Variable Step-size Algorithm Research Articles

Mean-square deviation analysis of the zero-attracting variable step-size LMS algorithm

The well-known variable step-size least-mean-square (VSSLMS) algorithm provides faster convergence rate while maintaining lower mean-square error than the conventional LMS algorithm. The performance of the VSSLMS algorithm can be improved further in a channel estimation problem if the impulse response of the channel is sparse. Recently, a zero-attracting (ZA)-VSSLMS algorithm was proposed to exploit the sparsity of a channel. This was done by imposing an \(\ell _1\)-norm penalty to the original cost function of the VSSLMS algorithm which utilizes the sparsity in the filter taps during the adaptation process. In this paper, we present the mean-square deviation (MSD) analysis of the ZA-VSSLMS algorithm. A steady-state MSD expression for the ZA-VSSLMS algorithm is derived. An upper bound of the zero-attractor controller (\(\rho \)) that provides the minimum MSD is also provided. Moreover, the effect of the noise distribution on the MSD performance is shown theoretically. It is shown that the theoretical and simulation results of the algorithm are in good agreement with a wide range of parameters, different channel, input signal, and noise types.

Applications of adaptive variable step-size algorithm in turbulence observation system

Applications of adaptive variable step-size algorithm in turbulence observation system

A shrinkage variable step size for normalized subband adaptive filters

The conventional normalized subband adaptive filter (NSAF) using a constant step-size generally faces an inherent trade-off between the steady-state misalignment and the convergence rate. We propose herein a variable step-size NSAF algorithm by minimizing the mean-square deviation (MSD) between the optimal weight vector and the weight vector estimate with the utilization of the shrinkage denoising technique. With the estimation error involved in the step-size adaptation for each subband individually, the proposed algorithm is capable of tracking non-stationary environments. Without the explicit whitening assumption of the input signal in each subband, the proposed algorithm exhibits low steady-state MSD even when the input signal of each subband is colored. Simulation results validate the low misalignment and good tracking ability of the proposed algorithm in system identification application.

Excision of Ocular Artifacts from EEG Using NVFF-RLS Adaptive Algorithm

This paper presents a technique for the removal of ocular artifacts from electro-encephalogram (EEG) by using adaptive filtering. The major concern is electro-oculogram (EOG) signal present in a recorded EEG signal, which appears due to abrupt eye movements. In the presented method, we use separately recorded horizontal EOG (HEOG) and vertical EOG (VEOG) signals as two reference inputs, which are processed using finite impulse response (FIR) filters. The linear filter coefficients are adaptively updated using a numerical variable forgetting factor (NVFF) recursive least squares (RLS) algorithm, which tracks nonstationary EOG signals. Subsequently, the processed HEOG and VEOG signals are subtracted from recorded EEG signal to obtain an artifact-free EEG signal. Simulation is conducted using synthetic EEG signal corrupted by noise, synthetic HEOG and VEOG signals. The real-time recorded EEG signal (corrupted by EOG and noise) is also refined using the separately recorded reference EOG signals and FIR filtering technique. For synthetic and real-time signals, the simulation results are presented to demonstrate that linear NVFF-RLS algorithm-based artifact and noise excision technique outperforms conventional fixed forgetting factor RLS, fixed step-size NLMS and generalized variable step-size NLMS algorithms, in terms of the reduction in mean-squared error, under low as well as high signal-to-noise ratio conditions.

Robust Uncertainty Control of the Simplified Kalman Filter for Acoustic Echo Cancelation

One of the main difficulties in acoustic echo cancelation (AEC) is the adaptation strategy of the adaptive filter in different situations. Recently, the Kalman filter theory has been introduced to accommodate for the adaptation control in AEC applications, due to its optimal performance in many system identification problems. In this paper, a frequency-domain simplified Kalman filter for partitioned-block-based AEC is studied. The contribution is twofold. First, the relationship between the Kalman filter and an optimal variable step-size algorithm is revealed, which contributes to the motivation of this paper. Second, the influence of system uncertainty on the performance of the Kalman filter is analyzed, and a new uncertainty control method is developed. Simulation results confirm the superiority of the proposed method to the conventional ones.

