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STABLE AND EFFICIENT LATTICE algorithms FOR ADAPTIVE IIR filtering

IEEE TRANSACTIONS ON SIGNAL PROCESSING 1992年第2期40卷 375-388页

作者： REGALIA, PA Départment Electronique et Communications Institut National de Télécommunications Evry France

Conventional direct-form adaptive IIR filters suffer from potential instability problems, and as such there is a general interest in adaptive filters based on alternate parametrizations. The normalized lattice filter is one example of a filter structure whose stability can be ensured theoretically in a time-varying environment, and thus the structure is well suited for adaptive IIR filtering. Previous attempts at applying lattice structures to adaptive IIR filtering have met with gradient computations of O(N2) complexity. To overcome this computational burden, two new lattice-based algorithms are proposed for adaptive IIR filtering and system identification, with both algorithms of O(N) complexity. The first algorithm is a reinterpretation of the Steiglitz-McBride method, while the second is a variation on the output error method. State space models are employed to make the derivations transparent, and the methods can be extended to other parametrizations if desired. The set of possible stationary points of the algorithms are shown to be consistent with the convergent points obtained from the direct-form versions of the Steiglitz-McBride and output error methods, whose properties are well studied. The derived algorithms are as computationally efficient as existing direct-form based algorithms, while overcoming the stability problems associated with time-varying direct-form filters.

关键词： Lattices filtering algorithms Adaptive filters IIR filters Finite impulse response filter Stability System identification Signal processing algorithms State-space methods Modeling

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Efficient least squares adaptive algorithms for FIR transversal filtering

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IEEE SIGNAL PROCESSING MAGAZINE 1999年第4期16卷 13-41页

作者： Glentis, GO Berberidis, K Theodoridis, S Technol Educ Inst Hereklion Dept Electr Khania Greece Univ Patras Dept Comp Eng & Informat Patras Greece Univ Athens Dept Informat Athens Greece

A unified view of algorithms for adaptive transversal FIR filtering and system identification has been presented. Wiener filtering and stochastic approximation are the origins from which all the algorithms have been derived, via a suitable choice of iterative optimization schemes and appropriate design parameters. Following this philosophy, the LMS algorithm and its offspring have been presented and interpreted as stochastic approximations of iterative deterministic steepest descent optimization schemes. On the other hand, the RLS and the quasi-RLS algorithms, like the quasi-Newton, the FNTN, and the affine projection algorithm, have been derived as stochastic approximations of iterative deterministic Newton and quasi-Newton methods. Fast implementations of these methods have been discussed. Block-adaptive, and block-exact adaptive filtering have also been considered. The performance of the adaptive algorithms has been demonstrated by computer simulations.

关键词： Least squares methods Adaptive algorithm Finite impulse response filter Iterative algorithms Least squares approximation Stochastic processes filtering algorithms Adaptive filters Wiener filter Transversal filters

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BINARY PARTITION algorithms AND VLSI ARCHITECTURES FOR MEDIAN AND RANK ORDER filtering

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1993年第9期41卷 2937-2942页

作者： LEE, CL JEN, CW NATL CHIAO TUNG UNIV INST ELECTRHSINCHUTAIWAN NATL CHIAO TUNG UNIV DEPT ELECTR ENGNHSINCHUTAIWAN

A class of selection algorithms by binary partition is very efficient for median and rank order filtering. A unified discussion of these algorithms is presented. Binary partition algorithms have better time-area complexity than sorting methods. Counting, firing, and updating are three basic steps. A generic structure is proposed to realize these algorithms. They can be implemented by simple and regular modules in VLSI.

