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Stochastic analysis of the nlms algorithm for nonstationary environment and deficient length adaptive filter

SIGNAL PROCESSING 2019年 160卷 190-201页

作者： Matsuo, Marcos Vinicius Kuhn, Eduardo Vinicius Seara, Rui Univ Fed Santa Catarina Dept Engn GEPS Elect & Signal Proc Grp BR-89036004 Blumenau SC Brazil Univ Fed Santa Catarina Dept Elect & Elect Engn LINSE Circuits & Signal Proc Lab BR-88040900 Florianopolis SC Brazil Univ Tecnol Fed Parana Dept Elect Engn LAPSE Elect & Signal Proc Lab BR-85902490 Toledo Parana Brazil

This paper presents a stochastic model of the normalized least-mean-square (nlms) algorithm assuming nonstationary environment, deficient length adaptive filter, as well as white and correlated Gaussian input data. Specifically, considering a system identification setup, the proposed stochastic model takes into account scenarios in which the adaptive filter may have lower order than the time-varying plant to be identified. Such an assumption (which is consistent with practical conditions) has not been considered in the research works discussed so far in the literature about stochastic analysis of adaptive algorithms operating under nonstationary environments. So, a stochastic model capable of describing the nlms algorithm behavior in more realistic operating scenarios is presented. Based on the proposed model, some interesting behaviors of the nlms algorithm are verified due to the mismatch between the order of the adaptive filter and the plant. In addition, the impact of the algorithm parameters on its performance is discussed, aiming to provide some useful design guidelines. The effectiveness of the proposed model is assessed through simulation results for different operating conditions. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Adaptive filtering Deficient length adaptive filter nlms algorithm Nonstationary environment Stochastic analysis

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Vibration reduction against modulated excitation using multichannel nlms algorithm for a structure with three active paths between plates

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JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY 2019年第10期33卷 4673-4680页

作者： Hong, Dongwoo Kim, Byeongil Yeungnam Univ Sch Mech Engn 280 Daehak Ro Gyongsan 712749 Gyeongsangbuk D South Korea

Electric and hybrid vehicle engines produce a complex spectrum of vibration and noise. Various active mounting techniques have been developed to isolate them. These are designed to continuously control the dynamic characteristics of the mounts and improve the noise, vibration, and harshness (NVH) performance under various operating conditions. Active mounts have attracted attention as replacement for existing mounts by simultaneously realizing static and dynamic stiffness, which is important for supporting an engine. Therefore, this study focuses on the vibration isolation performance of the upper plate and lower plate when the structure, including the active mounting system, is applied to multifrequency excitation. The overall modeling is based on the lumped parameter model, and the input signal is applied to the amplitude modulated and frequency modulated signals. The adaptive filter is applied for control, and the normalization least mean square (nlms) algorithm, which is commonly used in research, is extended to a multi-nlms algorithm. It is shown that when multifrequency input is applied, the adaptive filter is effectively applied to the active mounting system to control vibration.

关键词： Active engine mounting system Amplitude modulation Frequency modulation nlms algorithm NVH Piezo stack actuator Rubber mount

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New variable step-size fast nlms algorithm for non-stationary systems

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SIGNAL IMAGE AND VIDEO PROCESSING 2023年第6期17卷 3099-3107页

作者： Gueraini, Imen Benallal, Ahmed Tedjani, Ayoub Univ Blida1 Detect Informat & Commun Lab BP 270 Route Soumaa Blida 09000 Algeria Univ Blida1 Signal Proc & Image Lab LATSI BP 270 Route Soumaa Blida 09000 Algeria

In the field of echo cancellation, the normalized least mean squares (nlms) algorithm is the most popular adaptive algorithm due to its simplicity and ease of implementation. However, this category of algorithms presents a conflict between several performance criteria: the initial convergence speed, the tracking ability and the root mean square error of filtering (MSE) in the steady state. Variable-step algorithms (VSS) address the trade-off between convergence speed and low final MSE. Nevertheless, due to a fairly small adaptive step-size in the steady-state regime, they fail to adequately track variations of the unknown system and they are all implemented with the original nlms algorithm. In this contribution, a new improved variable adaptation step algorithm capable to track time variations of the unknown system even after good convergence in the steady state is suggested. It is based on the use of the fast-normalized adaptive algorithm (Fnlms) for system identification and acoustic echo cancellation context. The purposes of using the Fnlms algorithm in the field of VSS are on the one hand to improve its final MSE and, on the other hand, to obtain a VSS algorithm with better convergence and tracking compared to the VSS nlms algorithms. Simulation results show that the proposed VSS-Fast nlms algorithm outperforms the original Fnlms algorithm in terms of steady-state error reduction and minimization after the initial transition phase while maintaining similar convergence speed and tracking capacity. Furthermore, it achieves visible improvements in terms of two objective criteria, i.e., a faster initial convergence rate and a better tracking ability than the ones of the non-parametric VSS-nlms (NPVSS-nlms) and traditional nlms algorithms.