Fast and accurate measurement of harmonic parameters employing hybrid adaptive linear neural network and filtered‐x least mean square algorithm

This study proposes a novel algorithm for fast and accurate measurement of fundamental, harmonics, sub- and inter-harmonic parameters of a distorted current signal with additive noise. A novel hybrid technique called adaptive linear neural network and filtered-x least mean square (ADALINE-FXLMS) algorithm is employed for amplitude and phase estimation. The ADALINE-FXLMS algorithm is the advancement of ADALINE least mean square (ADALINE-LMS) algorithm. With the help of this proposed algorithm, the adaptive step-size parameter is expanded up to the upper-bound limit that results in further improvement of system stability. The convergence behaviour of the mean square errors for the noisy input signal is derived in details. By applying the proposed algorithm, the dynamic and steady-state response are analysed with different signal-to-noise ratio values. The simulated results obtained from the proposed algorithm are compared with the results generated by the variable step-size ADALINE-LMS algorithm in order to demonstrate the tracking capability. Finally, a laboratory prototype model is developed to justify the efficacy of the analytical results. The motivation of applying the proposed hybrid algorithm is due to its successful implementation in a real-time environment, faster convergence and simplicity structure.

음향 통신 채널 추정기를 이용한 대수학적 스텝크기 least mean fourth 알고리즘

ABSTRACT: The least-mean fourth (LMF) algorithm is well known for its fast convergence and low steady-state error especially in non-Gaussian noise environments. Recently, there has been increasing interest in the least mean square (LMS) algorithms with variable step size. It is because the variable step-size LMS algorithms have shown to outperform the conventional fixed step-size LMS in the various situations. In this paper, a variable step-size LMF algorithm is proposed, which adopts an algebraic optimal step size as a variable step size. It is expected that the proposed algorithm also outperforms the conventional fixed step-size LMF. The superiority of the proposed algorithm is confirmed by the simulations in the time invariant and time variant channels.Keywords: Acoustic communication, Channel estimation, LMF, Algebraic optimal step-sizePACS numbers: 43.60.Dh, 43.60.Mn†Corresponding author: Jun-Seok Lim (jslim@sejong.ac.kr) Department of Electrical Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea(Tel: 82-2-3408-3299, Fax: 82-2-3408-4329)

Implementation of FPGA Based Hybrid Power Generator for PV and Wind Grid Applications

This paper deals with implementation of Sinusoidal Pulse-Width-Modulation (SPWM) for a single-phase hybrid power filter generator for Photovoltaic (PV) and wind grid applications. Using policy iteration algorithm, an improved variable step-size perturbation and observation algorithm is contrived and it is implemented proficiently using a hard-ware description language (VHDL) (Very High Speed Integrated Circuit Hardware Description Language). Subsequently, the new generated grid source supplements the existing grid power in rural houses during its cut off or restricted supply period. The software is used for generating SPWM modulation integrated with a solar-power & wind power grid system which is implemented on the Spartan 3 FPGA. The proposed algorithm performs as a conventional controller in terms of tracking speed and mitigating fluctuation output power in steady state operation which is shown in the experimental results with a commercial PV array and HPW (Height Weight Proportional) show. Simulation results demonstrate the validity with load of the proposed algorithm.

Review and Comparison of Variable Step-Size LMS Algorithms

The inherent feature of the Least Mean Squares (LMS) algorithm is the step size, and it requires careful adjustment. Small step size, required for small excess mean square error, results in slow convergence. Large step size, needed for fast adaptation, may result in loss of stability. Therefore, many modifications of the LMS algorithm, where the step size changes during the adaptation process depending on some particular characteristics, were and are still being developed. The paper reviews seventeen of the best known variable step-size LMS (VS-LMS) algorithms to the degree of detail that allows to implement them. The performance of the algorithms is compared in three typical applications: parametric identification, line enhancement, and adaptive noise cancellation. The paper suggests also one general modification that can simplify the choice of the upper bound for the step size, which is a crucial parameter for many VS-LMS algorithms.

High-Frequency-Link-Based Grid-Tied PV System With Small DC-Link Capacitor and Low-Frequency Ripple-Free Maximum Power Point Tracking

This paper proposes a grid-tied photovoltaic (PV) system consisting of modular current-fed dual-active-bridge (CF-DAB) dc–dc converter with cascaded multilevel inverter. The proposed converter allows a small dc-link capacitor in the three-phase wye-connected PV system; therefore, the system reliability can be improved by replacing electrolytic capacitors with film capacitors. The low-frequency ripple-free maximum power point tracking (MPPT) is also realized in the proposed converter. First of all, to minimize the influence resulting from reduced capacitance, a dc-link voltage synchronizing control is developed. Then, a detailed design of power mitigation control based on CF-DAB dynamic model is presented to prevent the large low-frequency voltage variation propagating from the dc-link to PV side. Finally, a novel variable step-size MPPT algorithm is proposed to ensure not only high MPPT efficiency, but also fast maximum power extraction under rapid irradiation change. A downscaled 5-kW PV converter module with a small dc-link capacitor was built in the laboratory with the proposed control and MPPT algorithm, and experimental results are given to validate the converter performance.

