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To address the shortcomings of the widely-linear complex-valued distributed adaptive filtering algorithm that cannot combine convergence speed and steady-state performance when using a fixed step-size strategy. In this paper, by making the partial derivative of the square of the sum of a priori error and a posteriori error with respect to step-size equal to zero, we propose a novel variable step-size (VSS) strategy, which is formulated as a function of a priori error and a posteriori error. In addition, a corresponding adaptive filtering algorithm is proposed by using the VSS strategy. Then in the process of parameter update, the moving average method is used to avoid large perturbations in iteration of the algorithm. Secondly, the theoretically analysis of the transient and steady-state performance of the proposed algorithm is provided. Finally, in the numerical simulation experiments, the effect of each parameter on the algorithm is tested, the result of the comparison with the fixed-step algorithm illustrates that the proposed algorithm has more superiority, and the high degree of matching between theory and experiment also verifies the feasibility and accuracy of the theoretical analysis method. [ABSTRACT FROM AUTHOR]

Traditional piezoelectric materials cause serious environmental and health issues because of their lead–containing substances, and thus lead–free piezoelectric ceramics would have many applications. In this study, we successfully prepared the lead–free ceramics (1- x) (K 0 · 48 Na 0 · 48 Li 0.04) (Nb 0 · 975 Sb 0.025)O 3 – x (Bi 0 · 5 Na 0.5) (Zr 0 · 8 Ti 0.2)O 3 ((1- x)KNLNS– x BNZT, x = 0, 0.005, 0.0075, 0.01, 0.015, 0.02 and 0.03) with rhombohedral–tetragonal (R–T) phase coexistence near room temperature, employing con–entional solid sintering. The minimum cell volume of the ceramics and R–T phase coexistence in them were achieved at a doping amount x = 0.01, which facilitated the optimal performance of the ceramics (d 33 ∼467 pC/N ± 14 pC/N, T c∼272 °C, ε r ∼1676, k p ∼0.42, where d 33 : piezoelectric constant; T c: Curie temperature; ε r : dielectric constant; k p : electromechanical coefficient). The ceramics exhibited microstructures with high density and low porosity and had a maximum relative density of 95.68 %. At x = 0.01, the ceramics exhibited a uniformly distributed small domain structures with nanodomains, accounting for their high-voltage electrical properties. Because these stable and reliable piezoelectric (1- x)KNLNS– x BNZT ceramics exhibit excellent electrical performance, they can replace lead–based materials. The direct solid–phase sintering method provides prospects for the large–scale application of the lead–free piezoelectric ceramics. The 0.99(K 0 · 48 Na 0 · 48 Li 0.04)(Nb 0 · 975 Sb 0.025)O 3 –0.01(Bi 0 · 5 Na 0.5)(Zr 0 · 8 Ti 0.2)O 3 ceramics exhibit excellent piezoelectric properties owing to their nanodomain structures, rhombohedral–tetragonal coexistence phase boundaries at room temperature (25°C ± 5°C) and dense microstructures. [Display omitted] [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]

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 production process of the metallurgical industry generates a significant quantity of hazardous waste. At present, the common disposal method for metallurgical hazardous waste is landfilling, which synchronously leads to the leaching of toxic elements and the loss of valuable metals. This paper presents a comprehensive review of the research progress in the harmless treatment and resource utilization of stainless steel dust/sludge (including stainless steel dust and stainless steel pickling sludge) and aluminum ash (including primary aluminum ash and secondary aluminum dross), which serve as representative hazardous wastes in ferrous metallurgy and nonferrous metallurgy, respectively. Additionally, the general steps involved in the comprehensive utilization of metallurgical hazardous waste are summarized. Finally, this paper provides a prospective analysis on the future development and research trends of comprehensive utilization for metallurgical hazardous waste, aiming to offer a basis for the future harmless, high-value, resource-based treatment of metallurgical hazardous waste and the realization of industrial applications in China. [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 order to solve the problem of deteriorating performance of the conventional subband adaptive filtering algorithm when processing the EIV model with impulsive noise, this paper proposes the robust Total Least Mean M-Estimate normalized subband filter (TLMM-NSAF) adaptive algorithm based on the M-estimation function. In addition, we conduct a detailed theoretical performance analysis of the TLMM-NSAF algorithm, which allows us to determine the stable step size range and theoretical steady-state mean squared deviation of the algorithm. To further improve the algorithm's performance, we propose a new variable step size method. Finally, we compared the algorithm with other competition algorithms in applications of system identification and acoustic echo cancellation. Simulation results have demonstrated the superiority of our proposed algorithm, as well as the consistency between the theoretical values and the simulated values. [ABSTRACT FROM AUTHOR]