关键词： Adaptive filtering Acoustic Echo Cancellation Fast nlms algorithm Variable step-size nlms algorithm NPVSS-nlms Tracking capability Non-stationary system

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Optimal Sparsity Tradeoff in l₀-nlms algorithm

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IEEE SIGNAL PROCESSING LETTERS 2016年第8期23卷 1121-1125页

作者： Al-Shabili, Abdullah Weruaga, Luis Jimaa, Shihab Khalifa Univ Sci Technol & Res Sharjah U Arab Emirates

The l(0)-normalized least mean squares (l(0)-nlms) is arguably the reference gradient adaptive algorithm for sparse system estimation. However, alike all sparse gradient adaptive algorithms, the l(0)-nlms performance is sensitive to the (adequate) selection of the tradeoff parameter. Highlighted in this letter, the existence of two convergence modes, linked to the negligible and to the significant taps, paves the way for the convergence analysis, which results in a set of nonlinear (quadratic) convergence equations. Therefrom, the minimization of the steady-state misalignment concludes in the optimal tradeoff, which happens to relate to the nlms step size, filter length, plant sparsity, and noise level in an extremely compact fashion. Exhaustive simulation experiments show strong agreement between the analytical predictions and the empirical performance.

关键词： l(0)-norm nlms algorithm sparsity tradeoff

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H_∞ optimality and a posteriori output estimate of the forgetting factor nlms algorithm

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AUTOMATICA 2017年 75卷 244-248页

作者： Nishiyama, Kiyoshi Iwate Univ Fac Sci & Engn Dept Syst Innovat Engn 4-3-5 Ueda Morioka Iwate Japan

The normalized least mean squares (nlms) algorithm is widely used for adaptive filtering. The nlms algorithm may be extended using a variety of weight parameters that improve its performance. One such extension involves appropriately introducing a forgetting factor into the nlms algorithm using the H-infinity framework. The resultant forgetting factor nlms (FFnlms) algorithm may be regarded as a special case of the improved proportionate nlms (IPnlms) algorithm. This work reveals that the FFnlms algorithm is H-infinity-optimaL and the a posteriori output estimate is identical to the observation signal for sufficiently large times. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Adaptive filters Adaptive algorithm Forgetting factor nlms algorithm H-infinity filter

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A new nlms algorithm for slow noise magnitude variation

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IEEE SIGNAL PROCESSING LETTERS 2002年第11期9卷 348-351页

作者： Gazor, S Shahtalebi, K Queens Univ Dept Elect & Comp Engn Kingston ON K7L 3N6 Canada Minist Post Telegraph & Telephone Fac Appl Sci Post & Telecommun Esfahan Iran

A set-membership (SM) normalized least-mean-square (nlms) (SMnlms) algorithm is developed using SM theory in the class of optimal bounding ellipsoid (OBE) algorithms. This signed version of nlms algorithm requires a priori knowledge of a bound for the error magnitude, which is unknown in most applications. A very simple algorithm is proposed for the case in which the unknown magnitude of the measurement noise is slowly time-varying. The proposed algorithm is able to extract the noise magnitude information and exploit this magnitude to enhance or accelerate the learning process without risk of overbounding or performance loss due to underbounding. The performance of the proposed algorithm is compared with that of SMnlms using some simulation examples.

