References

• 1. 1)
     • 46. Wang, X.H., Ding, F.: ‘Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle’, Signal Process., 2015, 117, pp. 208–218.
  2. 2)
     • 35. Ljung, L.: ‘System identification: theory for the user’ (Prentice Hall, Englewood Cliffs, NJ, 1999, 2nd edn.).
  3. 3)
     • 47. Feng, L., Wu, M.H., Li, Q.X., et al: ‘Array factor forming for image reconstruction of one-dimensional nonuniform aperture synthesis radiometers’, IEEE Geosci. Remote Sensing Lett., 2016, 13, (2), pp. 237–241.
  4. 4)
     • 25. Hong, S., Lee, C., Borrelli, F., et al: ‘A novel approach for vehicle inertial parameter identification using a dual Kalman filter’, IEEE Trans. Intell. Transp. Syst., 2015, 16, (1), pp. 151–161.
  5. 5)
     • 38. Liu, Y.J., Ding, F.: ‘Convergence properties of the least squares estimation algorithm for multivariable systems’, Appl. Math. Model., 2013, 37, (1–2), pp. 476–483.
  6. 6)
     • 26. Azam, S.E., Chatzi, E., Papadimitriou, C.: ‘A dual Kalman filter approach for state estimation via output–only acceleration measurements’, Mech. Syst. Signal Process., 2015, 60–61, pp. 866–886.
  7. 7)
     • 41. Lakshminarayanan, S., Shah, S.L., Nandakumar, K.: ‘Identification of Hammerstein models using multivariate statistical tools’, Chem. Eng. Sci., 1995, 50, (22), pp. 3599–3613.
  8. 8)
     • 27. Stetzel, K.D., Aldrich, L.L., Trimboli, M.S., et al: ‘Electrochemical state and internal variables estimation using a reduced–order physics–based model of a lithium–ion cell and an extended Kalman filter’, J. Power Sources, 2015, 278, pp. 490–505.
  9. 9)
     • 12. Ding, F., Xu, L., Zhu, Q.M.: ‘Performance analysis of the generalized projection identification for time-varying systems’, IET Control Theory Appl., 2016, 10, (18), pp. 2506–2514.
  10. 10)
      • 24. Zhao, S., Huang, B., Liu, F.: ‘Minimum variance unbiased FIR filter for discrete time-variant systems’, Automatica, 2015, 53, (3), pp. 355–361.
  11. 11)
      • 20. Zhang, J., Welch, G., Bishop, G., et al: ‘A two–stage kalman filter approach for robust and real–time power system state estimation’, IEEE Trans. Sustain. Energy, 2014, 5, (2), pp. 629–636.
  12. 12)
      • 18. Ding, F.: ‘Hierarchical parameter estimation algorithms for multivariable systems using measurement information’, Inf. Sci., 2014, 277, pp. 396–405.
  13. 13)
      • 37. Wang, Y.J., Ding, F.: ‘The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique’, Signal Process., 2016, 128, pp. 212–221.
  14. 14)
      • 49. Wang, T.Z., Wu, H., Ni, M.Q., et al: ‘An adaptive confidence limit for periodic non-steady conditions fault detection’, Mech. Syst. Signal Process., 2016, 72–73, pp. 328–345.
  15. 15)
      • 14. Xu, L., Ding, F.: ‘The parameter estimation algorithms for dynamical response signals based on the multi-innovation theory and the hierarchical principle’, IET Signal Process., 2017, 11, doi: 10.1049/iet-spr.2016.0220.
  16. 16)
      • 30. Wang, D.Q.: ‘Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models’, Appl. Math. Lett., 2016, 57, pp. 13–19.
  17. 17)
      • 23. Zhao, S., Shmaliy, Y.S., Liu, F.: ‘Fast Kalman-like optimal unbiased FIR filtering with applications’, IEEE Trans. Signal Process., 2016, 64, (9), pp. 2284–2297.
  18. 18)
      • 16. Xu, L., Ding, F.: ‘Recursive least squares and multi-innovation stochastic gradient parameter estimation methods for signal modeling’, Circuits Syst. Signal Process., 2017, 36, doi: 10.1007/s00034-016-0378-4.
  19. 19)
      • 21. Pan, J., Yang, X.H., Cai, H.F., et al: ‘Image noise smoothing using a modified Kalman filter’, Neurocomputing, 2016, 173, pp. 1625–1629.
  20. 20)
      • 10. Wang, D.Q., Zhang, W.: ‘Improved least squares identification algorithm for multivariable Hammerstein systems’, J. Franklin Inst., 2015, 352, (11), pp. 5292–5307.
  21. 21)
      • 9. Wang, Y.J., Ding, F.: ‘The filtering based iterative identification for multivariable systems’, IET Control Theory Applic., 2016, 10, (8), pp. 894–902.
  22. 22)
      • 3. Xu, L.: ‘A proportional differential control method for a time-delay system using the Taylor expansion approximation’, Appl. Math. Comput., 2014, 236, pp. 391–399.
  23. 23)
      • 48. Wang, T.Z., Qi, J., Xu, H., et al: ‘Fault diagnosis method based on FFT-RPCA-SVM for cascaded-multilevel inverter’, ISA Trans., 2016, 60, pp. 156–163.
  24. 24)
      • 40. Golub, G.H., Van Loan, C.F.: ‘Matrix computations’ (Johns Hopkins University Press, Baltimore, MD, 1996, 3rd edn.).
