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The filtered-x least mean square algorithm is extensively employed for active control, which exhibits a trade-off between convergence speed and the steady-state control performance. In this paper, an affine combination strategy of the filtered-x least mean square and fourth algorithms is proposed, which can be regarded as a generalized convex combination. Unlike the convex combination, the combining parameter in this linear combination is not constrained to lie in a specific interval and plays a vital role in deciding the overall system performance. An adaptation rule is developed for updating the combining parameter. The proposed affine combination strategy is used to control white noise and multitone noise. The simulation results demonstrate that the proposed algorithm provides faster convergence and improved steady-state control performance. Furthermore, the proposed affine combination is also robust with an imperfect secondary path model.

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strategies for enhanced performance. By assigning a combination coefficient to each node, and using an adaptation mechanism to minimize the network error, we obtain a combined diffusion strategy that benefits from the best characteristics of all component strategies simultaneously in terms of excess-mean-square error (EMSE). Analyses of the universality are provided to show the superior performance of affine combination scheme and to characterize its behavior in the mean and mean-square sense. Simulation results are presented to demonstrate the effectiveness of the proposed strategies, as well as the accuracy of theoretical findings., 31 pages

In this paper, a modified Hestenes–Stiefel conjugate gradient method for unconstrained problems is developed, which can achieves the twin goals of generating sufficient descent direction at each iteration as well as being close to the Newton direction. In our methods, the hybridization parameter can also be obtained based on other kinds of conjugacy conditions. Under mild condition, we establish their global convergence for general objective functions. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising.

In this paper we present an affine combination strategy for two adaptive filters. One filter is designed to handle sparse impulse responses and the other one performs better if impulse response is dispersive. Filter outputs are combined using an adaptive mixing parameter and the resulting output shows a better performance than each of the combining filters separately. We also demonstrate that affine combination results in faster convergence than a convex combination of two adaptive filters.

Large-scale multiple-input multiple-output (MIMO) system is considered one of promising technologies to realise next-generation wireless communication system (5G). So far, channel estimation problem is a big obstacle to develop large-scale MIMO system design due to high computational complexity and curse of dimensionality, which are caused by the long delay spread as well as a large number of antennas. Hence, devising any low-complexity channel estimation method could promote the successful development of the large-scale MIMO system. Due to the fact that, large-scale MIMO channels often exhibit sparse or/and cluster-sparse structure, in this study, the authors propose an effective low-complexity large-scale MIMO channel estimation method by using affine combination of sparse adaptive filtering filters. First, problem formulation and standard affine combination of adaptive least mean square (LMS) filters are introduced. Then they propose an effective affine combination method with two sparse LMS filters and design an approximate optimum affine combiner according to stochastic gradient search method. Later, to verify the proposed algorithm for large-scale MIMO channel estimation, both theoretical analysis and numerical simulations are provided to confirm effectiveness of the proposed algorithm which can achieve better estimation performance than the traditional methods.

The detection of outliers and influential observations has received a great deal of attention in the statistical literature in the context of least-squares (LS) regression. However, the explanatory variables can be correlated with each other and alternatives to LS come out to address outliers/influential observations and multicollinearity, simultaneously. This paper proposes new influence measures based on the affine combination type regression for the detection of influential observations in the linear regression model when multicollinearity exists. Approximate influence measures are also proposed for the affine combination type regression. Since the affine combination type regression includes the ridge, the Liu and the shrunken regressions as special cases, influence measures under the ridge, the Liu and the shrunken regressions are also examined to see the possible effect that multicollinearity can have on the influence of an observation. The Longley data set is given illustrating the influence measures in affine combination type regression and also in ridge, Liu and shrunken regressions so that the performance of different biased regressions on detecting and assessing the influential observations is examined. © 2013 Copyright Taylor and Francis Group, LLC.