Improved variable step-size NLMS adaptive filtering algorithm for acoustic echo cancellation

Acoustic echo canceller (AEC) is used in communication and teleconferencing systems to reduce undesirable echoes resulting from the coupling between the loudspeaker and the microphone. In this paper, we propose an improved variable step-size normalized least mean square (VSS-NLMS) algorithm for acoustic echo cancellation applications based on adaptive filtering. The steady-state error of the NLMS algorithm with a fixed step-size (FSS-NLMS) is very large for a non-stationary input. Variable step-size (VSS) algorithms can be used to decrease this error. The proposed algorithm, named MESVSS-NLMS (mean error sigmoid VSS-NLMS), combines the generalized sigmoid variable step-size NLMS (GSVSS-NLMS) with the ratio of the estimation error to the mean history of the estimation error values. It is shown from single-talk and double-talk scenarios using speech signals from TIMIT database that the proposed algorithm achieves a better performance, more than 3 dB of attenuation in the misalignment evaluation compared to GSVSS-NLMS, non-parametric VSS-NLMS (NPVSS-NLMS) and standard NLMS algorithms for a non-stationary input in noisy environments.

VLSI implementation of a new LMS-based algorithm for noise removal in ECG signal

ABSTRACTLeast mean square (LMS)-based adaptive filters are widely deployed for removing artefacts in electrocardiogram (ECG) due to less number of computations. But they posses high mean square error (MSE) under noisy environment. The transform domain variable step-size LMS algorithm reduces the MSE at the cost of computational complexity. In this paper, a variable step-size delayed LMS adaptive filter is used to remove the artefacts from the ECG signal for improved feature extraction. The dedicated digital Signal processors provide fast processing, but they are not flexible. By using field programmable gate arrays, the pipelined architectures can be used to enhance the system performance. The pipelined architecture can enhance the operation efficiency of the adaptive filter and save the power consumption. This technique provides high signal-to-noise ratio and low MSE with reduced computational complexity; hence, it is a useful method for monitoring patients with heart-related problem.

A Comparative Analysis of Adaptive IIR Filtering Techniques using LabVIEW

Removal of noises from real-time speech signal is a typical problem. The signal interference initiated by background noise is a major problem in voice communication systems. Adaptive Filtering methods have emerged as an important technology for communication systems. This technique has been employed to improve the quality of the speech signal by cancelling the undesirable phenomenon such as acoustic noise. In this paper, for the removal of additional noise from speech signal an adaptive filter has been designed using LMS, NLMS, SLMS and VSS-LMS algorithms. This paper presents the instigation of Least Mean Square algorithm (LMS), Normalized Least Mean Square algorithm (NLMS), Sign Least mean square algorithm (SLMS) and Variable step size (VSS) algorithm on an infinite impulse response (IIR) filter using adaptive filter toolkit of LabVIEW software. User interface is designed using LabVIEW to obtain the learning curves for these adaptive algorithms. The final results show the comparison of the performance of the entire proposed algorithms with each other. The complete performance of the designed system in terms of stability and convergence rate has been observed.

Multichannel active noise control system using variable step size algorithms

This paper presents the feed-forward multichannel active noise control which was simulated on LabVIEW and experimented on two channel feed-forward active noise control in real-time. The simulation of feed-forward multichannel active noise control system was built on LabVIEW by using FxLMS algorithm and other algorithms such as Variable Step-size (VSS) and saturation compensation. Moreover, LMS and VSS LMS algorithm were used to train the secondary path in order to improve the convergence speed and stabilization of ANC system in the real-time. The experimental results show that the ANC system in real-time using variable step-size and without using variable step-size algorithm work effectively with noise sources which were synthesized from one to three frequencies. The noise level in these cases decreased around 12 dB - 35 dB and the noise reduction radius measured is about 3 cm around the microphone.

