The Transactions of the Korean Institute of Electrical Engineers D (대한전기학회논문지:시스템및제어부문D)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Geometric Analysis of Convergence of FXLMS Algorithm

FXLMS 알고리즘 수렴성의 기하학적 해석

  • Published : 2005.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper concerns on Filtered-x least mean square (FXLMS) algorithm for adaptive estimation of feedforward control parameters. The conditions for convergence in ensemble mean of the FXLMS algorithm are derived and the directional convergence properties are discussed from a new geometric vector analysis. The convergence and its directionality are verified along with some computer simulations.

Keywords

References

  1. S. Haykin, Adaptive Filter Theory, Prentice-Hall, Upper Saddle River, NJ, 2002
  2. B. Widrow, J. R. Glover, J. M. McCool, J. Kaunitz, C. S. Williams, R. H. Hern, J. R. Zeidler, E. Dong, and R.C. Goodlin, 'Active Noise Canceling: Principles and Applications,' Proc. IEEE, vol. 63, pp. 1692-1716, 1975 https://doi.org/10.1109/PROC.1975.10036
  3. B. Widrow and S. D. Stearns, Adaptive Signal rocessing, Prentice-Hall, Englewood Cliffs, NJ, 1985
  4. S. M. Kuo and D. R. Morgan, Active Noise Control Systems, A Wiley-Interscience Publication, John Wiley & Sons, Inc., 1996
  5. Y. D. Kim, M. M. Lee, and C. K. Chung, 'Single Channel Active Noise Control using Adaptive Model,' Trans. KIEE Vol. 49D-8-5, pp. 442-450, 2000
  6. J. Reason and W. Ren, 'Estimating the Optimal Adaptive Gain for the LMS Algorithm,' Proceedings of CDC, San Antonio, pp. 1587-1588, 1993
  7. M. T. White and M. Tomizuka, 'Increased Disturbance Rejection in Magnetic Disk Drives by Acceleration Feedforward Control and Parameter Adaptation,' Control Engineering Practice, vol. 5, no. 6., pp. 741-751, 1997 https://doi.org/10.1016/S0967-0661(97)00058-0
  8. M. S. Kang, 'Disturbance Compensation Control by FXLMS Algorithm', J. of KSPE, vol. 20, No. 11, pp. 100-107, 2003
  9. M. S. Kang and J. S. Jung, 'Disturbance Compensation Control of An Active magnetic Bearing System by Multiple FXLMS Algorithm-Theory', J. of KSPE, vol. 21, No. 2, pp. 74-82, 2004
  10. M. S. Kang and J. S. Jung, 'Disturbance Compensation Control of An Active magnetic Bearing System by Multiple FXLMS Algorithm-Experiment', J. of KSPE, vol. 21, No. 2, pp. 83-91, 2004
  11. L. Ljung, 'Analysis of Recursive Stochastic Algorithm,' IEEE Trans. on Automatic Control, vol. AC-22, no. 4, pp.551-575, 1977
  12. G. F. Franklin, J. D. Powell, and M. Workman, Digital Control of Dynamic Systems, Addison-Wesley, Longman, CA, 1998
  13. R. Bellman, Introduction to Matrix Analysis-2'nd edition, McGraw-Hill, p. 83, 1970
  14. T.A.C.M. Classen and W.F.G. Mecklanbrauker, 'Adaptive techniques for signal processing in communications,' IEEE Commun., vol. 23, pp.8-19, 1985 https://doi.org/10.1109/MCOM.1985.1092451