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Stability and operating constraints of adaptive lms-based feedback control

AUTOMATICA 2003年第4期39卷 595-605页

作者： Vaudrey, MA Baumann, WT Saunders, WR Adapt Technol Inc Blacksburg VA 24060 USA Virginia Polytech Inst & State Univ Blacksburg VA 24061 USA

The filtered-X lms algorithm has enjoyed widespread usage in both adaptive feedforward and feedback controller architectures. For feedforward controller designs the filtered-X lms algorithm has been shown to exhibit unstable divergence for plant estimation errors in excess of 90degrees. Typical implementations of this algorithm in adaptive feedback controllers such as filtered-U and filtered-E have previously been assumed to conform to these same identification constraints. Here we present two instability mechanisms that can arise in filtered-E control that violate the 90degrees error assumption: feedback loop instabilities and lms algorithm divergence. Analysis of the adaptive feedback system indicates that the conventionally interpreted plant estimation error can be arbitrarily small yet induce algorithm divergence;while other cases may have very large estimation errors and feedback loops cause controller instability. These analytical observations are supported by simulations. The implications of the actual plant estimation error, calculated here for the filtered-E controller, are extended to practical constraints placed on applications including filtered-U, on-line system identification, and self-excited system control. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： adaptive control filter stability feedback control lms algorithm active noise control adaptive digital filters

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Convergence analysis of chip- and fractionally spaced lms adaptive multiuser CDMA detectors

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2000年第8期48卷 2219-2228页

作者： Lim, TJ Gong, Y Farhang-Boroujeny, B NUS Ctr Wireless Commun Res Ctr Singapore Singapore Natl Univ Singapore Dept Elect Engn Singapore 117548 Singapore

This paper analyzes the convergence behavior of the least mean square (lms) filter when used in an adaptive code division multiple access (CDMA) detector consisting of a tapped delay line with adjustable tap weights. The sampling rate may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally spaced (FS) detection, respectively. It is shown that CS and FS detectors with the same time-span exhibit identical convergence behavior if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). This phenomenon is carefully explained with reference to the eigenvalues of the correlation matrix when the input signal is not perfectly bandlimited, The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of transient behavior and the influence of the initial tap weight vector on convergence speed are highlighted. Specifically, initialization within the signal subspace or to the origin leads to very much faster convergence compared with initialization in the noise subspace.

关键词： CDMA convergence analysis fractionally spaced lms algorithm

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Distributed lms for Consensus-Based In-Network Adaptive Processing

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第6期57卷 2365-2382页

作者： Schizas, Ioannis D. Mateos, Gonzalo Giannakis, Georgios B. Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

Adaptive algorithms based on in-network processing of distributed observations are well-motivated for online parameter estimation and tracking of (non)stationary signals using ad hoc wireless sensor networks (WSNs). To this end, a fully distributed least mean-square (D-lms) algorithm is developed in this paper, offering simplicity and flexibility while solely requiring single-hop communications among sensors. The resultant estimator minimizes a pertinent squared-error cost by resorting to i) the alternating-direction method of multipliers so as to gain the desired degree of parallelization and ii) a stochastic approximation iteration to cope with the time-varying statistics of the process under consideration. Information is efficiently percolated across the WSN using a subset of "bridge" sensors, which further tradeoff communication cost for robustness to sensor failures. For a linear data model and under mild assumptions aligned with those considered in the centralized lms, stability of the novel D-lms algorithm is established to guarantee that local sensor estimation error norms remain bounded most of the time. Interestingly, this weak stochastic stability result extends to the pragmatic setup where intersensor communications are corrupted by additive noise. In the absence of observation and communication noise, consensus is achieved almost surely as local estimates are shown exponentially convergent to the parameter of interest with probability one. Mean-square error performance of D-lms is also assessed. Numerical simulations: i) illustrate that D-lms outperforms existing alternatives that rely either on information diffusion among neighboring sensors, or, local sensor filtering;ii) highlight its tracking capabilities;and iii) corroborate the stability and performance analysis results.

关键词： Distributed estimation lms algorithm wireless sensor networks (WSNs)

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Necessary and sufficient conditions for stability of lms

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1997年第6期42卷 761-770页

作者： Guo, L Ljung, L Wang, GJ LINKOPING UNIV DEPT ELECT ENGNS-58183 LINKOPINGSWEDEN CENT UNIV NATIONAL DEPT MATHBEIJING 100081PEOPLES R CHINA

In a recent work [7], some general results on exponential stability of random linear equations are established which can be applied directly to the performance analysis of a wide class of adaptive algorithms, including the basic lms ones, without requiring stationarity, independency, and boundedness assumptions of the system signals, The current paper attempts to give a complete characterization of the exponential stability of the lms algorithms by providing a necessary and sufficient condition for such a stability in the case of possibly unbounded, nonstationary, and non-phi-mixing signals, The results of this paper can be applied to a very large class of signals, including those generated from, e.g., a Gaussian process via a time-varying linear filter. As an application, several novel and extended results on convergence and the tracking performance of lms are derived under various assumptions, Neither stationarity nor Markov-chain assumptions are necessarily required in the paper.

