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Signal Processing Magazine, IEEE

Issue 3 • Date July 1994

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  • A state-space approach to adaptive RLS filtering

    Page(s): 18 - 60
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3600 KB)  

    Adaptive filtering algorithms fall into four main groups: recursive least squares (RLS) algorithms and the corresponding fast versions; QR- and inverse QR-least squares algorithms; least squares lattice (LSL) and QR decomposition-based least squares lattice (QRD-LSL) algorithms; and gradient-based algorithms such as the least-mean square (LMS) algorithm. Our purpose in this article is to present yet another approach, for the sake of achieving two important goals. The first one is to show how several different variants of the recursive least-squares algorithm can be directly related to the widely studied Kalman filtering problem of estimation and control. Our second important goal is to present all the different versions of the RLS algorithm in computationally convenient square-root forms: a prearray of numbers has to be triangularized by a rotation, or a sequence of elementary rotations, in order to yield a postarray of numbers. The quantities needed to form the next prearray can then be read off from the entries of the postarray, and the procedure can be repeated; the explicit forms of the rotation matrices are not needed in most cases.<> View full abstract»

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  • A bibliography of higher-order spectra and cumulants

    Page(s): 61 - 70
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    Freely Available from IEEE

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IEEE Signal Processing Magazine publishes tutorial-style articles on signal processing research and applications, as well as columns and forums on issues of interest.

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Min Wu
University of Maryland, College Park
United States