An adaptive least mean M-estimate algorithm for censored regression (CR-LMM) is presented for the robust parameter estimation of the censored regression system. To correct the bias produced by censored observation, the estimated error derived from the probit regression model is employed to construct an M-estimate cost function. It can expel the adverse impact of the impulsive noise and is solved by the unconstrained optimization method. Furthermore, the robust variable step-size (VSS) strategy, which is also predicted on the robust cost function, is also utilized to improve the convergence performance of the proposed CR-LMM algorithm, i.e., convergence speed and steady-state mean square deviation. The condition which guarantees the CR-LMM algorithm stability is obtained by analyzing the convergence in the mean and mean-square sense, and the theoretical steady-state result is also derived. Computer simulations in system identification scenarios are carried out to demonstrate that the proposed algorithms are superior to the existing algorithms in the impulsive environment with different background noise and the theoretical results are verified. [ABSTRACT FROM AUTHOR]

In this work, we study the combination of adaptive filters in colored noise environments. First, a combination framework using delayed weights is introduced to tackle the colored noise. Based on this, delayed convex and affine combinations of two LMS filters are developed, resulting in the so-called Dcvx-LMS and Daff-LMS algorithms. Then, the convergence behaviors of the two algorithms are investigated using standard mean-square deviation analysis. In addition, to speed up the convergence and reduce the computational complexity, we propose delayed combination with periodic feedback, delayed combined-step-size and block implementation methods. Finally, simulation results demonstrate the superiority of our algorithms over previously reported techniques in the presence of colored noise. [ABSTRACT FROM AUTHOR]

Recently, the Bayesian decorrelation algorithms have gained attention because they can effectively avoid trade-off between learning rate and estimation accuracy by circumventing the problems associated with constant step-size and significantly enhance the convergence speed of adaptive filtering algorithms by decorrelation of signals. However, the present Bayesian decorrelation algorithms are constructed on the basis of the minimum-mean-square-error (MMSE) criterion, leading to deterioration in performance when confronted with non-Gaussian noise environments. Therefore, this paper introduces the maximum correntropy criterion in the decorrelation algorithm and develops a decorrelation recursive maximum correntropy criterion (DRMCC) algorithm based on the observation model to achieve robust performance. The proposed algorithm has a similar iterative equations as the Bayesian decorrelation algorithm. In addition, we present the convergence condition and analyze the transient behavior of the DRMCC algorithm. When the free parameters of the proposed algorithm are unknown, a common method of parameter estimation is provided. Finally, numerical simulations corroborate that the designed DRMCC algorithm can realize outstanding performance under system identification and acoustic echo cancellation (AEC) applications in non-Gaussian noise environments and the derived theoretical model can arrive at good agreement with simulation results for both stationary and nonstationary scenarios. • The decorrelation recursive maximum correntropy criterion algorithm is proposed. • The convergence condition and transient behavior of the DRMCC algorithm are analyzed. • The proposed algorithm has excellent performance in acoustic echo cancellation. [ABSTRACT FROM AUTHOR]

Multi-channel active noise control (ANC) systems can achieve effective attenuation of low-frequency noise in spatial areas and have been extensively studied. Recent works have focused on the application of multitask diffusion strategies in ANC systems based on wireless acoustic sensor and actuator networks (WASAN), which show the advantages of saving computational burden and enhancing flexibility. However, these works all adopt the mean-square error minimization as the optimization criterion, which leads to severe performance degradation in the presence of impulsive noise interference. Therefore, in this paper, we exploit the M-estimate function and the augmented weight vector of the control filter to formulate a robust minimization problem and propose a distributed augmented diffusion filtered-x least mean M-estimate (DADFxLMM) algorithm for multi-channel ANC systems. The proposed algorithm leverages the M-estimate function to overcome the influence of outliers in the error signal and achieves robustness against impulsive noise, and also eliminates the dependence on the symmetry of the acoustic paths by integrating the augmented weight vectors. Moreover, we replace the score function with the update probability of the weight vector to avoid the need for integration and Price's theorem, and analyze the mean and mean-square performance of the proposed DADFxLMM algorithm under the contaminated Gaussian (CG) noise model. Simulation results under different system configurations demonstrate that the proposed algorithm outperforms the existing multi-channel ANC algorithms in the presence of impulsive noise interference. • A robust DADFxLMM algorithm is proposed for multi-channel ANC systems. • Proposed algorithm overcomes the effects of acoustic asymmetry and impulsive noise. • The theoretical analysis of the DADFxLMM algorithm is carried out. • The proposed algorithm provides improved ANC performance. [ABSTRACT FROM AUTHOR]

