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Recently, there has been a strong interest in the minimum error entropy (MEE) criterion derived from information theoretic learning, which is effective in dealing with the multimodal non-Gaussian noise case. However, the kernel function is shift invariant resulting in the MEE criterion being insensitive to the error location. An existing solution is to combine the maximum correntropy (MC) with MEE criteria, leading to the MEE criterion with fiducial points (MEEF). Nevertheless, the algorithms based on the MEEF criterion usually require higher computational complexity. To remedy this problem, an improved MEEF (IMEEF) criterion is devised, aiming to avoid repetitive calculations of the a p o s t e r i o r i error, and an adaptive filtering algorithm based on gradient descent (GD) method is proposed, namely, GD-based IMEEF (IMEEF-GD) algorithm. In addition, we provide the convergence condition in terms of mean sense, along with an analysis of the steady-state and transient behaviors of IMEEF-GD in the mean-square sense. Its computational complexity is also analyzed. Simulation results demonstrate that the computational requirement of our algorithm does not vary significantly with the error sample number and the derived theoretical model is highly consistent with the learning curve. Ultimately, we employ the IMEEF-GD algorithm in tasks such as system identification, wind signal magnitude prediction, temperature prediction, and acoustic echo cancellation (AEC) to validate the effectiveness of the IMEEF-GD algorithm. • We propose an IMEEF criterion for the high computational complexity of the MEEF. • Based on the IMEEF criterion, we derive a gradient-based algorithm. • We analyze the performance of the proposed algorithm based on statistical properties. • The experimental results show that the proposed algorithm has excellent performance. [ABSTRACT FROM AUTHOR]

In order to improve the flexibility of the correntropy that is usually in the form of a single kernel, this brief proposes a novel combinatoric maximum correntropy criterion (C-MCC), where the combinatoric correntropy (C-C) consists of two different single-type kernels. As a new form of correntropy, the C-C has a more generalized form than the traditional single-kernel correntropy, and the corresponding properties and proofs of the C-C are given in this brief. It is noticed that the combined kernel can become a single kernel by changing the combined parameters. Moreover, the adaptive filtering algorithm based on C-MCC is derived and the theoretical performance analysis of the C-MCC algorithm is also provided. Finally, the experimental simulations show that the proposed algorithm has better convergence speed and steady-state performance than MCC-type and other algorithms, and the proposed method of the theoretical analysis of C-MCC agrees well with simulation results. [ABSTRACT FROM AUTHOR]

The adaptive filtering algorithm based on the maximum correntropy criterion (MCC) is very effective in suppressing non-Gaussian noises and therefore attracts widespread attentions. At present, some works have been done for study the convergence and steady-state performance analysis of the MCC algorithm, but its transient performance analysis is still an open problem. To provide a comprehensive theoretical foundation for the MCC algorithm, we propose a method for transient performance analysis based on moment generating function (MGF). Since this method can efficiently calculate the expected value of the exponential term in the iterative update equation, it can avoid the discrepancies caused by introducing some approximation methods such as Taylor expansions in the analysis process. To date, there is no precedent for using this method to analyze the transient performance of the MCC algorithm. In addition, the steady-state performance and stability conditions of the MCC algorithm are discussed based on this method. Finally, the proposed analytical method is applied to the system identification problem, and the results show that the theoretical analysis results are agree well with the Monte Carlo simulation results. [ABSTRACT FROM AUTHOR]

The constant kernel width of generalized maximum correntropy criteria (GMCC) has arisen that the steady-state error and convergence speed can be mutually exclusive. To solve this problem, this brief proposes the variable kernel width (VKW) GMCC algorithm. Actually, due to the censored problem, the output data value beyond the limit of the recording device can not be well observed. In this case, we further developed a variable kernel width GMCC algorithm based on censored regression (CR-VKWGMCC). Simulation results show that the proposed CR-VKWGMCC algorithm has excellent performance in both Gaussian and non Gaussian noise. [ABSTRACT FROM AUTHOR]

