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LMS Algorithm Step Size Adjustment for Fast Convergence

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Języki publikacji
EN
Abstrakty
EN
In the areas of acoustic research or applications that deal with not-precisely-known or variable condi- tions, a method of adaptation to the uncertainness or changes is usually necessary. When searching for an adaptation algorithm, it is hard to overlook the least mean squares (LMS) algorithm. Its simplicity, speed of computation, and robustness has won it a wide area of applications: from telecommunication, through acoustics and vibration, to seismology. The algorithm, however, still lacks a full theoretical analysis. This is probabely the cause of its main drawback: the need of a careful choice of the step size – which is the reason why so many variable step size flavors of the LMS algorithm has been developed. This paper contributes to both the above mentioned characteristics of the LMS algorithm. First, it shows a derivation of a new necessary condition for the LMS algorithm convergence. The condition, although weak, proved useful in developing a new variable step size LMS algorithm which appeared to be quite different from the algorithms known from the literature. Moreover, the algorithm proved to be effective in both simulations and laboratory experiments, covering two possible applications: adaptive line enhancement and active noise control.
Rocznik
Strony
31--40
Opis fizyczny
Bibliogr. 23 poz., tab., wykr.
Twórcy
autor
  • Institute of Automatic Control, Silesian University of Technology Akademicka 16, 44-100 Gliwice, Poland, Dariusz.Bismor@polsl.pl
Bibliografia
  • 1. Aboulnasr T., Mayyas K. (1997), A robust variable step-size LMS-type algorithm: Analysis and simulations, IEEE Transactions on Signal Processing, 45,3, 631-639.
  • 2. Ang W., Farhang-Boroujeny B. (2001), A new class of gradient adaptive step-size LMS algorithms, IEEE Transactions on Signal Processing, 49, 4, 805-810.
  • 3. Bi Y., Lai F., Ye Y. (2010), Gradient vector driven variable step size least mean square algorithm, [in:] 2nd International Asia Conference on Informatics in Control, Automation and Robotics 2010, pp. 41-44, Wuhan, China.
  • 4. Bismor D. (2008), Stability-based algorithm for LMS step size adjustment, [in:] Proceedings of the 15th International Congress on Sound and Vibration, Daejeon, Korea.
  • 5. Bismor D. (2009), Active noise control using stabilitybased LMS step size adjustment, [in:] Proceedings of the 16th International Congress on Sound and Vibration, Krak, Poland.
  • 6. Butterweck H. (1995), A steady-state analysis of the LMS adaptive algorithm without use of the independence assumption, Proceedings of ICASSP, pp. 1404-1407.
  • 7. Elliott S. (2001), Signal Processing for Active Noise Control, Academic Press, London.
  • 8. Evans J.B., Xue P., Liu B. (1993), Analysis and implementation of variable step size adaptive algorithms, IEEE Transactions on Signal Processing, 41, 8, 2517-2235.
  • 9. Harris R.W., Chabries D.M., Bishop F.A. (1986), A variable step (vs) adaptive filter algorithm, IEEE Transactions on Acoustics, Speech, and Signal Processing, ASSP, 34, 2, 309-316.
  • 10. Hassibi B., Sayed A.H., Kailath T. (1993), LMS is H∞ optimal, [in:] Proceedings of the 32nd IEEE Conference on Decision and Control, pp. 74-79, vol. 1.
  • 11. Hassibi B., Sayed A.H., Kailath T. (1996), H∞ optimality of the LMS algorithm, IEEE Transactions on Signal Processing, 44, 2, 267-280.
  • 12. Haykin S. (2002), Adaptive Filter Theory, Fourth Edition, Prentice Hall, New York.
  • 13. Hwang J., Li Y. (2009), Variable step-size LMS algorithm with a gradient-based weighted average, IEEE Signal Processing Letters, 16, 12, 1043-1046.
  • 14. Kaczorek T. (1993), Control and system theory [in Polish: Teoria sterowania i systemów], Wydawnictwo Naukowe PWN, Warszawa.
  • 15. Kuo S., Morgan D. (1996), Active Noise Control Systems, John Wiley & Sons, New York.
  • 16. Kwong R.H., Johnston E.W. (1992), Variable step size LMS algorithm, IEEE Transactions on Signal Processing, 40, 7, 1633-1642.
  • 17. Latos M., Pawelczyk M. (2010), Adaptive algorithms for enhancement of speech subject to a high-level noise, Archives of Acoustics, 35, 2, 203-212.
  • 18. Liu F., Zhang Y., Wang Y. (2009), A variable step size LMS adaptive filtering algorithm based on the number of computing mechanisms, [in:] Eighth International Conference on Machine Learning and Cybernetics, pp. 1904-1908, Baoding.
  • 19. Mathews V.J., Xie Z. (1993), A stochastic gradient adaptive filter with gradient adaptive step size, IEEE Transactions on Signal Processing, 41, 6, 2075-2087.
  • 20. Sayed A.H. (2003), Fundamentals of Adaptive Filtering, John Wiley & Sons, New York.
  • 21. Sun J., Huang B., Wei G., Liu D. (2009), Improved variable step size (IVSS) LMS for active noise control system, [in:] ICROS-SICE International Joint Conference, pp. 2054-2057, Fukuoka, Japan.
  • 22. Wang P., Kam P.Y., Chia M.W. (2009), A novel automatic step-size adjustment approach in the LMS algorithm, [in:] The First International Conference on Wireless VITAE, pp. 867-871, Aalborg, Denmark.
  • 23. Zou K., Zhao X. (2009), A new modified robust variable step size LMS algorithm, [in:] The 5th IEEE Conference on Industrial Electronics and Applications, pp. 2699-2703, Xi'an, China.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS8-0021-0071
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