  25. 25)
      • 2. Roman, R.C., Radac, M.B., Precup, R.E.: ‘Multi–input–multi–output system experimental validation of model-free control and virtual reference feedback tuning techniques’, IET Control Theory Applic., 2016, 10, (12), pp. 1395–1403.
  26. 26)
      • 42. Shen, Q., Ding, F.: ‘Iterative identification methods for input nonlinear multivariable systems using the key-term separation principle’, J. Franklin Inst., 2015, 352, (7), pp. 2847–2865.
  27. 27)
      • 34. Goodwin, G.C., Sin, K.S.: ‘Adaptive filtering prediction and control’ (Prentice Hall, Englewood Cliffs, NJ, 1984).
  28. 28)
      • 6. Wang, Y.J., Ding, F.: ‘Novel data filtering based parameter identification for multiple-input multiple-output systems using the auxiliary model’, Automatica, 2016, 71, pp. 308–313.
  29. 29)
      • 31. Eskinat, E., Johnson, S.H., Luyben, W.L.: ‘Use of Hammerstein models in identification of nonlinear systems’, AIChE J., 1991, 37, (2), pp. 255–268.
  30. 30)
      • 11. van der Veen, G., van Wingerden, J.W., Verhaegen, M.: ‘Global identification of wind turbines using a Hammerstein identification method’, IEEE Trans. Control Syst. Technol., 2013, 21, (4), pp. 1471–1478.
  31. 31)
      • 8. Gibson, S., Ninness, B.: ‘Robust maximum–likelihood estimation of multivariable dynamic systems’, Automatica, 2005, 41, (10), pp. 1667–1682.
  32. 32)
      • 15. Engel, Y., Mannor, S., Meir, R.: ‘The kernel recursive least-squares algorithm’, IEEE Trans. Signal Process., 2004, 52, (8), pp. 2275–2285.
  33. 33)
      • 39. Wang, X.H., Ding, F.: ‘Convergence of the recursive identification algorithms for multivariate pseudo–linear regressive systems’, Int. J. Adapt. Control Signal Process., 2016, 30, (6), pp. 824–842.
  34. 34)
      • 45. Mao, Y.W., Ding, F.: ‘Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique’, Nonlinear Dyn., 2015, 79, (3), pp. 1745–1755.
  35. 35)
      • 44. Mao, Y.W., Ding, F.: ‘A novel parameter separation based identification algorithm for Hammerstein systems’, Appl. Math. Lett., 2016, 60, pp. 21–27.
  36. 36)
      • 29. Jafari, M., Salimifard, M., Dehghani, M.: ‘Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm’, ISA Trans., 2014, 53, (4), pp. 1243–1252.
  37. 37)
      • 1. Jafari, S., Ioannou, P.A.: ‘Robust adaptive attenuation of unknown periodic disturbances in uncertain multi-input multi-output systems’, Automatica, 2016, 70, pp. 32–42.
  38. 38)
      • 17. Cao, Y., Liu, Z.: ‘Signal frequency and parameter estimation for power systems using the hierarchical identification principle’, Math. Comput. Model., 2010, 52, (5), pp. 854–861.
  39. 39)
      • 33. Ding, F.: ‘System identification—performances analysis for identification methods’ (Science Press, Beijing, 2014).
  40. 40)
      • 43. Xu, L.: ‘The damping iterative parameter identification method for dynamical systems based on the sine signal measurement’, Signal Process., 2016, 120, pp. 660–667.
  41. 41)
      • 4. Xu, L.: ‘Application of the Newton iteration algorithm to the parameter estimation for dynamical systems’, J. Comput. Appl. Math., 2015, 288, pp. 33–43.
  42. 42)
      • 5. Xu, L., Chen, L., Xiong, W.L.: ‘Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration’, Nonlinear Dyn., 2015, 79, (3), pp. 2155–2163.
  43. 43)
      • 36. Ding, F., Gu, Y.: ‘Performance analysis of the auxiliary model based least squares identification algorithm for one–step state delay systems’, Int. J. Comput. Math., 2012, 89, (15), pp. 2019–2028.
  44. 44)
      • 32. Le, F., Markovsky, I., Freeman, C.T., et al: ‘Recursive identification of Hammerstein systems with application to electrically stimulated muscle’, Control Eng. Pract., 2012, 20, (4), pp. 386–396.
  45. 45)
      • 7. Pan, J., Jiang, X., Wan, X.K., et al: ‘A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems’, Int. J. Control Autom. Syst., 2016, 15, doi: 10.1007/s12555-016-0081-z.
  46. 46)
      • 28. Zhang, W.G.: ‘Decomposition based least squares iterative estimation for output error moving average systems’, Eng. Comput., 2014, 31, (4), pp. 709–725.
  47. 47)
      • 13. Wan, X.K., Li, Y., Xia, C., et al: ‘A T-wave alternans assessment method based on least squares curve fitting technique’, Measurement, 2016, 86, pp. 93–100.
  48. 48)
      • 19. Wang, C., Zhu, L.: ‘Parameter identification of a class of nonlinear systems based on the multi-innovation identification theory’, J. Franklin Inst., 2015, 352, (10), pp. 4624–4637.
  49. 49)
      • 22. Simon, D.: ‘Kalman filtering with state constraints: a survey of linear and nonlinear algorithms’, IET Control Theory Applic., 2010, 4, (8), pp. 1303–1318.