Traditional active noise control (ANC) algorithms suffer from significant performance degradation when dealing with impulsive noise. Although some robust algorithms based on the maximum correntropy criterion (MCC) have been developed to improve the performance, they still have unsatisfactory noise reduction performance due to the steady-state misalignment. Therefore, we propose a filtered-x affine-projection-like exponential hyperbolic sine (FxAPLEHS) algorithm for feedforward ANC systems, inspired by the fast convergence property of the affine-projection-like (APL) algorithm. Here, the optimal step-size parameter of the proposed algorithm is derived mathematically from the a posteriori error via considering the time-varying step-size bound, which aims to enhance the performance of the algorithm in terms of convergence and steady-state misalignment. Moreover, to further improve the overall performance of the FxAPLEHS algorithm, a combined step-size FxAPLEHS (CSS-FxAPLEHS) algorithm is designed, which constructs a step-size mixing parameter using a modified sigmoidal activation function that is indirectly updated with the objective of minimizing the L 1 -norm of the error. The superiority of the proposed algorithms is verified through numerical simulations in symmetric α -stable (S α S) noise and multi-tone noise mixed with S α S noise environments, respectively. In addition, validation simulations based on a real single-channel duct ANC system model further demonstrate the superiority of the proposed algorithms in terms of convergence speed and noise reduction ratio. • The FxAPLEHS algorithm based ANC technique is proposed. • The CSS-FxAPLEHS algorithm to improve noise reduction performance is also proposed. • The computational complexity analysis of the proposed algorithm is carried out. • The proposed algorithms offer enhanced robust ANC performance. [ABSTRACT FROM AUTHOR]

The broad learning system (BLS) is an effective machine learning model that exhibits excellent feature extraction ability and fast training speed. However, the traditional BLS is derived from the minimum mean square error (MMSE) criterion, which is highly sensitive to non-Gaussian noise. In order to enhance the robustness of BLS, this paper reconstructs the objective function of BLS based on the maximum multi-kernel correntropy criterion (MMKCC), and obtains a new robust variant of BLS (MKC-BLS). For the multitude of parameters involved in MMKCC, an effective parameter optimization method is presented. The fixed-point iteration method is employed to further optimize the model, and a reliable convergence proof is provided. In comparison to the existing robust variants of BLS, MKC-BLS exhibits superior performance in the non-Gaussian noise environment, particularly in the multi-modal noise environment. Experiments on multiple public datasets and real application validate the efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

Traditional functional linked neural networks (FLNNs) impose a significant computational burden due to their input expansion, primarily stemming from the utilization of digital filters. This paper presents a Laguerre FLNNs filter for nonlinear active noise control (NANC) systems. By employing the truncated Laguerre series, the presented filter achieves effective approximation of long primary paths with a reduced filter length. Moreover, we develop adaptive algorithms rooted in information-theoretic learning (ITL) within the framework of the Laguerre-FLNNs NANC model. Using the ITL criterions, a Laguerre filtered-s maximum correntropy criterion (LFsMCC) algorithm is derived and a Laguerre filtered-s quantized minimum error entropy criterion (LFsQMEE) algorithm is proposed by minimizing Renyi's quadratic entropy. To reduce the computation cost, an online vector quantization method is utilized to improve the LFsQMEE. This technique selectively quantizes the error vectors, reducing them to a smaller subset of samples within the codebook. Moreover, an enhanced LFsQMEE with a fiducial point is introduced. The steady-state performance and the computational complexity are analyzed. Theoretical analysis is validated through simulations and the control performance of the proposed model and algorithms is tested in experiments with both simulated and real paths. [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]