Low complexity Normalized Least Mean Square (NLMS) adaptive algorithm is widely used in the adaptive system identification applications. To exploit the sparse impulse response of the system, different sparse penalties are introduced into the error function of the NLMS algorithm. Reweighted Zero Attracting-NLMS (RZA-NLMS) algorithm based on 11-norm relaxation offers improved performance in identifying the system with sparse echo path but when the system is non-sparse, NLMS algorithm dominates the sparse adaptive algorithm. In order to identify the system with varying sparseness, a new strategy is required. In this paper, we propose an affine combination of RZA-NLMS and NLMS filters used for system identification with variable sparsity. The robust performance of our proposed approach has been verified from the MATLAB simulations.

One of the difficult task in subdivision is to create new effective subdivision schemes. Therefore, aim of this paper is a systematic analysis of affine combination of known subdivision masks to generate new subdivision schemes with enhanced properties. This will be done in the stationary and the non stationary case for the univariate and bivariate settings.

In this paper, we propose an approach to the transient and steady-state analysis of the affine combination of one fast and one slow adaptive filters. The theoretical models are based on expressions for the excess mean-square error (EMSE) and cross-EMSE of the component filters, which allows their application to different combinations of algorithms, such as least mean-squares (LMS), normalized LMS (NLMS), and constant modulus algorithm (CMA), considering white or colored inputs and stationary or nonstationary environments. Since the desired universal behavior of the combination depends on the correct estimation of the mixing parameter at every instant, its adaptation is also taken into account in the transient analysis. Furthermore, we propose normalized algorithms for the adaptation of the mixing parameter that exhibit good performance. Good agreement between analysis and simulation results is always observed.

In this paper we present an affine combination strategy for two adaptive filters. One filter is designed to handle sparse impulse responses and the other one performs better if impulse response is dispersive. Filter outputs are combined using an adaptive mixing parameter and the resulting output shows better performance than each of the combining filters separately. We also demonstrate that affine combination results in faster convergence than convex combination of two adaptive filters.

Global Positioning System (GPS) is an all weather Position, Velocity and Time determination navigation system. Multipath is one of the prominent error sources in GPS. In this paper, various Least Mean Square (LMS) adaptive algorithms such as simple LMS, Normalized LMS, Variable length LMS and affine combination of two LMS filters are investigated to mitigate multipath error. Accurate step size parameter is estimated and the performance of each filter is examined critically. Affine combination of two LMS adaptive filters uses two step sizes, one for slower convergence and another for good steady state response. The results are encouraging with affine combination of two LMS filters. It has improved performance with higher computational complexity compared to other three filters. Hence, affine combination of two LMS adaptive filters is the choice best choice for multipath mitigation in GPS applications.

Sparse system identification problems often exist in many applications, such as echo interference cancellation, sparse channel estimation, and adaptive beamforming. One of popular adaptive sparse system identification (ASSI) methods is adopting only one sparse least mean square (LMS) filter. However, the adoption of only one sparse LMS filter cannot simultaneously achieve fast convergence speed and small steady-state mean state deviation (MSD). Unlike the conventional method, we propose an improved ASSI method using affine combination of two sparse LMS filters to simultaneously achieving fast convergence and low steady-state MSD. First, problem formulation and standard affine combination of LMS filters are introduced. Then an approximate optimum affine combiner is adopted for the proposed filter according to stochastic gradient search method. Later, to verify the proposed filter for ASSI, computer simulations are provided to confirm effectiveness of the proposed filter which can achieve better estimation performance than the conventional one and standard affine combination of LMS filters., Comment: 5 pages, 8 figures, submitted for VTC2014-spring

Large scale multiple-input multiple-output (MIMO) system is considered one of promising technologies for realizing next-generation wireless communication system (5G) to increasing the degrees of freedom in space and enhancing the link reliability while considerably reducing the transmit power. However, large scale MIMO system design also poses a big challenge to traditional one-dimensional channel estimation techniques due to high complexity and curse of dimensionality problems which are caused by long delay spread as well as large number antenna. Since large scale MIMO channels often exhibit sparse or/and cluster-sparse structure, in this paper, we propose a simple affine combination of adaptive sparse channel estimation method for reducing complexity and exploiting channel sparsity in the large scale MIMO system. First, problem formulation and standard affine combination of adaptive least mean square (LMS) algorithm are introduced. Then we proposed an effective affine combination method with two sparse LMS filters and designed an approximate optimum affine combiner according to stochastic gradient search method as well. Later, to validate the proposed algorithm for estimating large scale MIMO channel, computer simulations are provided to confirm effectiveness of the proposed algorithm which can achieve better estimation performance than the conventional one as well as traditional method., Comment: 7 pages, 7 figures