关键词： adaptive decision-feedback equalizer nlms algorithm OBE algorithm overbounding SMnlms algorithm underbounding

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Convergence Vectors in System Identification with an nlms algorithm for Sinusoidal Inputs

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2012年第10期E95A卷 1692-1699页

作者： Satomi, Yuki Kawamura, Arata Iiguni, Youji Osaka Univ Grad Sch Engn Sci Toyonaka Osaka 5608531 Japan

For an adaptive system identification filter with a stochastic input signal, a coefficient vector updated with an nlms algorithm converges in the sense of ensemble average and the expected convergence vector has been revealed. When the input signal is periodic, the convergence of the adaptive filter coefficients has also been proved. However, its convergence vector has not been revealed. In this paper, we derive the convergence vector of adaptive filter coefficients updated with the nlms algorithm in system identification for deterministic sinusoidal inputs. Firstly, we derive the convergence vector when a disturbance does not exist. We show that the derived convergence vector depends only on the initial vector and the sinusoidal frequencies, and it is independent of the step-size for adaptation, sinusoidal amplitudes, and phases. Next, we derive the expected convergence vector when the disturbance exists. Simulation results support the validity of the derived convergence vectors.

关键词： nlms algorithm sinusoidal inputs system identification convergence vector

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Performance analysis of the selective coefficient update nlms algorithm in an undermodeling situation

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DIGITAL SIGNAL PROCESSING 2013年第6期23卷 1967-1973页

作者： Mayyas, Khaled Jordan Univ Sci & Technol Dept Elect Engn Irbid 22110 Jordan

The selective coefficient update normalized least mean-square (SCU-nlms) algorithm was proposed to reduce computational complexity while preserving close performance to the full-update nlms algorithm, which brought it a lot of attention. In practical applications, the length of the unknown system impulse response is not known and, therefore, the length of the adaptive filter can be less than that of the unknown system particularly in situations when the unknown system impulse response is long. In all existing analysis of the SCU-nlms algorithm, exact modeling of the unknown system is assumed, i.e., the length of the adaptive filter is equal to that of the unknown system impulse response. In this paper, we present mean-square performance analysis for the SCU-nlms algorithm in an undermodeling situation and assuming independent and identically distributed (i.i.d.) input signals. The analysis model takes into account order statistics employed in the SCU-nlms algorithm leading to accurate transient and steady state theoretical results. Analysis extends easily to the exact modeling case where expressions quantifying the algorithm mean-square performance are presented and shown to be more accurate than the ones reported in the literature. Simulation experiments validate the accuracy of the theoretical results in predicting the actual behavior of the algorithm. (c) 2013 Elsevier Inc. All rights reserved.

关键词： Selective coefficient update nlms algorithm Mean-square analysis Undermodeling

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A New Formula to Compute the nlms algorithm at a Computational Complexity of O(2N)

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2019年第11期E102A卷 1545-1549页

作者： Nishiyama, Kiyoshi Sunohara, Masahiro Hiruma, Nobuhiko Iwate Univ Fac Sci & Engn Dept Syst Innovat Engn Morioka Iwate 0208551 Japan Rion Co Ltd Kokubunji Tokyo 1858533 Japan

The least mean squares (LMS) algorithm has been widely used for adaptive filtering because of easily implementing at a computational complexity of O(2N) where N is the number of taps. The drawback of the LMS algorithm is that its performance is sensitive to the scaling of the input. The normalized LMS (nlms) algorithm solves this problem on the LMS algorithm by normalizing with the sliding-window power of the input;however, this normalization increases the computational cost to O(3N) per iteration. In this work, we derive a new formula to strictly perform the nlms algorithm at a computational complexity of O(2N), that is referred to as the C-nlms algorithm. The derivation of the C-nlms algorithm uses the H-infinity framework presented previously by one of the authors for creating a unified view of adaptive filtering algorithms. The validity of the C-nlms algorithm is verified using simulations.

关键词： nlms algorithm LMS algorithm adaptive filter H-infinity filter fast H-infinity filter system identification

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A nlms algorithm for frequency offset estimation of OFDM communications

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IEICE TRANSACTIONS ON COMMUNICATIONS 2003年第9期E86B卷 2823-2827页

作者： Chang, AC Huang, ZF Natl Def Univ Chung Cheng Inst Technol Dept Elect Engn Taoyuan 335 Taiwan

In this letter, we present a normalized least-mean-square algorithm of blind estimator for carrier frequency offset estimation of orthogonal frequency division multiplexing systems. In conjunction with the closed-loop estimate structure, the proposed efficient algorithm eliminates the inter-carrier interference for time varying carrier frequency offset. The proposed algorithm offers faster convergence speed and more accuracy to the carrier frequency offset estimate. Several computer simulation examples are presented for illustrating and effectiveness of the proposed algorithm.

关键词： orthogonal frequency division multiplexing carrier frequency offset time varying tracking nlms algorithm

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