• The TLS-APL algorithm is proposed by using the gradient descent method and the unconstrained optimization method, which solves the problem of overall performance degradation of the APL algorithm in the EIV model. • By using some common assumptions, the local extremum of the TLS-APL algorithm is analyzed. Therefore, the expected parameter is the optimal value of the iterative estimation and fully demonstrates the correctness of the iterative update. • The mean, mean square, and steady-state MSD performance of the TLS-APL algorithm is derived by using the Kronecker product and vec operator respectively. In addition, the fitting effects of theoretical steady-state MSD curves and actual steady-state MSD curves under different parameters are analyzed, which proves the rationality of theoretical derivation. • The VSS method is presented from the maximum decrease of MSD from the current iteration to the next iteration. Compared to the TLS-APL algorithm with a fixed step size, the VSS-TLS-APL algorithm with the VSS method has both fast convergence speed and low steady-state error. In the errors-in-variables (EIV) model, the steady state characteristics of the affine-projection-like (APL) algorithm are poor. Hence, the total least squares APL (TLS-APL) algorithm different from the bias-compensated is proposed, which can reduce the adverse influence of input and output noise on weight update. Then, the local extremum of the TLS-APL algorithm is verified, that is, the expected parameter is the optimal value of the iterative estimation. Moreover, the mean, mean square, and steady-state mean square deviation (MSD) performance of the proposed TLS-APL algorithm are deduced by using the Kronecker product and vec operator, respectively. To balance the convergence characteristics and steady-state characteristics, the step size optimization of the TLS-APL algorithm, namely the variable step size TLS-APL (VSS-TLS-APL) algorithm, is derived from the analysis of MSD. Considering the existence of gradient errors, the fitting effects of theoretical steady-state MSD curves and actual steady-state MSD curves under different parameters are analyzed separately, which proves the rationality of theoretical derivation. In addition, the VSS-TLS-APL algorithm with optimized step size is compared with the TLS-APL algorithm with fixed step size in the application of system identification, and the effect of the variable step size (VSS) is verified. The experiments of system identification and acoustic echo cancelation prove that the VSS-TLS-APL algorithm is superior to the existing known algorithms. [ABSTRACT FROM AUTHOR]

In practical applications, the impulse responses (IRs) of some network echo paths are blocksparse (BS), while the traditional proportionate and zero attraction algorithms do not consider the prior sparsity of the BS system, so they do not perform well in the block-sparse system identification (BSSI). In addition, most of the current BS filtering algorithms are based on the assumption of Gaussian noise, so the performance will deteriorate seriously in the background of impulse noise. To overcome the shortcoming, we use the mixed $l_{2,1} $ norm of the filter weight vector to fully tap the sparsity of the BS system, and combine the anti impulse noise characteristic of the M-estimate function to design and derive the BS proportionate normalized least mean M-estimate (BSPNLMM) algorithm from the perspective of basis pursuit (BP), which well realizes the BSSI in the presence of impulse noise. Then, we analyze the mean performance of the BSPNLMM algorithm in detail and give the stable step size bound. Finally, the superiority of the proposed BSPNLMM algorithm is verified by numerical simulations [ABSTRACT FROM AUTHOR]

In this brief, an affine projection maximum correntropy criterion with correntropy induced metric (APMCCCIM) algorithm is proposed for robust sparse adaptive filtering, and it is derived by using the cost function based on affine projection maximum correntropy criterion and correntropy induced metric to eliminate the adverse effects of impulsive noise on filter weight update in sparse systems. In order to further improve the convergence speed and steady-state misalignment of the proposed APMCCCIM algorithm, the variable step-size method is incorporated into the APMCCCIM algorithm. Hence, the variable step-size APMCCCIM (VSS-APMCCCIM) algorithm is presented. Besides, the computational complexity and the range of step-size of the proposed APMCCCIM algorithm are analyzed. Simulation results show that the proposed APMCCCIM and VSS-APMCCCIM algorithms have faster convergence speed and lower steady-state misalignment for sparse system identification and echo cancellation scenarios in the impulsive noise environments. [ABSTRACT FROM AUTHOR]