Time series forecasting based on pattern matching has received a lot of interest in recent years due to its simplicity and the ability to predict complex nonlinear behaviours. The choice of the metric to measure the similarity between two time series depends mainly on the specific features of the considered data and it can influence on forecasting results. In this paper, unlike the conventional method, we propose an improved pattern matching-based prediction method using a linear combination of two measures, Euclidean distance and dynamic time warping, in order to achieve a better forecasting result. These two distance measures are chosen because they are the two most commonly used metrics for pattern matching in time series. The experimental results showed that our approach can produce better results on time series forecasting work in comparison to the pattern matching-based method under Euclidean distance or dynamic time warping in terms of prediction accuracy.

Combination approaches provide flexible and versatile solution to improve adaptive filter performance. In this paper, mean square performance of an affine combination of two time varying (TV) LMS adaptive filters is studied. The purpose of this combination is to obtain TV LMS adaptive filter with fast convergence and small mean square error (MSE).Two practical schemes proposed in [1] are used for this case. Simulation results indicate that these schemes yield overall MSE that is less than the MSE of either filter. Moreover this combination is better than combination of two LMS adaptive filters.

In this paper, a novel beamformer for adaptive combination of two adaptive filters is proposed for interference mitigation of sensor array. The proposed approach adaptively combines two individual filters by coefficient weights vector instead of one scale parameter and takes the constraint of affine combination into consideration rather than previous studies. Due to the more degrees of freedom offered by the mixing vector, the proposed beamformer significantly improves the convergence and tracking performances of the combined filter under both stationary and non-stationary environments, respectively. Based on the generalized sidelobe canceller (GSC) structure, the optimal mixing vector is derived by Lagrange method, and then several new effective iterative algorithms are developed for its updating in practical implementation. Furthermore, theoretical discussions of the convergent performances and complexities of the proposed iterative algorithms are also investigated to verify the feasibility of the proposed beamformer. Moreover, the proposed methods in application of beamforming for interference mitigation of antenna array are simulated based space-time processing technique. When compared to existing methods, the proposed approach exhibits faster convergence rate and higher output signal to interference plus noise ratio (SINR). Its good behavior is illustrated through simulation results. Published version

The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions.

A general affine combination of B-spline subdivision masks is here considered with the aim of generating new subdivision schemes with enhanced properties. This will be done using either stationary or non-stationary coefficients combining both B-splines and their non-stationary counterparts.

In the area of combination of adaptive filters, two main approaches, namely convex and affine combinations have been introduced. In this article, the relation between these two approaches is investigated. First, the problem of obtaining optimal convex combination coefficients is formulated as the projection of the optimal affine combination weights to the unit simplex in a weighted inner product space. Based on this formulation the closed form expressions for optimal combination weights and target MSE levels are obtained for two and three branch cases.

A recent paper [1] studied the statistical behavior of an affine combination of two LMS adaptive filters that simultaneously adapt on the same inputs. The filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying combining parameter λ(n). A scheme based on the ratio of error powers of the two filters was proposed in [1]. Monte Carlo simulations demonstrated nearly optimum performance for this scheme. The purpose of this paper is to analyze the statistitical behavior of such error power scheme. Expressions are derived for the mean behavior of λ(n) and for the weight mean-square deviation. Monte Carlo simulations show excellent agreement with the theoretical predictions.

This paper studies the statistical behavior of an affine combination of the outputs of two NLMS adaptive filters that simultaneously adapt using the same white Gaussian inputs. The behaviors of the mean optimal mixing parameter and combined mean-square deviation (MSD) are studied for a time-varying unknown channel. Simulation results are presented for the optimal unrealizable affine combiner and for a practical combining scheme. With proper design, the practical combiner scheme yields an overall MSD that is usually less than the MSD of either filter.

