IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v270y2015icp511-526.html
   My bibliography  Save this article

Statistical convergence behavior of affine projection algorithms

Author

Listed:
  • Zhi, Yongfeng
  • Li, Jieliang
  • Zhang, Jun
  • Wang, Zhen

Abstract

Class of algorithms referring to the affine projection algorithms (APA) applies updates to the weights in a direction that is orthogonal to the most recent input vectors. This speeds up the convergence of the algorithm over that of the normalized least mean square (NLMS) algorithm, especially for highly colored input processes. In this paper a new statistical analysis model is used to analyze the APA class of algorithms with unity step size. Four assumptions are made, which are based on the direction vector for the APA class. Under these assumptions, deterministic recursive equations for the weight error and for the mean-square error are derived. We also analyze the steady-state behavior of the APA class. The new model is applicable to input processes that are autoregressive as well as autoregressive-moving average, and therefore is useful under more general conditions than previous models for prediction of the mean square error of the APA class. Simulation results are provided to corroborate the analytical results.

Suggested Citation

  • Zhi, Yongfeng & Li, Jieliang & Zhang, Jun & Wang, Zhen, 2015. "Statistical convergence behavior of affine projection algorithms," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 511-526.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:511-526
    DOI: 10.1016/j.amc.2015.08.054
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315011091
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.08.054?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhi, Yongfeng & Yang, Yunyi & Zheng, Xi & Zhang, Jun & Wang, Zhen, 2016. "Statistical tracking behavior of affine projection algorithm for unity step size," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 22-28.
    2. Deng, Xinyang & Zhang, Zhipeng & Deng, Yong & Liu, Qi & Chang, Shuhua, 2016. "Self-adaptive win-stay-lose-shift reference selection mechanism promotes cooperation on a square lattice," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 322-331.
    3. Liu, Yang & Wei, Bo & Du, Yuxian & Xiao, Fuyuan & Deng, Yong, 2016. "Identifying influential spreaders by weight degree centrality in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 1-7.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:511-526. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.