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In the past decade, the augmented complex-valued least mean square adaptive filtering algorithm based on the minimum mean square error criterion and widely-linear model has attracted much attentions due to its simplicity and applicability to non-circular signals. However, the system noise with impulse characteristics will dramatically affect the convergence of the augmented complex-valued least mean square algorithm. Recently, a robust widely-linear complex-valued least mean M-estimate algorithm has been proposed, which significantly improves the robustness of the augmented complex-valued least mean square algorithm to impulsive noise. But it should be noted that the widely-linear complex-valued least mean M-estimate algorithm with fixed step size faces the trade-off between convergence speed and steady-state accuracy. To overcome this drawback, a variable step size widely-linear complex-valued least mean M-estimate algorithm is presented in this paper, in which the optimal step size at each iteration is obtained by maximizing the difference between the mean square deviations of the WL-CLMM algorithm at adjacent moments. In order to reveal the statistical convergence behavior of the proposed variable-step-size widely-linear complex-valued least mean M-estimate algorithm to better guide the parameter selection in practical applications. Theoretical transient and steady-state mean-square deviation convergence behaviors of the variable-step-size widely-linear complex-valued least mean M-estimate algorithm are analyzed and the corresponding mean-square deviation expressions are also derived. Computer simulations on system identification and stereophonic acoustic echo cancellation in impulsive noise environments confirm the validity of the analysis results and the performance improvement from the variable step size strategy. [ABSTRACT FROM AUTHOR]

The complex domain adaptive filtering algorithms has shown excellent performance in the field of signal processing. Among them, the well-known complex least mean square (CLMS) algorithm has been widely used in practical projects. However, the CLMS algorithm only considers the case where the output signal is disturbed by noise, ignores the input signal may also be interfered by noise. Moreover, the signal is likely to be disturbed by impulsive noise in practice. Based on the above problems, the complex total least mean M-estimation (CTLMM) adaptive algorithm based on the M-estimation function is put forward in this paper. The algorithm can well handle the case where both input and output signals are subject to complex domain noise interference, and it also shows robustness with impulsive noise. This paper also analyzes the local stability of the CTLMM algorithm and discuss the theoretical steady-state error of the algorithm. Finally, simulation results verify the advantages of CTLMM algorithm and the rightness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This study proposes a spline filtering algorithm-based generalized maximum correntropy criterion (GMCC), named the spline adaptive filter (SAF-)-GMCC algorithm. Compared with traditional spline algorithms, the SAF-GMCC can cope with impulsive interference effectively, because the GMCC has a low sensitivity to mutation signals. The GMCC-based variable step-size spline filtering algorithm (SAF-GMCC) is proposed to solve the limitation of the fixed step-size on the SAF-GMCC algorithm's performance and to improve the convergence rate and steady-state error performance. Combining these algorithms with the active noise control (ANC) model, this study proposes the filtered-c generalized maximum correntropy criterion (FcGMCC) and variable step-size filtered-c generalized maximum correntropy criterion (FcVGMCC) algorithms. Finally, the nonlinear system identification model simulates an experimental environment with impulsive interference. The SAF-GMCC and SAF-VGMCC algorithms offer better robustness than the existing algorithms. And the alpha-stable noise environment simulation with different impact strengths, in the ANC model verifies the FcGMCC and FcVGMCC algorithms' robustness in nonlinear and non-Gaussian noise environments. [ABSTRACT FROM AUTHOR]

