Regularized fast recursive least squares algorithms for finite memory filtering

Novel fast recursive least squares algorithms are developed for finite memory filtering, by using a sliding data window. These algorithms allow the use of statistical priors about the solution, and they maintain a balance between a priori and data information. They are well suited for computing a re...

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Vydáno v:IEEE transactions on signal processing Ročník 40; číslo 4; s. 758 - 769
Hlavní autor: Houacine, A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.04.1992
Témata:
Adaptive estimation
Covariance matrix
Equations
Filtering algorithms
Finite impulse response filter
Least squares approximation
Least squares methods
Numerical stability
Partitioning algorithms
Transversal filters
ISSN:1053-587X
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Shrnutí:Novel fast recursive least squares algorithms are developed for finite memory filtering, by using a sliding data window. These algorithms allow the use of statistical priors about the solution, and they maintain a balance between a priori and data information. They are well suited for computing a regularized solution, which has better numerical stability properties than the conventional least squares solution. The algorithms have a general matrix formulation, such that the same equations are suitable for the prewindowed as well as the covariance case, regardless of the a priori information used. Only the initialization step and the numerical complexity change through the dimensions of the intervening matrix variables. The lower bound of O(16m) is achieved in the prewindowed case when the estimated coefficients are assumed to be uncorrelated, m being the order of the estimated model. It is shown that a saving of 2m multiplications per recursion can always be obtained. The lower bound of the resulting numerical complexity becomes O(14m), but then the general matrix formulation is lost.< >
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ISSN:1053-587X
DOI:10.1109/78.127950