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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.

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.

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.