The errors-in-variables (EIV) model is widely used in linear systems where both input and output signals are contaminated with noise. For the parameter estimation in the EIV model, the adaptive filtering algorithm using total least squares (TLS) approach has shown better performance than classical least squares (LS) approach. However, the TLS approach which is based on minimizing the mean squared total error may be irrational in the presence of impulsive noise. To address this problem, a novel robust adaptive algorithm, named as the total least mean M-estimate (TLMM) algorithm, is proposed in this brief, which combines the advantages of TLS approach and M-estimate function. In addition, to further improve the performance of the TLMM algorithm, its variable step-size (VSS) version has been developed. Moreover, we carry out the local stability analysis and the computational complexity analysis. Simulation results show that the proposed algorithms outperform some well-known algorithms. [ABSTRACT FROM AUTHOR]

Highlights • This paper provides the development of the robust censored adaptive algorithm for the impulsive noise. • This paper gives Consideration of non-Gaussian background noise as different from previous literature which only consider the Gaussian noise. • Theoretical insights into the mean and mean square performance of the CR-MCC algorithm are provided. • Simulation examples to demonstrate the performance of the proposed algorithm in impulsive noise scenarios are given. Abstract Censored observations and impulsive measurement noise are encountered in many practical applications of adaptive signal processing. Traditional adaptive filtering algorithms may fail to work in such cases. This paper proposes a robust adaptive filter algorithm predicated on maximum correntropy criteria (MCC) for censored regression. A detailed performance analysis in terms of mean and mean-square behaviour is provided. Simulations with Gaussian and non-Gaussian noise are presented to verify the theoretical results, and to demonstrate the superior performance of the proposed algorithm over existing algorithms. [ABSTRACT FROM AUTHOR]

Highlights • The filtered-x least mean square/fourth (FXLMS/F) algorithm for active noise control. • A convex combination of the FXLMS/F algorithm (C-FXLMS/F) for active noise control. • The stability condition of the proposed algorithm is analyzed, and computational complexity is provided. • Computer simulations demonstrate good convergence speed and noise reduction performance for active noise control. Abstract The filtered-x least mean square (FXLMS) algorithm is widely used for active noise control (ANC) systems. However, due to the fixed step-size of FXLMS algorithm being used, the FXLMS algorithm results in a compromise between noise reduction performance and convergence speed. Therefore, this paper proposes the filtered-x least mean square/fourth (FXLMS/F) algorithm for ANC systems, which can be viewed as a variable step-size FXLMS (VSS-FXLMS) algorithm. In order to further improve the algorithm performance, the convex combination of the FXLMS/F (C-FXLMS/F) algorithm for ANC systems is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXLMS/F and C-FXLMS/F algorithms can achieve better convergence performance as compared to the FXLMS and FXLMF algorithms under various noise input conditions, and the C-FXLMS/F algorithm outperforms the FXLMS/F algorithm. [ABSTRACT FROM AUTHOR]

The standard adaptive filtering algorithm with a single error norm exhibits slow convergence rate and poor noise reduction performance under specific environments. To overcome this drawback, a filtered-x generalized mixed norm (FXGMN) algorithm for active noise control (ANC) system is proposed. The FXGMN algorithm is developed by using a convex mixture of l p and l q norms as the cost function that it can be viewed as a generalized version of the most existing adaptive filtering algorithms, and it will reduce to a specific algorithm by choosing certain parameters. Especially, it can be used to solve the ANC under Gaussian and non-Gaussian noise environments (including impulsive noise with symmetric α -stable ( S α S ) distribution). To further enhance the algorithm performance, namely convergence speed and noise reduction performance, a convex combination of the FXGMN algorithm (C-FXGMN) is presented. Moreover, the computational complexity of the proposed algorithms is analyzed, and a stability condition for the proposed algorithms is provided. Simulation results show that the proposed FXGMN and C-FXGMN algorithms can achieve better convergence speed and higher noise reduction as compared to other existing algorithms under various noise input conditions, and the C-FXGMN algorithm outperforms the FXGMN. [ABSTRACT FROM AUTHOR]

