Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 781856, 8 pages.

Convergence Analysis of EFOP Estimate Based on Frequency Domain Smoothing

Yulai Zhang, Kueiming Lo, and Yang Su

Full-text: Open access

Abstract

The classic methods for frequency domain transfer function estimation such as the Empirical Transfer Function Estimate (ETFE) and cross spectral method do not work well when the noise signal is complex. Combines the time domain and frequency domain methods the Empirical Frequency-domain Optimal Parameter (EFOP) Estimate was presented. It could improve the precision of system's transfer function estimation and identification efficiency. The convergence of the EFOP based on frequency domain smoothing is investigated in this paper. The transfer function is weighted by a frequency window and the GPE criterion is extended to the integral form. Convergence rate and consistent properties for the EFOP estimate are given. Finally, some simulation results are included to illustrate the advantage of the EFOP based smoothing method.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 781856, 8 pages.

Dates
First available in Project Euclid: 9 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1399645330

Digital Object Identifier
doi:10.1155/2013/781856

Mathematical Reviews number (MathSciNet)
MR3066316

Zentralblatt MATH identifier
1271.94012

Citation

Zhang, Yulai; Lo, Kueiming; Su, Yang. Convergence Analysis of EFOP Estimate Based on Frequency Domain Smoothing. J. Appl. Math. 2013, Special Issue (2013), Article ID 781856, 8 pages. doi:10.1155/2013/781856. https://projecteuclid.org/euclid.jam/1399645330


Export citation

References

  • L. Ljung, System Identification, Wiley Online Library, 1999.
  • C. Bingham, M. Godfrey, and J. Tukey, “Modern techniques of power spectrum estimation,” IEEE Transactions on Audio and Electroacoustics, vol. 15, no. 2, pp. 56–66, 1967.
  • P. C. W. Sommen, P. J. van Gerwen, H. J. Kotmans, and A. J. E. M. Janssen, “Convergence analysis of a frequency-domain adaptive filter with exponential power averaging and generalized window function,” IEEE Transactions on Circuits and Systems, vol. 34, no. 7, pp. 788–798, 1987.
  • R. Pintelon and J. Schoukens, System Identification: A Frequency Domain Approach, Wiley-IEEE Press, 2004.
  • A. Stenman, F. Gustafsson, D. E. Rivera, L. Ljung, and T. McKelvey, “On adaptive smoothing of empirical transfer function estimates,” Control Engineering Practice, vol. 8, no. 11, pp. 1309–1315, 2000.
  • H. Hjalmarsson and B. Ninness, “Least-squares estimation of a class of frequency functions: a finite sample variance expression,” Automatica, vol. 42, no. 4, pp. 589–600, 2006.
  • J. C. Agüero, J. I. Yuz, G. C. Goodwin, and R. A. Delgado, “On the equivalence of time and frequency domain maximum likelihood estimation,” Automatica, vol. 46, no. 2, pp. 260–270, 2010.
  • K. Lo and W. H. Kwon, “A new identification approach for FIR models,” IEEE Transactions on Circuits and Systems II, vol. 49, no. 6, pp. 439–446, 2002.
  • K. Lo and H. Kimura, “Recursive estimation methods for discrete systems,” IEEE Transactions on Automatic Control, vol. 48, no. 11, pp. 2019–2023, 2003.
  • J. C. Agüero, W. Tang, J. I. Yuz, R. Delgado, and G. C. Goodwin, “Dual time-frequency domain system identification,” Automatica, vol. 48, no. 12, pp. 3031–3041, 2012.
  • K. Lo, H. Kimura, W. H. Kwon, and X. Yang, “Empirical frequency-domain optimal parameter estimate for black-box processes,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 2, pp. 419–430, 2006.
  • H. J. Vermeulen, J. M. Strauss, and V. Shikoana, “Online estimation of synchronous generator parameters using PRBS perturbations,” IEEE Transactions on Power Systems, vol. 17, no. 3, pp. 694–700, 2002.