Variable step‐size sign algorithm against impulsive noises

This paper proposes a new variable step-size sign algorithm through the minimisation of mean-square deviation (MSD). As it is difficult to obtain the MSD accurately, the upper bound of the MSD is derived for calculating the step size at each iteration. The proposed algorithm is not only robust to impulsive noises, but also has improved filter performance in aspects of convergence rate and steady-state estimation error owing to the proposed variable step-size strategy. The simulation results verify that the proposed algorithm has better performance than the existing algorithms in a system-identification scenario in the presence of impulsive noises.

A single-sensor PV system featuring an innovative auto-adjustment variable step-size MPPT method

This paper proposes a new maximum power point tracking (MPPT) method by introducing an auto-adjustment variable step-size algorithm that uses only a single sensor. This novel scheme solves the problem encountered by traditional variable step-size methods, which require an additional calculation of the constant value. The naturally varying trend of the proposed function in this paper is applied to serve as the auto-adjustment variable step size in the MPPT algorithm, thereby enabling the system to provide reliable transient and steady-state responses even during sharp weather changes. Furthermore, the proposed new MPPT method can also be applied in the presence of a partial shadow condition. The digital signal processor handles the feedback value and directs the PWM signal to drive the switch of the converter. The simulation and experimental results verify the reliable transient and steady-state performance of the PV system with the proposed method.

An Alternating Direction Approximate Newton Algorithm for Ill-Conditioned Inverse Problems with Application to Parallel MRI

An alternating direction approximate Newton (ADAN) method is developed for solving inverse problems of the form \(\min \{\phi (Bu) +(1/2)\Vert Au-f\Vert _{2}^{2}\},\) where \(\phi \) is convex and possibly nonsmooth, and A and B are matrices. Problems of this form arise in image reconstruction where A is the matrix describing the imaging device, f is the measured data, \(\phi \) is a regularization term, and B is a derivative operator. The proposed algorithm is designed to handle applications where A is a large dense, ill-conditioned matrix. The algorithm is based on the alternating direction method of multipliers (ADMM) and an approximation to Newton’s method in which a term in Newton’s Hessian is replaced by a Barzilai–Borwein (BB) approximation. It is shown that ADAN converges to a solution of the inverse problem. Numerical results are provided using test problems from parallel magnetic resonance imaging. ADAN was faster than a proximal ADMM scheme that does not employ a BB Hessian approximation, while it was more stable and much simpler than the related Bregman operator splitting algorithm with variable stepsize algorithm which also employs a BB-based Hessian approximation.

A simplified variable step-size LMS algorithm for Fourier analysis and its statistical properties

In this paper, several typical variable step-size LMS (VSS-LMS) algorithms are first applied to adaptive Fourier analysis of noisy sinusoidal signals, which were developed in the context of system identification. A simplified VSS-LMS (SVSS-LMS) algorithm is then proposed to perform the same task, which, on the whole, indicates nice performance comparable to that of most of the typical VSS-LMS algorithms, and requires fewer multiplications as well as user parameters. In-depth performance analysis is provided for the proposed algorithm. Difference equations are derived that describe its dynamics, and elegant closed-form expressions are also worked out for its steady-state performance. Extensive simulations are conducted to confirm its effectiveness, and to clarify the validity of the analytical findings.

An optimal variable step-size affine projection algorithm for the modified filtered-x active noise control

This paper introduces an optimal variable step-size affine projection algorithm for the modified filtered-x active noise control systems. First, the recursion form of the error covariance from the tap weight update equation is constructed, not ignoring the dependency between the estimation error and the secondary noise signal. Such consideration has not been concerned previously for the analysis of the modified filtered-x affine projection algorithm. Second, a recursion form of the mean square deviation is derived from that of the error covariance. From the recursion form, an optimal step size is decided to get the fastest convergence rate. Both the recursion forms of the mean square deviation and the optimal step size require scalar additions and multiplications that do not contribute to the overall complexity seriously. The simulation results on the active noise control environments show both fast convergence rate and low steady-state error.

A novel algorithm for wavelet neural networks with application to enhanced PID controller design

This paper presents a variable step-size updating algorithm for wavelet neural network (WNN) in setting the enhanced PID controller parameters. Compared to the iterative method with constant step-size, the most innovative character of the algorithm proposed is its capability of shortening tracking time and improving the convergence in weights updating process for complex systems or large-scale networks. By combining the relationship among WNN, the Kalman filter and the normalized least mean square (NLMS), we introduce the T–S fuzzy inference mechanism for activation derived functions. Furthermore, a once-through steam generator (OTSG) model is established for validating the practicability and reliability in a real complicated system. Finally, simulation results are presented to exhibit the effectiveness of the proposed variable step-size algorithm.