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]

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]

Recently, the kernel adaptive filtering algorithm with the generalized maximum correntropy criterion (GMCC) has gained attention due to its excellent nonlinear system modeling ability and robustness to non-Gaussian noise. However, since the default center of the GMCC is located at zero, it hampers its performance in the non-zero mean noise environment. To overcome the problem, this paper proposes a kernel adaptive filtering algorithm based on the GMCC with variable center (GMCC-VC) called generalized kernel maximum correntropy criterion with variable center (GKMCC-VC). In addition, the online vector quantization (VQ) method is introduced to the GKMCC-VC algorithm for suppressing the increasing network size. The probability of divergence, the mean-square steady-state behavior, and the convergence condition of the GKMCC-VC algorithm are also obtained under some assumptions. The potential relationship between the GMCC-VC and the generalized minimum error entropy (GMEE) criteria is discussed in the paper. Finally, the simulation results verify the superiority of the proposed algorithm in modeling nonlinear systems and the correctness of the theoretical model. • This paper proposes the GKMCC-VC algorithm for non-zero mean and non-Gaussian noise. • The steady-state performance of the proposed algorithm is analyzed. • Simulation results show the effectiveness and feasibility of the proposed algorithm. [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]

Donor‐acceptor Stenhouse adducts (DASAs) as a species of novel photochromic molecules, have been developing rapidly and attracting broad researchers' sights since 2014. DASAs show visible/near‐infrared (NIR) light induced linear‐to‐cyclic isomerization and heat induced cyclic‐to‐linear isomerization, therefore they are attractive in photoresponsive hydrogels, drug delivery, cell culturing and tissue engineering. As a series of well‐known photoresponsive molecules, spiropyrans (SPs) show similar molecular properties and comparable photoswitching with DASAs. UV light triggers closed‐to‐open (also known as spirocyclic (SC)‐to‐merocyanine (MC)) isomerization of SPs, while the reversed open‐to‐closed isomerization occurs under visible light or heat. Light irradiation switches the molecular color, scale, geometry, and polarity of SPs and DASAs reversibly. Since the researches on DASAs are still in the infancy, the chemical structures, isomerization mechanisms and potential applications need to be further investigated and explored. The well‐studied SPs have important reference values to the comprehensive developments of DASAs. In the present review, we summarized, compared and discussed SPs and DASAs with regards to their molecular structures, synthesis, photoswitching and applications. We also make our perspective on the developments of DASA in future. [ABSTRACT FROM AUTHOR]

We consider the DOA estimation problem by using adaptive nulling antenna technology and bias-compensated adaptive filtering framework. The adaptive nulling antenna array consists of one reference antenna element and multiple auxiliary antenna elements, which forms nulls in certain directions. By defining the reciprocal of array pattern as the spatial spectrum, the DOA estimation problem is considered as the peak searching for it. In this paper, we present an efficient bias-compensated adaptive filtering algorithm for DOA estimation based on the adaptive nulling array. First of all, a new noise-free mean square error (NF-MSE) cost function associated with the adaptive nulling array is provided. Secondly, the proposed algorithm, called variable step-size bias-compensated least mean square (VSS-BC-LMS) algorithm, can be derived by minimizing the NF-MSE. Due to the bias compensation, the bias of the estimated weight vector caused by noises is canceled. More importantly, in order to resist the unsatisfactory DOA estimation performance when using the fixed step-size, a variable step size scheme is introduced. And then, its mean stability, steady state mean square performance and computational complexity are discussed. Additionally, we also explore a noise variance estimation method for calculating the bias term. Simulation results indicate that the proposed algorithm achieves an improved DOA estimation performance compared with other adaptive methods. [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]

A robust technique based on maximum correntropy criterion (MCC) is proposed for frequency estimation in an unbalanced power system using error in phase angle. This is achieved by replacing the magnitude error used in the standard cost function of the MCC with the phase error and by extending the concept of the augmented (widely linear) complex statistics for the processing of unbalanced voltages and other abnormal system conditions. The idea emanates from the facts that: (i) useful information is primarily conveyed over the phase in power system frequency estimation, and (ii) the performance degradation of the well‐known minimum mean squared error criterion based adaptive filters in impulsive noise environments can be overcome by the MCC due to the non‐quadratic and higher order moments imbedded in its cost function. The proposed phase error‐based MCC method also utilises all the second‐order information within the complex valued system voltage through the Clarke's transformation. Simulation studies conducted using both synthetic and experimental data verify that the proposed algorithm provides better estimations compared to the considered 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]