To enhance the convergence performance of the affine projection sign subband adaptive filter (AP-SSAF) algorithm under highly correlated inputs, the novel AP-SSAF (NAP-SSAF) algorithm was proposed through fully utilizing the decorrelation characteristic of SAF, which obtains quicker convergence behavior than the AP-SSAF algorithm. However, under unknown system identification, the estimation accuracy of the NAP-SSAF algorithm may unavoidably decrease when the input of the adaptive filter is contaminated by noise. To alleviate this issue, in this paper, we propose the bias-compensated NAP-SSAF (BC-NAP-SSAF) algorithm to alleviate the estimated bias through employing unbiasedness criterion. Benefiting from the unbiased criterion, the proposed BC-NAP-SSAF algorithm achieves an asymptotically unbiased estimation. Moreover, the convergence bounds of the proposed BC-NAP-SSAF algorithm in the mean and mean-square senses are provided to ensure stability, which are obtained by resorting to Price's theorem along with some reasonable assumptions. The effectiveness of the derived theoretical convergence bounds is also corroborated. Finally, numerical simulations under system identification and acoustic echo cancellation applications demonstrate that the proposed BC-NAP-SSAF algorithm outperforms other algorithms in terms of estimation accuracy and tracking capability for noisy input under impulsive noise environment. [ABSTRACT FROM AUTHOR]

This paper presents a robust distributed adaptive algorithm called diffusion recursive least M-estimate (DRLM), which enhances the robustness of the diffusion recursive least square (DRLS) algorithm against impulsive noise by incorporating the strong resistance to impulsive noise of the modified Huber function (MHF). However, the tracking speed of the proposed DRLM algorithm is not favorable in scenario where the network parameter vector of interest changes abruptly. To overcome this drawback, a new variable forgetting factor (VFF) strategy is devised and the VFF-DRLM algorithm is obtained. Then, the asymptotic unbiasedness and steady-state network mean square deviation (NMSD) performance of the DRLM algorithm are analyzed. Finally, the accuracy of the steady-state analysis result of the DRLM algorithm and the superiority of the proposed algorithms compared to other competing algorithms are demonstrated by extensive numerical simulations. [ABSTRACT FROM AUTHOR]

The distributed estimation performance of multitask diffusion affine projection (AP) algorithm (MD-APA) will be greatly reduced under the impulsive noise interference. To overcome this defect, a robust MD-APA is derived by using M-estimate function (MD-APM) to resist the impulsive noise interference. The mean performance, mean square performance and steady-state performance of MD-APM algorithm are studied, and the convergence range of the step-size and the theoretical steady-state MSD are obtained. In addition, the computational complexity of MD-APM algorithm is analyzed in detail. Simulation experiments show that the proposed MD-APM algorithm has better estimation performance compared with MD-APA and MD-APSA under the impulsive noise interference, and its theoretical steady-state mean square deviation (MSD) can provide accurate prediction. [ABSTRACT FROM AUTHOR]

In this paper, a generalized maximum correntropy normalized subband adaptive filter (GMCNSAF) algorithm is proposed for enhancing the convergence behavior of generalized maximum correntropy criterion algorithm under correlated signals. To promote the convergence behavior of GMCNSAF when identifying the sparse system, the polynomial zero attraction constraint is incorporated into it to yield the PZAGMCNSAF algorithm. Furthermore, to alleviate the conflicting requirements with regard to convergence rate and steady-state misalignment, a variable step-size scheme is applied into the PZAGMCNSAF, obtaining the VSSPZAGMCNSAF algorithm. Also, we analyze the convergence condition of GMCNSAF and give the step-size bound. Simulations prove that the proposed algorithms obtain superior performance for sparse system identification and echo cancelation scenario under impulsive interference as compared to related algorithms. [ABSTRACT FROM AUTHOR]

When the distributed nodes are contaminated by the different types of noises, including Gaussian and generalized Gaussian distribution noises, the diffusion distributed least mean square algorithm suffers severely from performance degradation. To address this problem, this paper proposes background and impulsive noise indicators to identify the background noise non-Gaussianity and detect the impulsive noise, respectively. Then, according to the results of noise indicators, different distributed algorithms are selected for distributed in-network identification where different nodes share different noise types. The proposed algorithm is called distributed conditional selection algorithm, which is superior to the existing diffusion-based algorithms due to its combining the advantages of the related algorithms. Simulations with non-impulsive and impulsive interference confirm the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Constrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs. [ABSTRACT FROM AUTHOR]

