A Unified Approach to Structured Covariances: Fast Generalized Sliding Window RLS Recursions for Arbitrary Basis

This paper extends the existing fast RLS recursions originally intended to exponentially windowed problems for general models, to a generalized sliding window formulation (GSWRLS). From a matrix algebra perspective, we show explicitly how the displacement rank of the underlying inverse covariance ma...

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Vydáno v:	IEEE transactions on signal processing Ročník 61; číslo 23; s. 6060 - 6075
Hlavní autor:	Merched, Ricardo
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.12.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Applied sciences Covariance matrices Data structures Detection, estimation, filtering, equalization, prediction Exact sciences and technology Information, signal and communications theory lattice Matrix decomposition orthonormal model Polynomials regularized least-squares Signal and communications theory Signal processing Signal processing algorithms Signal, noise Sliding window RLS algorithm Telecommunications and information theory Breakpoint Recurrence orthonormal model Matrix algebra Generating function Equalizer Covariance matrix Recursive algorithm Kernel method Covariance Inverse matrix Least squares method First order lattice regularized least-squares Signal processing Sliding window RLS algorithm Data structure
ISSN:	1053-587X, 1941-0476
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Abstract	This paper extends the existing fast RLS recursions originally intended to exponentially windowed problems for general models, to a generalized sliding window formulation (GSWRLS). From a matrix algebra perspective, we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast GSWRLS calculates these rank factors in a fast manner. The recursions hold regardless of the (first order) data structure induced and show that fast fixed order and order recursive RLS algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors. Our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models, showing that efficient representations of their inverse covariances are not limited to factor circulants, but rather constructed from any arbitrary operator. These Bezoutians, usually expressed via reproducing kernel relations, can be represented exactly in matrix form, along with a precise correspondence to variables of a GSWRLS. As a fallout, we obtain a vector relation stating the so-called minimality property, for extended models and windows, as opposed to analogous generating function arguments normally seen in original approaches. These results pave the way to a more general framework of polynomial Vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials. This has further impact on several signal processing applications, including superfast realization of equalizers in communications scenarios.
AbstractList	This paper extends the existing fast RLS recursions originally intended to exponentially windowed problems for general models, to a generalized sliding window formulation (GSWRLS). From a matrix algebra perspective, we show explicitly how the displacement rank of the underlying inverse covariance matrix associated to any operator is defined as a function of the number of window breakpoints and how the fast GSWRLS calculates these rank factors in a fast manner. The recursions hold regardless of the (first order) data structure induced and show that fast fixed order and order recursive RLS algorithms can still be obtained for unwindowed data matrices exhibiting a fixed arbitrary relation between successive regressors. Our approach highlights the existence of a certain degree of freedom inherent to structured data matrices induced by general models, showing that efficient representations of their inverse covariances are not limited to factor circulants, but rather constructed from any arbitrary operator. These Bezoutians, usually expressed via reproducing kernel relations, can be represented exactly in matrix form, along with a precise correspondence to variables of a GSWRLS. As a fallout, we obtain a vector relation stating the so-called minimality property, for extended models and windows, as opposed to analogous generating function arguments normally seen in original approaches. These results pave the way to a more general framework of polynomial Vandermonde covariance decompositions which arise naturally via a proper choice of recurrence related polynomials. This has further impact on several signal processing applications, including superfast realization of equalizers in communications scenarios.