As a robust nonlinear similarity measure in kernel space, correntropy has received increasing attention in domains of machine learning and signal processing. In particular, the maximum correntropy criterion (MCC) has recently been successfully applied in robust regression and filtering. The default kernel function in correntropy is the Gaussian kernel, which is, of course, not always the best choice. In this paper, we propose a generalized correntropy that adopts the generalized Gaussian density (GGD) function as the kernel, and present some important properties. We further propose the generalized maximum correntropy criterion (GMCC) and apply it to adaptive filtering. An adaptive algorithm, called the GMCC algorithm, is derived, and the stability problem and steady-state performance are studied. We show that the proposed algorithm is very stable and can achieve zero probability of divergence (POD). Simulation results confirm the theoretical expectations and demonstrate the desirable performance of the new algorithm. [ABSTRACT FROM AUTHOR]

To improve the performance and reduce the computational complexity, a novel sign adaptation scheme for convex combination of adaptive filters is proposed. By using a sign adaptation scheme, the proposed scheme slightly reduces the computational complexity of the basic combination of mixing parameter, and improves the robustness of mixing parameter. Moreover, to obtain fast convergence property during the period of convergence transition in different environments, the instantaneous transfer scheme is applied to the proposed algorithm. The instantaneous transfer scheme has lower computational complexity than that of the basic combination of least mean square (basic-CLMS) algorithms. Simulation results in the context of system identification under time-invariant and time-variant systems demonstrate that the proposed algorithm based on the instantaneous transfer scheme has lower computational complexity and faster convergence rate than that of the basic-CLMS algorithm during period of convergence transitions. [ABSTRACT FROM AUTHOR]

• In this paper, we analyze the transient performance of the geometric algebra based least mean M-estimate (GA-LMM) filtering algorithm in detail under some simplifying assumptions and give the step size range that ensure the mean square stability of the GA-LMM. Further, to eliminate the constraint of the constant step size on the performance of the GA-LMM, a novel variable step-size algorithm called VSS-GA-LMM is designed and the optimal step size is obtained by maximizing the difference of mean square deviation (MSD) between successive iterations, which effectively balances the contradiction between convergence rate and steady-state error. • The validity of the transient performance analysis about GA-LMM and the advantages of the GA-LMM and VSS-GA-LMM algorithms over other existing GA based algorithms are confirmed through numerical simulations. In this paper, the transient performance of the geometric algebra based least mean M-estimate (GA-LMM) filtering algorithm is analyzed in detail under some simplifying assumptions. Further, the variable step-size variant VSS-GA-LMM is designed to eliminate the constraint of the constant step size on the performance of the GA-LMM and the optimal step size is obtained by maximizing the difference of mean square deviation (MSD) between successive iterations, which effectively balances the contradiction between convergence rate and steady-state error. Finally, numerical simulations are presented to verify the validity of the theoretical analysis of the GA-LMM and the advantages of the GA-LMM and VSS-GA-LMM algorithms. [ABSTRACT FROM AUTHOR]

• In this paper, we propose a diffusion recursive total least squares (DRTLS) algorithm by using the single inverse power iterations in the distributed network. Further, to reduce the computational complexity of the DRTLS algorithm, an improved algorithm called DCD-DRTLS is also proposed by using the dichotomous coordinate descent (DCD) iterations. • we analyze the mean and mean square behaviors of the proposed DRTLS algorithm. • Simulation results illustrate the superiority of the proposed algorithms than other compared algorithms and the validity of the theoretical analysis results. In most existing distributed estimation algorithms, many scholars adopted the assumption that the output signal of the system is noisy and the input signal is sufficiently accurate. However, in real applications, the filter input vector usually contains noise. In such situations, it has been proved that the adaptive filtering algorithm using total least squares (TLS) method has shown better performance than classical least squares (LS) method. So in this paper, we propose a diffusion recursive total least squares (DRTLS) algorithm by using the single inverse power iterations in the distributed network. Then, we analyze the mean and mean square behaviors of the proposed DRTLS algorithm. In addition, to reduce the computational complexity of the DRTLS algorithm,an improved algorithm called DCD-DRTLS is also proposed by using the dichotomous coordinate descent (DCD) iterations. At last, simulation results illustrate the superiority of the proposed algorithms and the validity of the theoretical analysis results. [ABSTRACT FROM AUTHOR]