Due to its low computational burden, the affine-projection-like (APL) adaptive filtering algorithm has been extensively studied for colored signal input. Recently, a robust APL algorithm was designed by adopting the M-estimate cost function in impulsive noise environment; however, its convergence rate is very slow for sparse system identification. This paper proposed a proportionate APL M-estimate (PAPLM) algorithm, which is derived by using the proportionate matrix to heighten the convergence rate. To maintain good steady-state performance of the PAPLM algorithm, a time-varying parameter PAPLM (TV-PAPLM) algorithm is proposed, which uses a modified exponential function to adjust the time-varying parameter according to the ratio of the mean square score function to the system noise variance. Moreover, the steady-state excess mean-square error performance of PAPLM algorithm is analyzed and obtained in detail. Simulation results reveal that the proposed PAPLM and TV-PAPLM algorithms achieve fast convergence rate and good steady-state performance in sparse system identification. [ABSTRACT FROM AUTHOR]

The generalized variable step-size diffusion continuous mixed p-norm (GVSS-DCMPN) algorithm is proposed in this paper, which is derived based on the improved continuous mixed p-norm (CMPN) strategy. In detail, a linear function is designed for the CMPN strategy. The proposed GVSS-DCMPN algorithm capable of exploiting various error norms to obtain performance improvement in non-Gaussian noise environment can be viewed as the generalization of the traditional p-norm-based algorithms in the sense of continuous errors. In particular, the GVSS-DCMPN algorithm transforms into the VSS-DCMPN algorithm when the slope of the linear function is set to 0. The computational complexity as well as the mean convergence is analyzed in the paper. Simulation results over the diffusion network show that the proposed algorithm achieves performance gain over some existing diffusion algorithms. [ABSTRACT FROM AUTHOR]

To improve the performance of the diffusion Huber-based normalized least mean square algorithm in the presence of impulsive noise, this paper proposes a distributed recursion scheme to adjust the thresholds. Because of the decreasing characteristic of the thresholds, the proposed algorithm can also be interpreted as a robust diffusion normalized least mean square algorithm with variable step sizes so that it has not only fast convergence but also small steady-state estimation error. Based on the contaminated Gaussian model, we analyze the mean square behavior of the algorithm in impulsive noise. Moreover, to ensure good tracking capability of the algorithm for the sudden change of parameters of interest, a control strategy is given that resets the thresholds with their initial values. Simulations in various noise scenarios show that the proposed algorithm performs better than many existing diffusion algorithms. [ABSTRACT FROM AUTHOR]

In reality, the range of sensor response is limited in many sensor systems due to the saturation characteristics of the sensor. That is, the value exceeding the sensor response range is not observed. Using traditional adaptive algorithms to identify the system of this type may lead to the performance degradation. To address this problem, the censored regression algorithms have been proposed. However, when the mixed sub-Gaussian and super-Gaussian/impulsive noises occur, these algorithms may fail to work. To overcome these drawbacks, a family of robust M-shaped (FRMS) functions for censored regression (CR-FRMS) is proposed in this paper. When the system to be identified exhibits a certain degree of sparsity, the CR-FRMS algorithm cannot fully utilize the characteristics of the sparse system. Therefore, in this paper, proportionate FRMS (PFRMS) algorithm based on l 0 -norm constraint for censored regression ( l 0 -CRPFRMS) is also proposed accordingly. The simulations using Gaussian white noise as the input signal and the non-Gaussian mixed noise as the background noise show that the proposed algorithm performs better than other algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a novel affine projection sign subband adaptive filter (NAPSSAF) which could achieve better performance than the conventional APSSAF. The proposed NAPSSAF is obtained by solving the optimal problems regarding the l1-norm of the subband a posteriori error vectors rather than overall a posteriori error vector, which fully uses the subband adaptive filter's inherent decorrelating property. However, since the NAPSSAF algorithm uses the fixed step size, it has an inherent trade-off between low steady-state error and fast convergence rate. Thus, we also propose a combined step size NAPSSAF (CSS-NAPSSAF) to further improve the performance of the NAPSSAF. Finally, simulations are carried out to exhibit the advantages of the NAPSSAF and CSS-NAPSSAF algorithms. The results of simulations demonstrate that the NAPSSAF is superior to the existing algorithms. Besides, the results of simulations also exhibit the improved performance of the CSS-NAPSSAF compared to NAPSSAF. [ABSTRACT FROM AUTHOR]