Author	Merched, Ricardo
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Keywords	Breakpoint Recurrence orthonormal model Matrix algebra Generating function Equalizer Covariance matrix Recursive algorithm Kernel method Covariance Inverse matrix Least squares method First order lattice regularized least-squares Signal processing Sliding window RLS algorithm Data structure
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References	ref35 ref13 ref12 ref37 ref36 ref14 ref31 merched (ref2) 2012 ref33 ref11 ref32 ref10 eidelman (ref24) 2007; 420 ref39 maouche (ref30) 1995; 1 ref17 ref38 ref19 ref18 sayed (ref1) 2003 ref45 ref23 ref26 ref25 ref20 ref42 bella (ref27) 0 ref41 ref22 ref21 ammar (ref44) 1990; iii ref43 szeg (ref34) 1975 bella (ref28) 2010; 199 heinig (ref29) 1984 ref8 ref7 ref9 ref4 ref3 ref6 ref5 ref40 b zout (ref16) 1764 euler (ref15) 1748
References_xml	– ident: ref39 doi: 10.1117/12.57512 – ident: ref11 doi: 10.1109/TSP.2003.815385 – ident: ref5 doi: 10.1109/PROC.1982.12429 – ident: ref22 doi: 10.1016/S0024-3795(96)00315-1 – ident: ref43 doi: 10.1109/ICDSP.2011.6004909 – ident: ref32 doi: 10.1109/ACSSC.2004.1399468 – start-page: 288 year: 1764 ident: ref16 article-title: Recherches sur le degr des quations r sultantes de l' vanouissement des inconnues et sur les moyens qu'on doit employer pour trouver ces quations publication-title: Histoire de l'Acad mie royale des sciences partie M moires – ident: ref17 doi: 10.1098/rstl.1853.0018 – ident: ref35 doi: 10.1109/ISCAS.2006.1693020 – ident: ref45 doi: 10.1016/S0024-3795(98)10076-9 – ident: ref41 doi: 10.1117/12.57673 – year: 2003 ident: ref1 publication-title: Fundamentals of Adaptive Filtering – ident: ref37 doi: 10.1109/TWC.2010.062910.091638 – ident: ref10 doi: 10.1109/78.969510 – ident: ref36 doi: 10.1109/TSP.2007.893753 – ident: ref31 doi: 10.1109/ICASSP.1995.479482 – volume: iii start-page: 421 year: 1990 ident: ref44 article-title: New decompositions of the inverse of a Toeplitz matrix publication-title: Signal Process Scattering Operator Theory Proc Int Symp (MTNS-89) – ident: ref38 doi: 10.1109/SPAWC.2008.4641586 – volume: 199 start-page: 127 year: 2010 ident: ref28 article-title: A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order publication-title: Operator Theory Adv Appl – year: 1984 ident: ref29 publication-title: Algebraic Methods for Toeplitz-Like Matrices and Operators doi: 10.1007/978-3-0348-6241-7 – ident: ref19 doi: 10.1515/crll.1856.52.39 – ident: ref13 doi: 10.1137/1020006 – start-page: 42 year: 1975 ident: ref34 publication-title: Orthogonal Polynomials – ident: ref20 doi: 10.1109/31.68295 – year: 0 ident: ref27 article-title: Characterization of <formula formulatype="inline"><tex Notation="TeX">$(H,1)$</tex> </formula> quasiseparable matrices and their subclasses via recurrence relations and signal flow graphs – ident: ref21 doi: 10.1007/BF02576000 – ident: ref23 doi: 10.1016/S0024-3795(98)10099-X – volume: 1 start-page: 685 year: 1995 ident: ref30 article-title: Performance analysis and FTF version of the generalized sliding window recursive least-squares (GSWRLS) algorithm publication-title: Proc 29th IEEE Annu Asilomar Conf Signals Syst Comput – ident: ref3 doi: 10.1109/ICCNC.2013.6504134 – ident: ref9 doi: 10.1109/TASSP.1984.1164427 – ident: ref33 doi: 10.1016/0022-247X(79)90282-8 – year: 1748 ident: ref15 publication-title: Introductio in Analysin Infinitorum – ident: ref8 doi: 10.1080/00207177808922343 – ident: ref18 doi: 10.1515/crll.1857.53.366 – ident: ref14 doi: 10.1016/0022-247X(79)90124-0 – ident: ref25 doi: 10.1016/j.laa.2009.08.016 – ident: ref26 doi: 10.1007/978-94-007-0602-6_2 – start-page: 1860 year: 2012 ident: ref2 article-title: A unified approach to structured covariances: Polynomial vandermonde bezoutian representations publication-title: Proc EUSIPCO – ident: ref42 doi: 10.1007/BF01200697 – volume: 420 start-page: 634 year: 2007 ident: ref24 article-title: A Bjorck-Pereyra-type algorithm for Szego-Vandermonde matrices based on properties of unitary Hessenberg matrices publication-title: Linear Algebra Appl doi: 10.1016/j.laa.2006.08.032 – ident: ref12 doi: 10.1155/ASP.2005.1235 – ident: ref6 doi: 10.1109/18.45275 – ident: ref7 doi: 10.1137/S0895479892238804 – ident: ref4 doi: 10.1109/TSP.2013.2264919 – ident: ref40 doi: 10.1109/78.218139
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SubjectTerms	Applied sciences Covariance matrices Data structures Detection, estimation, filtering, equalization, prediction Exact sciences and technology Information, signal and communications theory lattice Matrix decomposition orthonormal model Polynomials regularized least-squares Signal and communications theory Signal processing Signal processing algorithms Signal, noise Sliding window RLS algorithm Telecommunications and information theory
Title	A Unified Approach to Structured Covariances: Fast Generalized Sliding Window RLS Recursions for Arbitrary Basis
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