关键词： Partitioning algorithms filtering algorithms Very large scale integration Signal processing algorithms Filters Interpolation Sorting Signal processing Speech processing Statistics

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REGULARIZED FAST RECURSIVE LEAST-SQUARES algorithms FOR ADAPTIVE filtering

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1991年第4期39卷 860-871页

作者： HOUACINE, A Institute of Electronics University of Sciences and Technology of Algiers U. S. T. H. B. Algiers Algeria

We develop here new fast recursive least squares (FRLS) algorithms by using factorization techniques which represent an alternative way to the geometrical projections approach or the matrix partitioning based derivations. The estimation problem is formulated within a regularization approach, and priors are used to get a regularized solution which presents better numerical stability properties than the conventional least squares one. The numerical complexity of the algorithms we present here is explicity related to the displacement rank of the priori covariance matrix of the solution. It then varies between 0(5m) and that of the slow RLS algorithms to update the Kalman gain vector, m being the order of the solution. An important advantage of our algorithms is that they admit a unified formulation such that the same equations may treat equally the prewindowed and the covariance cases independently from the used priors. The difference lies only in the involved numerical complexity, which modifies through a change of the dimensions of the intervening variables. Simulation results are given to illustrate the the performances of these algorithms.

关键词： Least squares methods filtering algorithms Adaptive filters Numerical stability Least squares approximation Equations Linear regression Covariance matrix Resonance light scattering Kalman filters

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NEW LEVINSON, SCHUR, AND LATTICE TYPE algorithms FOR LINEAR-PHASE filtering

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IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING 1990年第11期38卷 1879-1892页

作者： BERBERIDIS, K THEODORIDIS, S UNIV PATRAS INST COMP TECHNOLGR-26500 PATRASGREECE

The LS estimate of the impulse response of FIR filters with linear phase is known to be given by a structured linear set of equations. Three new algorithms are presented for the efficient solution of such systems. One is the unwindowed extension of a previously derived Levinson-type structurally symmetric algorithm. The second is a novel exact least squares lattice algorithm for time-recursive processing. The third is a Schur-type structurally symmetric algorithm with high degree of parallelism. The new structures have considerably lower computational complexity and more parsimonious parametrization compared to previously derived algorithms. This is because, in contrast to the previously derived algorithms, the new algorithms are developed so as to respect the symmetry which is intrinsic in the linear phase problem.< >

关键词： Lattices filtering algorithms Nonlinear filters Finite impulse response filter Signal processing algorithms Equations Least squares methods System identification Spectral analysis Transversal filters

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Normalized sliding window constant modulus and decision-directed algorithms: A link between blind equalization and classical adaptive filtering

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1997年第1期45卷 231-235页

作者： Papadias, CB Slock, DTM EURECOM INST F-06904 SOPHIA ANTIPOLISFRANCE

By minimizing a deterministic criterion of the constant modulus (CM) type or of the decision-directed (DD) type, we derive normalized stochastic gradient algorithms for blind linear equalization (BE) of QAM systems, These algorithms allow us to formulate CM and DD separation principles, which help obtain a whole family of CM or DD BE algorithms from classical adaptive filtering algorithms, We focus on the algorithms obtained by using the affine projection adaptive filtering algorithm (APA), Their increased convergence speed and ability to escape from local minima of their cost function make these algorithms very promising for BE applications.

关键词： Signal processing algorithms filtering algorithms Decision feedback equalizers Delay Quadrature amplitude modulation Adaptive filters Adaptive equalizers Attenuation Blind equalizers Least squares approximation

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EFFICIENT TIME-RECURSIVE LEAST-SQUARES algorithms FOR FINITE-MEMORY ADAPTIVE filtering

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS 1987年第4期34卷 400-408页

作者： MANOLAKIS, D LING, F PROAKIS, JG CODEX CORP DEPT TRANSMISS PRODMANSFIELDMA 02148

This paper deals with efficient algorithms in the sense of minimization of the computational complexity for least-squares (LS) adaptive filters with finite memory. These filters obtain the current estimate of the desired response using only a fixed finite number of past data. First, two new fast recursive least-squares algorithms with computational complexities14mand15mmultiplications and divisions per recursion (MADPR), respectively, are introduced (mis the filter order). Then a new estimation-error-oriented recursive modified Gram-Schmidt (RMGS) scheme with a complexity of2m^algorithms + 10mMADPR is given. Finally, the learning characteristics of these algorithms are discussed and some simulation results are included.