In this paper, a robust adaptive filter based on kernel risk-sensitive loss for bilinear forms is proposed. The proposed algorithm, called minimum kernel risk-sensitive loss bilinear form (MKRSL-BF), is derived by minimizing the cost function based on the minimum kernel risk-sensitive loss (MKRSL) criterion. The proposed algorithm can obtain the excellent performance when the system is corrupted by the impulsive noise. In addition, to further improve the performance of the MKRSL-BF algorithm, the novel algorithm based on the convex scheme is proposed, which can suppress the confliction between the fast convergence rate and the low steady-state error. Finally, simulations are carried out to verify the advantages of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes an improved variable regularization parameter (VRP) for sign subband adaptive filter, which is derived on the basis of the mean-square deviation (MSD) analysis. Since it is difficult to get access to the exact values of some quantities in the MSD, the VRP is calculated by minimizing the upper bound of a certain term which is employed to update the MSD. Moreover, a re-initialization mechanism that can enhance the tracking capability is developed. We also discuss the computational complexity of our finding. The proposed scheme enjoys more merits than several prior algorithms, which is illustrated by sufficient simulations designed for both the system identification and acoustic echo cancelation applications in the presence of impulsive noise. [ABSTRACT FROM AUTHOR]

To solve the conflicting requirement of fast convergence and low steady-state misalignment, a variable step-size shrinkage set-membership affine projection algorithm is proposed, which is efficient for the correlated input signal and noisy input environments. The new variable step size is derived by minimizing the square of noise-free a posteriori error, and the shrinkage method is employed to estimate the second-order statistics of the noise-free a priori error vector. Moreover, the stability analysis of the algorithm is conducted. Simulations demonstrate the effectiveness of the proposed algorithm for various noisy input environments. [ABSTRACT FROM AUTHOR]

Recently, the distributed incremental affine projection algorithm (DIAPA) has attracted much attention owing to its good performance for correlated input. However, the DIAPA algorithm with high projection order achieves fast convergence rate but suffers from large steady-state misalignment, and that with low projection order has small steady-state misalignment, but it converges slowly. To overcome this trade-off, in this brief, an adaptive combination of the distributed incremental affine projection algorithm with different projection orders (ACDIAPA-DPO) is proposed, which combines the DIAPA using high projection order with that using low projection order by an adaptive mixing parameter. The mixing parameter is obtained by minimizing the mean square deviation. We discuss the computational complexity of the proposed algorithm and other existing algorithms. Moreover, a novel re-initialization mechanism is introduced to further improve the tracking capability of the ACDIAPA-DPO when the system suddenly changes. Simulations results over the incremental network show the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

As a robust adaptation criterion, the maximum correntropy criterion (MCC) has gained increased attention due to its successful application in the adaptation, especially in nonlinear and non-Gaussian situations. In this paper, the second-order Volterra (SOV) filter based on MCC is derived, which is called MCC-SOV. It combines the advantages of the SOV filter and MCC. However, similar to the conventional adaptive algorithm, the proposed MCC-SOV filter has a tradeoff between convergence rate and steady-state error. In order to solve this problem, we present a combination of the MCC-SOV filter by combining Volterra kernels, which is called CK-MCC-SOV. In addition, a weight transfer method is applied to improve the performance of the proposed filter in terms of the convergence rate and the steady-state error. Finally, simulations are carried out to demonstrate the advantages of the proposed filters. [ABSTRACT FROM AUTHOR]

