Variable Weight Mixed-Norm Adaptive Algorithm

The problem of distributed estimation is considered for distributed network. A diffusion model on adaptive affine projection sign algorithm based on least mean fourth algorithm is introduced according to an Adapt-Then-Combine (ATC) design for the distributed framework. Least mean fourth (LMF) algorithm is defined by taking the fourth power of error to against the non-Gaussian environment. An adaptive affine projection sign algorithm based on LMF algorithm is proposed firstly. Then, an ATC diffusion model on adaptive affine projection sign algorithm based on LMF algorithm is presented in terms of the low complexity of sign approach with the order of adaptation and combination, named as ATC-DAPS-LMF. Numerical simulations verify that the proposed algorithm can perform significantly to the conventional affine projection sign algorithm.

Adaptive equalization is undoubtedly one of the cornerstones of digital communication as it allows for fast and reliable data transmission over practical channels that are non-ideal and that are plagued with serious problems such as signal dispersion and non-Gaussian interferences. In such cases, the performance of the well-known least-mean square (LMS) algorithm or that of any of its variants remains sub-optimal at best. As a remedy to this, the least-mean fourth (LMF) algorithm was later proposed but its high computational load was found to be a constraining factor in its practical implementation, particularly for real-time applications. Inspired from a previous work done on the LMS [1], we recently proposed a new algorithm [2], termed LMF-PTQ, combining the power of the LMF with the implementational advantages of the power-of-two quantization scheme. In this work, we demonstrate, through an extensive simulation study, the effectiveness of our proposed LMF-PTQ algorithm in the equalization of a time-varying channel in a CDMA system which suffers from both signal dispersion and non-Gaussian disturbances. The results obtained so far are very encouraging and provide us with ample enthusiasm to investigate the proposed algorithm further.

Least-Mean Square algorithm, or simply the LMS, is generally one of the most commonly used techniques for optimized solution in adaptive schemes especially in the Gaussian environment. However, least mean fourth (LMF) algorithm and its variants, such as normalized LMF (NLMF), perform better in the non-Gaussian environment. The conventional LMF algorithms usually diverge in non-Gaussian environment with dynamic input. Conventionally, regularization is archived by using a small constant compensation term in the denominator of the learning rate to protect the algorithm from divergence. This paper introduces an efficient time-varying regularized normalized least mean fourth (R-NLMF) algorithm. In the proposed algorithm, the regularization term is made time varying and gradient adaptive according to steepest descent approach. Thus the proposed algorithm adapts its learning rate according to the environment and the input signal dynamics. A similar approach, namely Generalized Normalized Gradient Descent (GNGD) algorithm, has been previously applied to the normalized least mean-square (NLMS) algorithm in the Gaussian environment. However, due to its dependence on NLMS, the GNGD algorithm performance degrades in non-Gaussian environment. In order to overcome this problem, an efficient regularized NLMF algorithm for non-Gaussian environment is proposed. The algorithm shows promising results and achieves faster convergence while maintaining lesser steady-state miss-adjustment. Simulations are carried out to support the theoretical development.

Recently, it has been shown that the stability of the least mean fourth (LMF) algorithm depends on the nonstationarity of the plant. The present paper investigates the possibility of overcoming this problem by normalization of the weight vector update term. A rigorous mean-square stability analysis is provided for a recent normalized LMF algorithm, which is normalized by a term that is second order in the estimation error and fourth order in the regressor. The analysis is done for a Markov plant with a stationary white input with even probability density function and a stationary zero-mean white noise. It is proved that the mean-square deviation (MSD) of the algorithm is bounded for all finite values of the input variance, noise variance, initial MSD, and mean-square plant parameter increment. Analytical results are supported by simulations.

A simplified forms of adaptive set-membership affine projection based on least mean fourth algorithm is proposed. Least mean fourth (LMF) algorithm is defined by taking the fourth power of error to against the non-Gaussian environment. A set-membership adaptive filtering is described firstly. Then, an affine projection algorithm is based on LMF algorithm. A simplified set-membership affine projection algorithm based on LMF is introduced. Adaptive threshold parameter and learning rate are presented for improvement of convergence rate. Numerical simulations show that the proposed algorithm can provide significantly to the conventional affine projection algorithm.

