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The performance of conventional active noise control (ANC) systems degrades under non-Gaussian conditions. In the recent past, generalized filtered-x maximum correntropy criterion (FxGMCC) algorithm has been widely used to tackle such non-Gaussian noises. However, noise reduction performance of maximum correntropy criterion (MCC) based algorithms degrades due to the high steady-state misalignment. To overcome this limitation, a filtered-x exponential hyperbolic cosine adaptive filter (FxEHCAF) algorithm is proposed in this paper. Later, an affine combination technique has been applied and the corresponding affine FxEHCAF (A-FxEHCAF) algorithm has been developed here showing faster convergence rate in transient state along with low residual error in steady-state. Simulation study shows that the proposed FxEHCAF and A-FxEHCAF algorithms provide enhanced noise control performance over other existing algorithms. • A robust FxEHCAF algorithm based ANC technique is proposed. • Affine-FxEHCAF algorithm for enhanced noise control is also proposed. • The theoretical analysis of FxEHCAF and Affine-FxEHCAF are carried out. • Proposed algorithms provide improved ANC performance. [ABSTRACT FROM AUTHOR]

We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a linear combination of two copulas. This generalizes a recent result of Fernández-Sánchez, Quesada-Molina, and Úbeda-Flores who considered linear combinations of discrete copulas. [ABSTRACT FROM AUTHOR]

• We propose affine combining of two ACLMS filters and present its optimal mixing parameter, based on which an explicit expression describing the steady state mean behavior of the optimal mixing parameter is quantified for doubly white noncircular Gaussian input data. The so established physical insight shows that in steady state, the optimal mixing parameter is, statistically, negative and monotonically increases against the input SO noncircularity coefficient. • Upon applying the optimal mixing parameter, we perform the MSE analysis of the proposed affine-combined ACLMS filters. The so derived explicit MSE expression not only theoretically presents the universality of the combination scheme, that is, smaller or equal steady state MSE than either of the individual ACLMS subfilters, but also demonstrates that the overall MSE in steady state is approximately a monotonic increasing function of the input SO noncircularity coefficient. • Considering that the optimal affine combiner is unacquirable in practical applications, we provide an error power based scheme to iterate the affine combiner. Numerical examples verify that the proposed iterative combiner converges to the optimal one. The overall MSE curves respectively obtained via the iterative and optimal combiners are shown to be in close agreement. This paper investigates the statistical behavior of an affine combination of two augmented complex least mean-square (ACLMS) adaptive filters for processing noncircular Gaussian signals. First, the optimal affine combiner is studied and its steady state mean behavior is explicitly quantified. This makes it possible to reveal the impact of the input second-order noncircularity coefficient on the combiner. Next, the mean square error analysis of the proposed affine-combined ACLMS filters is provided, proving that the combined scheme performs no less than the best of the individual ACLMS subfilters. Besides, to facilitate physically realization of the combination strategy, an error power based algorithm that can iterate the affine combiner to the optimal one is also proposed. Finally, illustrative numerical simulations are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Generalizing the result in Lemma of Baksalary and Baksalary [J.K. Baksalary, O.M. Baksalary, Commutativity of projectors, Linear Algebra Appl. 341 (2002) 129–142], Baksalary et al. [J.K. Baksalary, O.M. Baksalary, T. Szulc, Linear Algebra Appl. 354 (2002) 35–39] have shown that if P 1 and P 2 are orthogonal projectors, then, in all nontrivial situations, a product of any length having P 1 and P 2 as its factors occurring alternately is equal to another such product if and only if P 1 and P 2 commute, in which case all products involving P 1 and P 2 reduce to the orthogonal projector P 1 P 2 (= P 2 P 1). In the present paper, further generalizations of this property are established. They consist in replacing a product of the type specified above, appearing on the left-hand side (say) of the equality under considerations, by an affine combination of two or three such products. Comments on the problem when the number of components in a combination exceeds three are also given. [Copyright &y& Elsevier]

• New second-order interpolative-based M2 maximum-entropy closure for constructing approximate solutions of the radiative transport equation in gray-participating media governed Bose-Einstein statistics. • Review of and new insight into the necessary and sufficient conditions for realizability of predicted moments up to second order in multiple space dimensions. • Demonstration of hyperbolicity of proposed interpolative-based M2 closure via numerical experiments. • Development of boundary conditions for M2 moment closure based on partial moment approach. • Illustration of predictive capabilities of interpolative-based M2 closure for several one and twodimensional canonical test problems. A new interpolative-based approximation to the second-order maximum-entropy, M 2 , moment closure for predicting radiative heat transfer in gray participating media is proposed and described. In addition to preserving many of the desirable mathematical properties of the original M 2 closure, the proposed interpolative approximation provides significant reductions in computational costs compared to the costs of the original M 2 closure by avoiding repeated numerical solution of the corresponding optimization problem for entropy maximization. Theoretical details of the proposed interpolative-based closure, along with a description of an efficient Godunov-type finite-volume scheme that has been developed for the numerical solution of the resulting system of hyperbolic moment equations, are presented. The finite-volume method makes use of limited linear solution reconstruction, multi-block body-fitted quadrilateral meshes with anisotropic adaptive mesh refinement (AMR), and an efficient Newton-Krylov-Schwarz (NKS) iterative method for solution of the resulting non-linear algebraic equations arising from the spatial discretization procedure. The predictive capabilities of the proposed interpolative M 2 closure are assessed by considering a number of model problems involving radiative heat transfer within one- and two-dimensional enclosures, the results for which are compared to solutions of the first-order maximum entropy, M 1 , moment closure, as well as those of the more commonly adopted spherical harmonic moment closure techniques (first-order P 1 and third-order P 3) and the popular discrete ordinates method (DOM). The latter is used as a benchmark for comparisons, whenever exact solutions are not available. The numerical results illustrate the promise of the proposed M 2 closure, with the closure outperforming the M 1 , P 1 and P 3 closures for virtually all cases considered. [ABSTRACT FROM AUTHOR]