on evolutionary computation (pp. 69–73).
  • Sun, J., & Liu, X. (2013). A novel APSO-aided maximum likelihood identification method for Hammerstein systems. Nonlinear Dynamics, 73(1–2), 449–462.
  • Vörös, J. (2010). Modeling and identification of systems with backlash. Automatica, 46(2), 369–374.
  • Wang, X. H., Ding, F, Alsaadi, F. E., & Hayat, T. (2016). Convergence analysis of the hierarchical least squares algorithm for bilinear-in-parameter systems. Circuits, Systems and Signal Processing, 35(12), 4307–4330.
  • Wang, D. Q., Zhang, Z., & Yuan, J. Y. (2017). Maximum likelihood estimation method for dual-rate Hammerstein systems. International Journal of Control, Automation, and Systems, 15(2), 698–705.
  • Xu, L. (2017). The parameter estimation algorithms based on the dynamical response measurement data. Advances in Mechanical Engineering, 9(11), 1–12. doi:10.1177/1687814017730003
  • Xu, L., & Ding, F. (2017a). Parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle. IET Signal Processing, 11(2), 228–237.
  • Xu, L., & Ding, F. (2017b). Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling. Circuits, Systems and Signal Processing, 36(4), 1735–1753.
  • Xu, L., & Ding, F. (2017c). Parameter estimation for control systems based on impulse responses. International Journal of Control, Automation and Systems, 15(6), 2471–2479.
  • Xu, L., & Ding, F. (2018). Iterative parameter estimation for signal models based on measured data. Circuits, Systems and Signal Processing, 37(7), 3046–3069.
  • Xu, L., Ding, F., Gu, Y., Alsaedi, A., & Hayat, T. (2017). A multi-innovation state and parameter estimation algorithm for a state space system with d-step state-delay. Signal Processing, 140, 97–103.
  • Yalcinkaya, A., Senoglu, B., & Yolcu, U. (2018). Maximum likelihood estimation for the parameters of skew normal distribution using genetic algorithm. Swarm and Evolutionary Computation, 38, 127–138.
  • Yang, X. Q., Huang, B., & Gao, H. J. (2016). A direct maximum likelihood optimization approach to identification of LPV time-delay systems. Journal of the Franklin Institute, 353(8), 1862–1881.
  • Zhang, Y. Z., Cao, Y., Wen, Y. H., Liang, L., & Zou, F. (2018). Optimization of information interaction protocols in cooperative vehicle-infrastructure systems. Chinese Journal of Electronics, 27(2), 439–444.
  • Zhang, X., Ding, F., Alsaadi, F. E., & Hayat, H. (2017). Recursive parameter identification of the dynamical models for bilinear state space systems. Nonlinear Dynamics, 89(4), 2415–2429.
  • Zhang, W., Lin, X., & Chen, B. S. (2017). LaSalle-type theorem and its applications to infinite horizon optimal control of discrete-time nonlinear stochastic systems. IEEE Transactions on Automatic Control, 62(1), 250–261.
  • Zhang, X., Xu, L., Ding, F., & Hayat, T. (2018). Combined state and parameter estimation for a bilinear state space system with moving average noise. Journal of the Franklin Institute, 355(6), 3079–3103.
  • Zhao, N., Wu, M., & Chen, J. (2017). Android-based mobile educational platform for speech signal processing. Computers & Electrical Engineering, 54(1), 3–16.
  • Zheng, W. X. (2002). A bias correction method for identification of linear dynamic errors-in-variables models. IEEE Transactions on Automatic Control, 47(7), 1142–1147.
  • Zhu, Q. M. (2003). A back propagation algorithm to estimate the parameters of nonlinear dynamic rational models. Applied Mathematical Modelling, 27(3), 169–187.
  • Zhu, Q. M. (2005). An implicit least squares algorithm for nonlinear rational model parameter estimation. Applied Mathematical Modelling, 29(7), 673–689.
  • Zhu, D. Q., Cao, X., Sun, B., & Luo, C. M. (2018). Biologically inspired self-organizing map applied to task assignment and path planning of an AUV system. IEEE Transactions on Cognitive and Developmental Systems, 10(2), 304–313.
  • Zhu, Q. M., Yu, D. L., & Zhao, D. Y. (2017). An enhanced linear Kalman filter (EnLKF) algorithm for parameter estimation of nonlinear rational models. International Journal of Systems Science, 48(3), 451–461.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.