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For the identification of long impulse response systems in impulsive noise environments, existing algorithms have disadvantages such as slow convergence speed, large steady-state error, and poor tracking performance. In this brief, we propose the nearest Kronecker product decomposition based robust hyperbolic tangent Geman-McClure adaptive filter (NKP-HTGM) and analyze its performance. This algorithm uses the Geman-McClure function under hyperbolic tangent framework to remove the characteristic of the abnormal amplitude in the dataset, significantly improving the robustness against impulsive noise. Moreover, a novel variable step-size method (VSS) is introduced to further enhance the performance of NKP-HTGM (VSS-NKP-HTGM). Finally, the simulation results validate the effectiveness of the NKP-HTGM algorithm in system identification and the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Adaptive filtering algorithms are currently successfully employed in a number of fields.But, a disadvantage of traditional real-valued fixed step-size adaptive filtering algorithm is that it is unable to meet both requirement of convergence rate and the steady-state error.In this article, we presented cosine function and geometric algebra(GA) based variable step-size technique for adaptive filtering.Initially, a multi-dimensional signal is represented as a GA multi-vector for the vectorization process in the proposed approach of adaptive filtering with variable step-size based on GA.Then, by establishing a non-linear function relationship between error signal e(n) and the step-size factor μ , given method of adaptive filtering resolves the contradiction among steady-state error and the convergence rate.Finally, simulation results illustrate that in comparison with other existing adaptive filtering algorithms, the defined approach performs better in terms of convergence rate, steady-state error, robustness against impulsive noise and the computational complexity. [ABSTRACT FROM AUTHOR]

This paper introduces two pairs of numerical embedded methods of Runge-Kutta (RK) type, known as ERKMF methods, for directly solving a class of quasi-linear ordinary differential equations (ODEs) of 5th-order with the form φ (5) (τ) = Ψ (τ , φ (τ)) φ (5) (τ) = Ψ (τ , φ (τ)). The first pair, ERKMF6(5), is a 5th-order embedded in 6th-order method that satisfies the condition first the same as last (FSAL), and the vector output is represented by the coefficient matrix's final row. The second pair, ERKMF7(6), is also an embedded method. The paper then applies these methods to solve specific 5th-order problems using variable step-size codes and compares the results to those obtained using an existing embedded RK method. The ERKMF methods have shown to be advantageous and effective compared to existing methods, as demonstrated by the numerical findings. In conclusion, these new pairs of ERKMF methods provide a promising approach to directly solve quasi-linear ODEs of 5th-order and could have significant implications for the field of numerical methods for differential equations. [ABSTRACT FROM AUTHOR]

The two-step backward difference formula (BDF) method on variable grids for parabolic equations with self-adjoint elliptic part is considered. Standard stability estimates for adjacent time-step ratios r j : = k j / k j - 1 ⩽ 1.8685 and 1.9104, respectively, have been proved by Becker (BIT 38:644–662, 1998) and Emmrich (J Appl Math Comput 19:33–55, 2005) by the energy technique with a single multiplier. Even slightly improving the ratio is cumbersome. In this paper, we present a novel technique to examine the positive definiteness of banded matrices that are neither Toeplitz nor weakly diagonally dominant; this result can be viewed as a variant of the Grenander–Szegő theorem. Then, utilizing the energy technique with two multipliers, we establish stability for adjacent time-step ratios up to 1.9398. [ABSTRACT FROM AUTHOR]

The LMS algorithm is widely employed in adaptive systems due to its robustness, simplicity, and reasonable performance. However, it is well known that this algorithm suffers from a slow convergence speed when dealing with colored reference signals. Numerous variants and alternative algorithms have been proposed to address this issue, though all of them entail an increase in computational cost. Among the proposed alternatives, the affine projection algorithm stands out. This algorithm has the peculiarity of starting from $N$ data vectors of the reference signal. It transforms these vectors into as many data vectors suitably normalized in energy and mutually orthogonal. In this work, we propose a version of the LMS algorithm that, similar to the affine projection algorithm, starts from $N$ data vectors of the reference signal but corrects them by using only a scalar factor that functions as a convergence step. Our goal is to align the behavior of this algorithm with the behavior of the affine projection algorithm without significantly increasing the computational cost of the LMS.