关键词： exponential stability lms algorithm nonstationary signals tracking performance

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A performance bound for the lms estimator

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IEEE TRANSACTIONS ON INFORMATION THEORY 2000年第3期46卷 1150-1158页

作者： Quirk, KJ Milstein, LB Zeidler, JR Univ Calif San Diego Dept Elect & Comp Engn La Jolla CA 92093 USA

The least-mean-square (lms) estimator is a nonlinear estimator with information dependencies spanning the entire set of data fed into it. The traditional analysis techniques used to model this estimator obscure these dependencies;to simplify the analysis they restrict the estimator to the finite set of data sufficient to span the Length of its tilter. Thus the finite Wiener filter is often considered a bound on the performance of the lms estimator. Several papers bare reported the performance of the lms filter exceeding that of the finite Wiener filter, In this correspondence, we derive a hound on the lms estimator which does not exclude the contributions from data outside its filter length. We give examples of this bound in eases where the LR IS estimator outperforms the finite Wiener filter.

关键词： adaptive filter lms algorithm multidimensional filtering noise canceler spectral factorization Wiener filter

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Pipelined architecture of the lms adaptive digital filter with the minimum output latency

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1998年第8期E81A卷 1578-1585页

作者： Harada, A Nishikawa, K Kiya, H Tokyo Metropolitan Univ Dept Elect Engn Grad Sch Hachioji Tokyo 1920397 Japan

In this paper, we propose two new pipelined adaptive digital filter architectures. The architectures are based on an equivalent expression of the least mean square (lms) algorithm. It is shown that one of the proposed architectures achieves the minimum output latency, or zero without affecting the convergence characteristics. We also show that, by increasing the output latency be one, the other architecture can be obtained which has a shorter critical path.

关键词： pipelining lms algorithm output latency adaptive digital filter

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Analysis of Convergence of a Frequency-Domain lms Adaptive Filter Implemented as a Multi-Stage Adaptive Filter

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JOURNAL OF SIGNAL PROCESSING SYSTEMS FOR SIGNAL IMAGE AND VIDEO TECHNOLOGY 2009年第2-3期56卷 341-350页

作者： Ogunfunmi, Tokunbo Paul, Thomas Santa Clara Univ Dept Elect Engn Santa Clara CA 95053 USA

We present an analysis of the convergence of the frequency-domain lms adaptive filter when the DFT is computed using the lms steepest descent algorithm. In this case, the frequency-domain adaptive filter is implemented with a cascade of two sections, each updated using the lms algorithm. The structure requires less computations compared to using the FFT and is modular suitable for VLSI implementations. Since the structure contains two adaptive algorithms updating in parallel, an analysis of the overall system convergence needs to consider the effect of the two adaptive algorithms on each other, in addition to their individual convergence. Analysis was based on the expected mean-square coefficient error for each of the two lms adaptive algorithms, with some simplifying approximations for the second algorithm, to describe the convergence behavior of the overall system. Simulations were used to verify the results.

关键词： Adaptive filter VLSI implementation Convergence analysis lms algorithm

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NOISE-REDUCTION BASED ON MICROPHONE ARRAY WITH lms ADAPTIVE POST-FILTERING

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ELECTRONICS LETTERS 1990年第24期26卷 2036-2037页

作者： ZELINSKI, R Deutshe Bundespost Telekom Res. Inst. Berlin Germany

The author presents a self-adapting noise reduction system which is based on a 4-microphone array combined with an adaptive Wiener filter. The lms algorithm is used for adaptation. This filtering structure allows a si... 详细信息

关键词： lms adaptive post-filtering lms algorithm acoustic noise acoustic room noise acoustic signal processing adaptive Wiener filter adaptive systems audio systems filters interference suppression microphone array microphones sample-by-sample basis self-adapting noise reduction system signal processing equipment

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Combined adaptive filter with lms-based algorithms

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2003年第4期57卷 295-299页

作者： Krstajic, B Stankovic, L Uskokovic, Z Univ Montenegro Dept Elect Engn YU-81000 Podgorica Montenegro Yugoslavia

A combined adaptive filter is proposed. It consists of parallel lms-based adaptive FIR filters and an algorithm for choosing the better among them. As a criterion for comparison of the considered algorithms in the proposed filter, we take the ratio between bias and variance of the weighting coefficients. Simulations results confirm the advantages of the proposed adaptive filter.

关键词： adaptive filter lms algorithm combined algorithm bias and variance trade-off

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Steady-state analysis of the long lms adaptive filter

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SIGNAL PROCESSING 2011年第4期91卷 690-701页

作者： Butterweck, H. J. Tech Univ Eindhoven Dept Elect Engn NL-5600 MB Eindhoven Netherlands

For the well-known lms adaptive algorithm no general analytic solutions are available for the steady-state weight-error statistics under stationary stochastic excitation. Only approximate tools have been developed using certain assumptions (like the "independence assumption") and producing more or less reliable results in practical situations. It is only for the case of a vanishingly small stepsize that such assumptions are not required. There a closed-form solution can be determined for any colouring of the input signal and the additive noise. Here another particular problem is analyzed: the long filter, i.e. a tapped-delay line structure with a large number of taps. For the limiting case of an infinitely long filter, exact closed-form solutions are derived for the steady-state weight-error correlations and the associated "misadjustment", again valid for any colouring of the input signal and the additive noise, and now also for any stepsize guaranteeing stability. The analysis is based upon a feedback approach, with a forward branch generating the above-mentioned solution for vanishing stepsize and a peculiar feedback branch responsible for higher-order corrections. As in any feedback structure, instability can occur beyond a critical value of the feedback parameter. In our case an experimentally supported maximum stepsize is found, beyond which spontaneous oscillations might occur. (C) 2010 Elsevier B.V. All rights reserved.

关键词： lms algorithm Long filter Steady-state behaviour Misadjustment

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