This paper studies the statistical behavior of an affine combination of the outputs of two least mean-square (LMS) adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor lambda(n) is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the mean-square error (MSE). First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSDs of either filter.

Adaptive combinations of adaptive filters are an efficient approach to alleviate the different tradeoffs to which adaptive filters are subject. The basic idea is to mix the outputs of two adaptive filters with complementary capabilities, so that the combination is able to retain the best properties of each component. In previous works, we proposed to use a convex combination, applying weights lambda(n) and 1-lambda(n), with lambda(n) isin (0,1), to the filter components, where the mixing parameter lambda(n) was updated to minimize the overall square error using stochastic gradient descent rules. In this paper, we present a new adaptation scheme for lambda(n) based on the solution to a least-squares (LS) problem, where the mixing parameter is allowed to lie outside range [0,1]. Such affine combinations have recently been shown to provide additional gains. Unlike some previous proposals, the new LS combination scheme does not require any explicit knowledge about the component filters. The ability of the LS scheme to achieve optimal values of the mixing parameter is illustrated with several experiments in both stationary and tracking situations.

Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalized scheme and the sign-regressor scheme. Then, we conduct theoretical analysis for one of the schemes, i.e., the power-normalized one. An analysis of universality shows that it cannot perform worse than any of its component strategies in terms of the excess mean-square-error (EMSE) at steady state, and sometimes even better. An analysis of stability also reveals that it is more stable than affine combination schemes already proposed by the authors in the literature. Next, several adjustments are proposed to further improve the performance of convex combination schemes. A discussion about the computational and communication complexity is provided, as well as a comparison between convex and affine combination schemes. Finally, simulation results are shown to demonstrate their effectiveness, the accuracy of the theoretical results, and the improved stability of the convex power-normalized scheme over the affine one.

An affine combination of two adaptive filters (AFs) based control is developed for a three-phase single stage grid tied photo voltaic (PV) array and ultra-capacitor (UC) charging electric vehicle spot (CEVS) of a charging station (CS). This algorithm is a combination of low complexity normalized least mean square (NLMS) and improved sparse channel identification reweighted zero attracting-NLMS (RZA-NLMS) filters. This combination offers the variable sparsity identification and improves the power quality of the CS. This CS is capable of grid to vehicle (G2V), PV source to vehicle (S2V), PV source to grid (S2G) and PV source to home (S2H). This CS also incorporates the vehicle to grid (V2G) and vehicle to home (V2H) functions when solar generation is reduced due to cloud crossing or in night time and state of charge (SOC) of the battery is sufficient to discharge battery. The DC link voltage is regulated through a bidirectional converter (BDC) using a cascaded PI controller. To improve the stability of the BDC, the loop shaping method is used. The loop shaping method is incorporated using k-factor approach. The efficacy of CS is demonstrated through the simulated results using MATLAB Simulink Library.

Spectra from a single intimate (nonlinear) mixture can be modeled as data points drawn from a smooth manifold. Spectral data sets containing hyperspectral observations of multiple intimate mixtures with some constituent materials in common can, therefore, be modeled as data clouds, in which each point is drawn from a union of manifolds that share a boundary. Two important steps in the processing of such data are to: 1) identify the different mixture manifolds present in the data and 2) invert the nonlinear mixing function by mapping each mixture manifold into some low-dimensional Euclidean space (manifold embedding). The present state-of-the-art algorithms for joint manifold clustering and embedding perform poorly for hyperspectral data, particularly in the embedding task. We propose a novel reconstruction-based algorithm for the improved clustering and the embedding of mixture manifolds. The algorithm attempts to reconstruct each target point as an affine combination of its nearest neighbors with an additional rank penalty on the neighborhood to ensure that only the neighbors on the same manifold as the target point are used in the reconstruction. The reconstruction matrix generated by this technique is both block diagonal and neighborhood-based, leading to improved clustering and embedding. The improved performance of the algorithm against its competitors is exhibited on a variety of simulated and real mixture data sets.