This paper presents a new statistical analysis of the least mean fourth (LMF) adaptive algorithm behavior. Nonlinear recursive equations are derived which predict the behavior of the first and second order moments of the adaptive weights for Gaussian inputs. These recursions can be used to predict the mean square error (MSE) behavior. The new model improves the available models in that it predicts both the transient and steady-state behaviors for measurement noise having any zero-mean probability density function (pdf) and for any signal-to-noise ratio. This is important because the LMF algorithm is known to outperform the LMS algorithm for non-Gaussian noise distributions and for large signal-to-noise ratios. In addition, the new model explicitly shows the dependence of the algorithm's dynamics on the initial weight conditions. Computer simulations illustrate the accuracy of the new model in predicting the algorithm behavior.

Recently, in the world wide the use of power electronics devices increases sharply. As a result, harmonic pollution becomes a vital problem than before. Harmonics rotate in the power system network and interfere with the system equipments, disturbing their normal operation which can deteriorate the quality of the delivered power. Therefore, efficient method with low computational time is a critical tool to estimate and quantify the harmonic that can be used in online control and mitigation of harmonics. Least Mean Square (LMS) is simple and popular algorithm that has been applied in many applications, but, noise can affect its performance. This paper presents and compare the performance of Least Mean Square (LMS), Least Mean Fourth (LMF) and a combined (LMS/LMF) in estimation harmonic component for the signal corrupted with noise contain low signal to noise ratio (SNR). The results show that LMF and LMS/LMF have better steady state performance as compared to LMS.

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.

An adaptive filtering algorithm that minimizes the variance on the squared error subject to a constraint on the mean-squared error (MSE) is proposed. For the adaptive-linear-combiner signal-processing configuration, this algorithm, called the LVCMS algorithm (for least variance subject to a constraint on mean squared error) has a gradient that is a weighted linear combination of the least-mean-square (LMS) and least-mean-fourth (LMF) algorithm gradients. Theoretical expressions are derived for the LVCMS algorithm convergence factor and misadjustment, and comparisons are made with the LMS and LMF adaptive rules for Gaussian, Laplacian, and uniform plant noise nd driving term distributions. Performance comparisons of the LVCMS, LMS, and LMF algorithms based on Monte Carlo simulation studies indicate that the LVCMS adaptation rule not only can yield a small variance of the squared error but it also produces favorable values of the mean-squared error and the mean-squared coefficient error. >

In this paper, we propose an iterative mixed norm image restoration algorithm. A functional which combines the least mean squares (LMS) and the least mean fourth (LMF) functionals is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed approach.

In this paper, we propose an iterative mixed norm image restoration algorithm. A functional which combines the least mean squares (LMS) and the least mean fourth (LMF) functionals is proposed. A function of the kurtosis is used to determine the relative importance between the LMS and the LMF functionals. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed approach.

In this paper, we present a regularized mixed norm multichannel image restoration algorithm. The problem of multichannel restoration using both within- and between-channel deterministic information is considered. For each channel a functional which combines the least mean squares (LMS), the least mean fourth (LMF), and a smoothing functional is proposed. We introduce a mixed norm parameter that controls the relative contribution between the LMS and the LMF, and a regularization parameter that defines the degree of smoothness of the solution, both updated at each iteration according to the noise characteristics of each channel. The novelty of the proposed algorithm is that no knowledge of the noise distribution for each channel is required, and the parameters mentioned above are adjusted based on the partially restored image.

Mean-square stability of the Normalized Least-Mean Fourth algorithm for white Gaussian inputs

In this paper, we propose a new mixed norm LMS-LMF adaptive algorithm. The algorithm minimizes an objective function defined as a weighted sum of the least mean fourth (LMF) and least mean square (LMS) cost functions. The weighting factor is time varying and adapts itself so as to emphasize one cost function over the other based on proximity to the optimum. Improved convergence is illustrated by examples. Bounds on the step size to ensure mean convergence are also derived.

This paper presents a robust generalized modified Blake-Zisserman adaptive filter (GMBZAF)-based control scheme for a three-phase grid-tied single-stage photovoltaic system (GTPVS) to improve power quality (PQ). The GMBZAF-based control scheme enables GTPVS to integrate maximum PV power into the grid with power quality (PQ) improvement at the grid side, such as maintaining balanced sinusoidal grid currents, current harmonics mitigation, reactive power assistance to the inductive load at steady-state, and even during dynamic conditions (variable load and irradiance). The GMBZAF is implemented to accurately calculate the active and reactive weight components of load current. The GTPVS is modeled using MATLAB/Simulink, and its response is observed at steady-state, unbalanced loading, and variable solar irradiance conditions. The comparative assessment between the proposed control scheme and the existing adaptive filtering-based control schemes such as least mean square (LMS) and least mean fourth (LMF) is done.