The family of least mean square (LMS) based adaptive filtering algorithms suffers from convergence performance limitation due to the sensitivity of such algorithms to the eigenvalue spread of the input correlation matrix. The quasi-Newton family of adaptive filtering algorithms addresses this limitation, but its performance is restricted by the estimation accuracy of the correlation matrix inverse, especially for highly correlated input signals. Furthermore, the convergence rate and the steady-state performance of both LMS and quasi-Newton families are thoroughly depending on their step-sizes. In this paper, a variable step-size regularized quasi-Newton adaptive algorithm is proposed in the context of system identification. In this algorithm, inspired by the matrix inversion lemma, a modified regularized matrix inverse with a time-varying regularization is computed such that during the convergence, the contribution of matrix inverse in the weight update is reduced, resulting in a more noise-robust algorithm. The paper further provides a convergence analysis of the proposed quasi-Newton algorithm, wherein a variable step-size is proposed to achieve a high initial convergence rate and a low steady-state error in the context of system identification applications.

In order to improve the problem that the filtered-x least mean square(FxLMS) algorithm can not give consideration to both the convergence speed and the steady-state error in active noise control, the SSFxLMS algorithm based on sigmoidsinh subsection function was proposed, and the ant lion algorithm was introduced to optimize the parameters of sigmoid filtered-x least mean square(SFxLMS), sinh filtered-x least mean square(ShFxLMS), and SSFxLMS algorithms. Gaussian white noise and actual tufted carpet loom noise were used as input signals respectively, and FxLMS, SFxLMS, ShFxLMS, SSFxLMS algorithms were used for active noise control simulation, and the performance of these four algorithms was compared and analyzed. The results show that compared with the other three algorithms, when SSFxLMS algorithm is used to control Gaussian white noise and tufted carpet loom noise, the average absolute value of error signal is smaller, and the average noise reduction and convergence speed are also greatly improved. It can be seen that SSFxLMS algorithm effectively improves the problem that FxLMS algorithm can not give consideration to both the convergence speed and the steady-state error. The research results provide a certain reference for the design of active noise control algorithm. [ABSTRACT FROM AUTHOR]

The standard proportionate normalized least mean square (PNLMS) adaptive algorithm suffers from convergence performance limitation due to a constant step-size during the convergence period. In this paper, a switching-based variable step-size PNLMS is proposed to improve the convergence performance in sparse system identification. To adjust the step-size, the convergence performance of PNLMS is first analysed in the statistical sense and by exploiting the analysis, a switching-based method is then proposed, which brings about a fast convergence towards the desired steady-state mean-square weight deviation. The step-size reduces during the convergence period in a few steps, while in the case of abrupt change in the system impulse response, the step-size increases to its initial value. A sub-band version of the proposed adaptive algorithm is further proposed for highly correlated input signals. Simulation results confirm the superiority of the proposed full-band and sub-band algorithms in terms of convergence performance compared to some competing adaptive algorithms. [ABSTRACT FROM AUTHOR]

This work proposes a variable step-size strategy for estimation over distributed networks using the incremental scheme. The proposed algorithm employs the ratio of filtered squared instantaneous error to the squared instantaneous error in a windowed format. This reduces the dependency on the error power which is particularly beneficial in low signal-to-noise power ratio situations. A comprehensive theoretical analysis has been performed, and closed-form solutions of mean squared error, excess mean squared error and mean squared deviation have been derived. The theoretical results are verified via simulation results. Extensive testing has been done through experiments under various scenarios to show the supremacy of the proposed algorithm in comparison with several other algorithms. [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]

The censored observations of adaptive signal processing have widely occurred in plenty of utility applications. Using traditional adaptive algorithms to recognize systems will confront convergence reduced under these circumstances. To address the above problem, the least mean square algorithm for censored regression (CR-LMS) has been proposed. However, the CR-LMS algorithm will converge slowly under colored inputs. In this paper, a pseudo affine projection algorithm based on censored regression (CR-PAP) is present to process colored input signals. Moreover, the variable step-size strategy is used to enhance the convergence performance. Computer simulations verify the better convergence of the proposed algorithm over the CR-LMS algorithm in system identification scenarios. [ABSTRACT FROM AUTHOR]