• The variable step-size widely linear complex-valued NLMS (VSS-WL-CNLMS) algorithm which is applicable to the case of highly correlated input is proposed, where the variable step-size (VSS) is derived by minimizing the mean-square deviation (MSD). • The proposed VSS-WL-CNLMS algorithm is convergent in the mean square sense. • Based on the approximate uncorrelating transform and Rayleigh distribution, the theoretical transient and stead-state behaviors of the VSS-WL-CNLMS algorithm are analyzed in detail. The shrinkage widely linear complex-valued least mean square (SWL-CLMS) algorithm with a variable step-size (VSS) overcomes the tradeoff between fast convergence and low steady-state misalignment, but meanwhile suffers from instability for highly correlated input signals because of the gradient noise amplification problem. To obtain a VSS that is also applicable to the case of highly correlated input signals, in this paper, we propose the VSS widely linear complex-valued normalized least mean square (VSS-WL-CNLMS) algorithm, where the VSS is derived by minimizing the mean-square deviation (MSD). Owing to the normalization, the VSS-WL-CNLMS algorithm is convergent in the mean square sense. By using the Rayleigh distribution, we calculate the mean step-size, which is then combined with the approximate uncorrelating transform to analyze the transient and steady-state mean square error (MSE) behaviors. Simulations for system identification scenario show that the proposed VSS-WL-CNLMS algorithm outperforms some well-known techniques and verify the accuracy of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Highlights • Phase error based Widely Linear LMK Algorithm is proposed for Frequency estimation. • It uses best features like widely linear modelling, phase error and robust cost function. • It achieves enhanced frequency estimation performance for several critical cases. • Retains the inherent simplicity of the gradient descent based algorithms. Abstract In this paper, an augmented (widely linear) complex Least Mean Kurtosis (WL-LMK) algorithm that uses the negated kurtosis of the phase angle error instead of the conventional magnitude error is proposed for robust frequency estimation of three-phase power systems. The motivation of the proposed method is based on two underlying facts. First, it is primarily the phase rather than the amplitude that conveys useful information in frequency estimation. Second, the negated kurtosis based cost function is computationally efficient and most celebrated in applications where the noise contamination degrades the performance of the classical adaptive filtering algorithms. To further achieve robust frequency estimation for both balanced and unbalanced conditions, the proposed method makes use of the full second-order information within the complex-valued system voltage through the Clarke's αβ transformation and the concept of augmented complex statistics and widely linear modelling. The estimation performance of the proposed method is evaluated for several critical cases that often arise in power system. Simulation results of both synthetic cases and experimental studies show that the proposed method achieves more accurate frequency estimates than its developed widely linear counterparts in the literature. [ABSTRACT FROM AUTHOR]

• The combined regularization parameter for normalized least-mean-square (CRP-NLMS) algorithm is proposed, in which the mixing parameter is derived by minimizing the energy of noise-free a posteriori error. • A novel reset method is designed to improve the tracking capability of the proposed algorithm. We also illustrate that the proposed algorithm is available for the nonstationary system modeled by a random walk process. • The theoretical analyses including the transient and steady-state mean-square error (MSE) are performed in a stationary system. This paper presents a combined regularization parameter for normalized least-mean-square (CRP-NLMS) algorithm. The proposed algorithm adaptively combines two different regularization parameters by employing a time-varying mixing parameter that is derived by minimizing the energy of noise-free a posteriori error. To avoid large fluctuations, the mixing parameter is updated in a moving-average method. A novel reset method is designed to improve the tracking capability when the unknown system encounters a sudden change. We illustrate that the proposed mixing parameter is also available for the nonstationary system modeled by a random walk process. In particular, the theoretical analyses including the transient and steady-state mean-square error (MSE) are performed. Simulations for system identification scenarios demonstrate the merits of Kour finding and support the theoretical analysis. [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]