Variable step size norm-constrained adaptive filtering algorithms are proposed in the paper. A variable step size is derived by minimizing the variance of the noise-free a posterior error. Thus, the update equation can obtain a reasonable step size at each iteration. Due to the introduction of variable step size, the proposed algorithms based on the constrained conditions of $$L_{1}$$ and $$L_{0}$$ norm have a significant advantage that the convergence rate is faster than some well-known algorithms in the sparse system. The simulation results illustrate the good performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Recently, the diffusion sign subband adaptive filtering (DSSAF) algorithm has attracted great attention because of its robustness against the impulsive noise and its decorrelation power to the correlated input signals. However, the DSSAF converges slowly when the system to be identified is sparse. In order to solve the problem of slow convergence rate in the sparse system, this paper proposes a diffusion proportionate sign subband adaptive filtering (DPSSAF) algorithm by minimizing $$L_{1}$$ -norm of the subband a posteriori error vector subject to weighted constraint for each node in the diffusion network. The proposed DPSSAF algorithm is robust against the impulsive noise in the sparse system. To further improve the performance of the DPSSAF in the very sparse system, an efficient version (EDPSSAF) based on $$L_{0}$$ -norm is obtained, which can better measure the sparseness level of the unknown system with high sparsity. Simulation results are presented to illustrate the good performance of proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes a robust set-membership affine projection algorithm with coefficient vector reuse (RSM-APA-CVR) for high background noise environment. In the proposed algorithm, the sum of the squared $$L_{2}$$ norms of the differences between the updated weight vector and past weight vectors is minimized and a new robust error bound is designed. Simulation results in acoustic echo cancellation context show that the proposed algorithm has faster convergence rate and smaller steady-state misalignment as compared to the conventional RSM-APA. [ABSTRACT FROM AUTHOR]

A new diffusion sign subband adaptive filtering algorithm with an individual weighting factor (IWF-DSSAF) for each subband is proposed for distributed estimation in the impulsive noise environment. Since the inherent decorrelating property of subband adaptive filtering is fully used, the proposed algorithm obtains better performance in terms of convergence rate and tracking capability as compared with the diffusion sign subband adaptive filtering (DSSAF) algorithm. In addition, the stability analysis of the IWF-DSSAF algorithm is performed based on Price's theorem. After that, in order to obtain a faster convergence rate in sparse distributed system identification, the improved proportionate IWF-DSSAF algorithm is proposed, in which a gain distribution matrix is incorporated into the IWF-DSSAF algorithm. Finally, simulations are carried out in the distributed system identification context. The results of simulations demonstrate that the proposed algorithms achieve better convergence performance than their counterparts. [ABSTRACT FROM AUTHOR]

The least mean kurtosis (LMK) algorithm has been successfully applied to linear system identification. It outperforms the conventional least mean square method for Gaussian and non-Gaussian noises. The purpose of this work is to apply the LMK algorithm to active noise control (ANC) systems, i.e., to develop a filtered-x LMK (FxLMK) algorithm. The proposed FxLMK algorithm is robust against the attenuation of various noise interferences in ANC system. To further improve the noise reduction performance, a recursive sampled variance method is incorporated into the FxLMK algorithm, resulting in an improved FxLMK (IFxLMK) algorithm without significantly increasing the computational burden. Simulations in the various noise inputs show the effectiveness of the proposed algorithms. Moreover, the traction substation noise control problem is considered in our simulations, and an overall system scheme and simulation studies are conducted. Simulation results demonstrate that the IFxLMK algorithm can improve the convergence rate of adaptive filter and improve the performance of noise reduction. [ABSTRACT FROM AUTHOR]