In the field of echo cancellation, the normalized least mean squares (NLMS) algorithm is the most popular adaptive algorithm due to its simplicity and ease of implementation. However, this category of algorithms presents a conflict between several performance criteria: the initial convergence speed, the tracking ability and the root mean square error of filtering (MSE) in the steady state. Variable-step algorithms (VSS) address the trade-off between convergence speed and low final MSE. Nevertheless, due to a fairly small adaptive step-size in the steady-state regime, they fail to adequately track variations of the unknown system and they are all implemented with the original NLMS algorithm. In this contribution, a new improved variable adaptation step algorithm capable to track time variations of the unknown system even after good convergence in the steady state is suggested. It is based on the use of the fast-normalized adaptive algorithm (FNLMS) for system identification and acoustic echo cancellation context. The purposes of using the FNLMS algorithm in the field of VSS are on the one hand to improve its final MSE and, on the other hand, to obtain a VSS algorithm with better convergence and tracking compared to the VSS NLMS algorithms. Simulation results show that the proposed VSS-Fast NLMS algorithm outperforms the original FNLMS algorithm in terms of steady-state error reduction and minimization after the initial transition phase while maintaining similar convergence speed and tracking capacity. Furthermore, it achieves visible improvements in terms of two objective criteria, i.e., a faster initial convergence rate and a better tracking ability than the ones of the non-parametric VSS-NLMS (NPVSS-NLMS) and traditional NLMS algorithms. [ABSTRACT FROM AUTHOR]

In order to improve the conversion efficiency of photovoltaic cells and reduce the energy loss, the maximum power point tracking (MPPT) method needs to be studied. Aiming at the problem that the tracking speed and steady-state accuracy of the traditional perturbation observation method (P&O) cannot be balanced, and misjudgment occurs when the environment changes greatly, a variable-step P&O control strategy that can adapt to the environmental changes is proposed. Firstly, the short-circuit current under current illumination is obtained by using the characteristics of the photovoltaic cell similar to the constant current source when it first starts, and the reference voltage of the maximum power point (MPP) is derived by the fixed current method. Secondly, when the illuminance changes abruptly, the power correction method is proposed, and the variable step size adjustment strategy is given. Finally, a fractional order proportion integration differentiation (FOPID) controller based on linear extended state observer (LESO) is designed, which can further track and compensate the reference voltage output by the algorithm. Simulation results show that the proposed control strategy can improve the steady-state accuracy and tracking speed, and effectively improve the output power of photovoltaic cells.

The idea of variable step-size was introduced into the Hybrid Affine Projection Algorithm (H-APA) and we propose two variable step size algorithms based on H-APA, which are called the Variable Step-Size Hybrid Affine Projection Algorithm (VSS-H-APA) and the Modified Variable Step-Size Hybrid Affine Projection Algorithm (MVSS-H-APA). These are two variable-step algorithms aim to further improve the robust performance and convergence speed of H-APA under non-Gaussian noise. This allows for faster convergence while maintaining stability. The MVSS-H-APA goes further than VSS-H-APA to estimate the noise in order to achieve better convergence performance. The proposed algorithm performs better than the existing algorithms in system identification under symmetric non-Gaussian noise. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Engineering Technology is the property of Editorial Department of Electric Power Engineering Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article presents an analysis of co-simulation defects for a system of coupled ordinary differential equations. The research builds on the theorem that the co-simulation error is bounded if the co-simulation defect is bounded. The co-simulation defect can be divided into integration, output, and connection defects, all of which can be controlled. This article proves that the output and connection defect can be controlled by the co-simulation master by varying the communication step size. A non-iterative co-simulation method with variable communication step size is presented to demonstrate the applicability of the presented research. The orders of the interpolation polynomials used in the co-simulation method are varied in the experimental analysis. The experimental analysis shows how each component of a co-simulation defect affects the co-simulation error. The analysis presented is used to verify the applicability of the proposed approach and to provide guidelines for the configuration of the co-simulation. [ABSTRACT FROM AUTHOR]

Active noise control (ANC) is a successful technique to reduce unwanted noise based on the superposition principle. In a conventional ANC system, the extent of unwanted noise can be attenuated at the error microphone location, thus making a silent zone at the desired location. However, in certain situations, it is impossible to place the error microphone at the desired location. In that case, the error microphone cannot assure adequate noise suppression at the desired location. To overcome that, the virtual sensing technique (VST) has been implemented in ANC to shift the zone of silence to the desired position. This paper proposes a supplemental filter in VST to avoid interference issues between secondary and virtual paths..In the virtual ANC, the supplemental filter H provides the required information to measure optimal noise control filter and also increases noise reduction in the ANC system at the virtual location. A Real-Time Simulink model is designed for the proposed virtual sensing ANC and evaluate its efficiency. The computer simulation findings showed that the ANC system performance with the proposed virtual sensing method had good noise reduction at the virtual location compared to the physical location. The proposed supplemental filter preserves reasonable noise reduction efficiency in the ANC system if the physical microphone is positioned far from the location of the silence zone. [ABSTRACT FROM AUTHOR]