关键词： filtering algorithms Adaptive filters Finite impulse response filter Minimization methods Computational complexity Recursive estimation Interference Application software Kalman filters Computational modeling

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COMPARISON OF algorithms FOR STANDARD MEDIAN filtering

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 1991年第1期39卷 204-208页

作者： JUHOLA, M KATAJAINEN, J RAITA, T LINKOPING UNIV DEPT COMP & INFORMAT SCILINKOPINGSWEDEN

In standard median filtering we search repeatedly for a median from a sample set which changes only slightly between the subsequent searches. We review several well-known methods for solving this running median problem, analyze the (asymptotical) time complexities of the methods, and propose simple variants which are especially suited for small sample sets, a frequent situation. Although we have restricted our discussion to the one-dimensional case, the ideas are easily extended to higher dimensions.

关键词： filtering algorithms Data structures Computer science Information science Sorting

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LATTICE algorithms FOR RECURSIVE LEAST-SQUARES ADAPTIVE 2ND-ORDER VOLTERRA filtering

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING 1994年第3期41卷 202-214页

作者： SYED, MA MATHEWS, VJ UNIV UTAH DEPT ELECT ENGNSALT LAKE CITYUT 84112

This paper presents two computationally efficient recursive least-squares (RLS) lattice algorithms for adaptive nonlinear filtering based on a truncated second-order Volterra system model. The lattice formulation transforms the nonlinear filtering problem into an equivalent multichannel, linear filtering problem and then generalizes the lattice solution to the nonlinear filtering problem. One of the algorithms is a direct extension of the conventional RLS lattice adaptive linear filtering algorithm to the nonlinear case. The other algorithm is based on the QR decomposition of the prediction error covariance matrices using orthogonal transformations. Several experiments demonstrating and comparing the properties of the two algorithms in finite and ''infinite'' precision environments are included in the paper. The results indicate that both the algorithms retain the fast convergence behavior of the RLS Volterra filters and are numerically stable.

关键词： Lattices filtering algorithms Least squares methods Adaptive filters Nonlinear filters Signal processing algorithms Resonance light scattering Transversal filters Maximum likelihood detection Covariance matrix

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Online Graph Models: Tackling the Challenges of Non-Gaussian Noise in Adaptive filtering

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2025年

作者： Zhong, Shan Wang, Gang Teh, Kah Chan He, Jiacheng Cheng, Tee Hiang Peng, Bei Univ Elect Sci & Technol China Sch Mech & Elect Engn Chengdu 611731 Peoples R China Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Sichuan EIR Technol Co Ltd Chengdu 610041 Peoples R China

Adaptive filtering faces significant challenges in handling complex non-Gaussian noise, while graph signal processing (GSP) excels at processing data with intricate structures. This brief introduces a novel method for solving non-Gaussian noise from the perspective of the graph domain for the first time. Specifically, we develop an online time-varying graph model based on the filter error signal and propose a corresponding graph topology transformation strategy. Utilizing a graph smoothness measure, we introduce a new adaptive filtering cost function, in which the graph Laplacian matrix plays a direct role in the filter update process. Subsequently, we derive the graph smoothness recursive adaptive filtering (GS-RAF) algorithm, rigorously analyze its theoretical performance, and validate its efficacy through simulations and echo cancellation experiments. The corresponding MATLAB (MathWorks, USA) codes of the simulations are publicly available at: https://***/smartXiaoz/***.

关键词： Noise Cost function Germanium filtering Adaptive filters Vectors Laplace equations Adaptation models filtering algorithms Topology Adaptive filtering graph Laplacian matrix graph signal processing (GSP) non-Gaussian noise

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