This paper presents a new proportionate normalized subband adaptive filter (PNSAF) algorithm, called the IAF-PNSAF, which assigns an individual activation factor for each filter coefficient instead of a common one for all filter coefficients as in the standard PNSAF algorithm. This algorithm achieves an improved performance in terms of the convergence rate and tracking capability for identifying a highly sparse system. Moreover, to overcome the trade-off of the fixed-step-size IAF-PNSAF algorithm between the fast convergence rate and small steady-state misalignment, its adaptive combination version is proposed. Simulation results for identifying the impulse response with high sparseness have demonstrated that the proposed algorithms outperform their counterparts. [ABSTRACT FROM AUTHOR]

To improve the robustness of subband adaptive filter (SAF) against impulsive interferences, we propose two modified SAF algorithms with an individual scale function for each subband, which are derived by maximizing correntropy-based cost function and minimizing logarithm-based cost function, respectively, called MCC-SAF and LC-SAF. Whenever the impulsive interference happens, the subband scale functions can sharply drop the step size, which eliminate the influence of outliers on the tap-weight vector update. Therefore, the proposed algorithms are robust against impulsive interferences and exhibit the faster convergence rate and better tracking capability than the sign SAF (SSAF) algorithm. Besides, in impulse-free interference environments, the proposed algorithms achieve similar convergence performance as the normalized SAF (NSAF) algorithm. Simulation results have demonstrated the performance of our proposed algorithms. [ABSTRACT FROM AUTHOR]

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies. [ABSTRACT FROM AUTHOR]

Proposed is a novel variable step size normalized subband adaptive filter algorithm, which assigns an individual step size for each subband by minimizing the mean square of the noise-free a posterior subband error. Furthermore, a noniterative shrinkage method is used to recover the noise-free priori subband error from the noisy subband error signal. Simulation results using the colored input signals have demonstrated that the proposed algorithm not only has better tracking capability than the existing subband adaptive filter algorithms, but also exhibits lower steady-state error. [ABSTRACT FROM AUTHOR]

In order to reduce the steady-state misalignment of real-coefficient proportionate affine projection sign algorithm (RP-APSA) for sparse impulse responses, a memory RP-APSA is proposed in this paper by exploiting the historical values of proportionate factors, called MP-APSA. Further, to improve the robustness of MP-APSA and the recently proposed memory-improved RP-APSA (MIP-APSA) for impulse responses with mutative sparseness, two sparseness-controlled algorithms (SC-MP-APSA and SC-MIP-APSA) are developed by estimating the sparseness of the impulse response at each iteration. Simulation results in the context of acoustic echo cancellation show that the proposed algorithms retain good robustness against impulsive interferences. More importantly, the proposed sparseness-controlled algorithms can not only obtain low steady-state misalignment in both the sparse and dispersive situations, but also adapt to the variations in the sparseness of the impulse response. [ABSTRACT FROM AUTHOR]

This paper proposes a bias-compensated normalized least-mean fourth (NLMF) algorithm to compensate for the bias caused by noisy input. In the proposed algorithm, we add a bias-compensation vector to the conventional NLMF algorithm, and the bias-compensation vector is then derived based on the unbiasedness criterion. Simulation results in system identification context show that the proposed algorithm provides lower steady-state misalignment as compared to the conventional NLMF algorithm. [ABSTRACT FROM AUTHOR]

Sparse adaptive filtering algorithms are utilized to exploit system sparsity as well as to mitigate interferences in many applications such as channel estimation and system identification. In order to improve the robustness of the sparse adaptive filtering, a novel adaptive filter is developed in this work by incorporating a correntropy-induced metric (CIM) constraint into the least logarithmic absolute difference (LLAD) algorithm. The CIM as an $$l_{0}$$ -norm approximation exerts a zero attraction, and hence, the LLAD algorithm performs well with robustness against impulsive noises. Numerical simulation results show that the proposed algorithm may achieve much better performance than other robust and sparse adaptive filtering algorithms such as the least mean p-power algorithm with $$l_{1}$$ -norm or reweighted $$l_{1}$$ -norm constraints. [ABSTRACT FROM AUTHOR]