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]

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 work develops robust diffusion recursive least-squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate update at each node. A recursive strategy for computing the constraint is proposed using side information from the neighboring nodes to further improve the robustness. We also analyze the mean-square convergence behavior of the proposed algorithm. The second proposed algorithm is a modification of the first one based on the dichotomous coordinate descent iterations. It has a performance similar to that of the former, however, its complexity is significantly lower especially when input regressors of agents have a shift structure and it is well suited to practical implementation. Simulations show the superiority of the proposed algorithms over previously reported techniques in various impulsive noise scenarios. [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]

Highlights • We propose an improved diffusion total least-squares (DTLS) algorithm, where the estimated value at each node is passed through a first order recursive filter with adjustable parameter in order to enhance the identification performance. • We develop robust adaptive strategies to update various internal system parameters of the proposed DTLS algorithm. • The convergence behavior of the adaptive weight vector and related system parameters of the new algorithm are analyzed by means of Lyapunov stability theory. • Simulation results in the context of distributed system identification demonstrate the superiority of the proposed DTLS algorithm. Abstract The errors-in-variables (EIV) system model has been widely studied under the assumption that both input and output signals are contaminated with noise. For the in-network distributed linear system identification problem under the EIV model, the total least-squares (TLS) approach which has the ability to minimize perturbations in both input and output signals offers an efficient solution. In this paper, we propose an improved diffusion total least-squares algorithm, where the estimated (i.e. filtered) value at each node is passed through a first order recursive filter with adjustable parameter in order to enhance the identification performance. The resulting outputs from all the nodes are subsequently used to adapt the unknown linear system weight vector in real-time through a cooperative diffusion scheme based on the adapt-then-combine (ATC) policy. We also present robust adaptive strategies to tune various internal system parameters, such as the steps sizes, normalization factors, etc., under practical conditions of operation. The convergence behavior of the adaptive weight vector and related system parameters is analyzed by employing Lyapunov stability theory. Simulation results for various distributed system identification scenarios demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract As one of the most commonly used nonlinear active noise control (NANC) algorithms, the filtered-s least mean square (FsLMS) algorithm outperforms the conventional filtered-x least mean square (FxLMS) algorithm when the primary path has a quadratic nonlinearity. However, it still suffers from performance degradation under strong interferences. In this paper, two new algorithms, named filtered-s q -least mean p -norm (FsqLMP) and filtered-s q -least mean square (FsqLMS), based on the concept of Jackson's derivative, are proposed. By using new Jackson's derivative method, the proposed algorithms are less sensitive to the interferences in NANC system. Additionally, it is shown that the family of q -least mean square algorithms are special cases of the proposed FsqLMP algorithm. To further improve performance of the FsqLMS algorithm and solve the parameter selection problem, a time varying q scheme is developed. Simulation studies indicate that the proposed algorithms provide superior performance in various noise environments as compared to the existing algorithms. [ABSTRACT FROM AUTHOR]

The filtered-s maximum correntropy criterion (FsMCC) algorithm was developed for nonlinear active noise control (NANC) in impulsive noise environments with the use of functional linked artificial neural networks (FLANNs) structure. However, the kernel-width of the FsMCC is constant, which is dull and cannot self-regulate to achieve both the fast convergence and low steady-state error performance. For better convergence ability, in this paper, a fractional-order gradient ascent filtered-s maximum correntropy criterion algorithm (FGA-FsMCC) is presented for multi-channel NANC system. The fractional lower-order moments supersede the non-existent second-order moments. To come up with a more reliable algorithm, by merging two kernels with complementary width, the fractional-order gradient ascent filtered-s mixture correntropy criterion (FGA-FsMMCC) was presented. The computational complexity and convergence conditions are analyzed. To verify the robustness of proposed algorithms, simulations are carried out to discuss parameters and control effects of algorithms for alpha-stable noise in different nonlinear environments. • Design multi-channel nonlinear active noise control system with functional linked artificial neural networks. • Proposing a fractional-order gradient ascent filtered-s maximum correntropy criterion algorithm. • Defining the maximum mixture correntropy criterion. • Deriving a fractional-order gradient ascent filtered-s maximum mixture correntropy criterion algorithm. • Computational complexity analysis of proposed algorithms. [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]