A New Quantized Input RLS, QI-RLS, Algorithm

  • A. Amiri
  • M. Fathy
  • M. Amintoosi
  • H. Sadoghi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4707)


Several modified RLS algorithms are studied in order to improve the rate of convergence, increase the tracking performance and reduce the computational cost of the regular RLS algorithm. . In this paper a new quantized input RLS, QI-RLS algorithm is introduced. The proposed algorithm is a modification of an existing method, namely, CRLS, and uses a new quantization function for clipping the input signal. We showed mathematically the convergence of the QI-RLS filter weights to the optimum Wiener filter weights. Also, we proved that the proposed algorithm has better tracking than the conventional RLS algorithm. We discuss the conditions which one have to consider so that he can get better performance of QI-RLS against the CRLS and standard RLS algorithms. The results of simulations confirm the presented analysis.


Adaptive Filter Recursive Least Square (RLS) Weiner Optimum Weights Tracking 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Deivasigamani, L.: A fast clipped-data LMS algorithm. IEEE Trans. Acoustics, Speech, and Signal Processing 30(4), 648–649 (1982)CrossRefGoogle Scholar
  2. 2.
    Eweda, E.: Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data. IEEE Trans. Circuits Syst. 37(11), 1367–1374 (1990)CrossRefGoogle Scholar
  3. 3.
    Eweda, E.: Comparison of RLS, LMS, and sign algorithms for tracking randomly time-varying channels. IEEE Trans. Signal Processing 42(11), 2937–2944 (1994)CrossRefGoogle Scholar
  4. 4.
    Feur, A., Weinstein, E.: Convergence analysis of LMS filters with uncorrelated Gaussian data. IEEE Trans. Acoust, Speech, Signal Processing 33, 222–230 (1985)CrossRefGoogle Scholar
  5. 5.
    Haykin, S.: Adaptive Filter Theory. Prentice-Hall, Englewood Cliffs (1996)Google Scholar
  6. 6.
    Haykin, S., Sayed, A.H., Zeidler, J., Yee, P., Wei, P.: Tracking of linear time-variant systems. In: Proc. IEEE Military Communications Conference (MILCOM ’95), San Diego, Calif, USA, vol. 2, pp. 602–606 (1995)Google Scholar
  7. 7.
    Kwong, C.: Dual sign algorithm for adaptive filtering. IEEE Trans. Commun. 34(12), 1272–1275 (1986)CrossRefGoogle Scholar
  8. 8.
    Mathews, V., Cho, S.H.: Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm. IEEE Trans. Acoustics, Speech, and Signal Processing 35(4), 450–454 (1987)zbMATHCrossRefGoogle Scholar
  9. 9.
    Sadoghi Yazdi, H., Fathy, M., Lotfizad, M.: Vehicle tracking at traffic scene with modified RLS. In: Campilho, A., Kamel, M. (eds.) ICIAR 2004. LNCS, vol. 3212, pp. 623–632. Springer, Heidelberg (2004)Google Scholar
  10. 10.
    Sadoghi Yazdi, H., Lotfizad, M., Kabir, E., Fathy, M.: Application of trajectory learning in tracking vehicles in the tra.c scene. In: Proc. 9th Annual Computer Society of Iran Computer Conference(CSICC ’04), vol. 1, Tehran, Iran, pp. 180–187 (2004)Google Scholar
  11. 11.
    Sadoghi Yazdi, H., Lotfizad, M., Kabir, E., Fathy, M.: Clipped input RLS Applied to Vehicle Tracking. EURASIP Journal on Applied Signal Processing 8, 1229–1234 (2005)Google Scholar
  12. 12.
    Vaseghi, S.: Advanced Signal Processing and Digital Noise Reduction. JohnWiley & Sons, New York (1996)Google Scholar
  13. 13.
    Widrow, B., Stearns, S.D.: Adaptive Signal Processing, Chs. 2-6. Prentice-Hall, Englewood Cliffs (1985)Google Scholar
  14. 14.
    Sethares, W.A., Mareels, I.M.Y., Anderson, B.D.O., Johnson Jr., C.R., Bitmead, R.R.: Excitation conditions for signed regressor least mean squares adaptation. IEEE Trans. Circuits Syst. 35(6), 613–624 (1988)CrossRefGoogle Scholar
  15. 15.
    Eleftheriou, E., Falconer, D.: Tracking properties and steady-state performance of RLS adaptive filter algorithms. IEEE Trans. Acoustics, Speech, and Signal Processing 34(5), 1097–1110 (1986)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • A. Amiri
    • 1
    • 2
  • M. Fathy
    • 2
  • M. Amintoosi
    • 2
    • 3
  • H. Sadoghi
    • 3
  1. 1.Islamic Azad University-Zanjan Branch 
  2. 2.Faculty of Computer Engineering, Iran University of Science and Technology 
  3. 3.Faculty of Engineering, Tarbiat Moallem University of SabzevarIran

Personalised recommendations