Quasi-periodic orbits around the libration point orbits have attracted significant attention since they can provide more opportunities for space missions. This paper proposes a variable step-size multistep method that can effectively calculate long-term quasi-periodic orbits around the Sun-Earth L 1 / L 2 in the Sun-Earth-Moon bicircular model. In this method, periodic orbits in the Sun-Earth L 1 / L 2 serve as the initial reference trajectories for quasi-periodic orbits. Then a two-level multiple shooting is introduced to transition periodic orbits to the short-term quasi-periodic orbits. Finally, a variable step-size multistep method is proposed to obtain long-term quasi-periodic orbits based on the approximately linear relationship between the two-level multiple shooting method and step size. Numerical results show that this method can effectively obtain a large set of long-term quasi-periodic orbits whether the quasi-periodic orbits have free or fixed initial positions. Furthermore, this method is also extended to design long-term quasi-periodic orbits with differential phase angles of the Moon. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To enhance the filtering accuracy of the traditional sign subband adaptive filter (SSAF) algorithm and its individual-weighting-factors variant, this brief proposes the logarithmic hyperbolic cosine normalized subband adaptive filter algorithm (LHCNSAF) and its sparsity-aware version through minimizing the LHC cost function. As the combination of mean-square-error and mean-absolute-error criterion, the presented LHCNSAF demonstrates higher filtering accuracy under white Gaussian background noise and impulse noise environments than SSAF-type algorithms, with almost no increase in computational complexity. To tackle the trade-off between filtering accuracy and convergence behavior caused by the fixed step-size, an effective variable step-size scheme is also devised based on the transient model of proposed algorithms through minimizing the mean-square deviation (MSD) at each iteration with some reasonable assumptions. Additionally, the stability and complexity analysis are also provided. Finally, the computer simulations certify the proposed algorithms possess good performance in terms of convergence speed, steady-state error, and tracking capability via contrasting with the considering algorithms under system identification application. [ABSTRACT FROM AUTHOR]

The problem of sparse adaptive system identification such as acoustic echo cancellation (AEC) needs robust adaptive filtering algorithms in the situation where the system is often corrupted by impulsive noise. To solve this problem this work proposes a robust proportionate constrained optimization method based on the proportionate matrix weighted norm, and a proportionate affine projection tanh algorithm (PAPTA) is derived. To keep both fast convergence speed and low misalignment, a variable step-size is derived for the proposed algorithm. In addition, by expanding the tanh function and considering the dependence between the adaptive filter weight vector and the noise vectors, the weighted energy conservation method is utilized to analyze the steady-state performance and stability of the proposed algorithm. Finally, through simulations, the superior performance of the proposed algorithm is demonstrated in terms of convergence speed and robustness in sparse systems, and the accuracy of the theoretical steady-state analysis is verified. • This work proposes a proportionate affine projection tanh algorithm robust against impulsive noise. • The proportionate can speed convergence rate. • The steady-state performance and stability conditions are analyzed. • The step-size is optimized to address the problem of trade-off between fast convergence rate and small misalignment. [ABSTRACT FROM AUTHOR]

Electrocardiogram (ECG) is a critical type of biological signal that brings significant data about the patients. The morphological structure of ECG signals is usually distorted by the recording and transmission processes. As a result of this distortion, the proper diagnosis of diseases related to the cardiac system is getting affected. In this paper, a new FPGA design of variable step-size variable tap length delayed error normalized least mean square (VSS-VT-DENLMS) noise removal algorithm is proposed that modifies the weight update equation of DENLMS algorithm by varying the step sizes and the tap lengths simultaneously to find better trade-off among the fast convergence and error tracking. Also, the adaptive filter structure of the proposed VSS-DENLMS is developed by considering both systolic and folding structure with compressor-based booth multiplier for improving the performance in terms of speed and area. The proposed filter design is validated by considering different ECG signals from MIT-BIH Arrhythmia database, and the filtered outputs are investigated using certain performance measures including signal-to-noise ratio (SNR), mean square error (MSE), root-mean-square error (RMSE) and hardware complexity in terms of area and delay. The simulation results illustrate that the proposed filter overtakes existing filters and minimizes hardware complexities, which proves the suitability of this approach on real-time applications of ECG signals. [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]

Detection and recovery of noise corrupted signals using adaptive filters are becoming popular due to their application in several fields, including communication and biomedical. Adaptive filters broadly utilize the LMS algorithm since it has low computational complexity and is robust in behavior. However, it fails to achieve a faster speed of convergence and minimum steady-state MSE simultaneously. Therefore, the objective is to estimate the noise-free signal faster with improved accuracy and obtain a lower steady-state MSE with a higher convergence speed. This paper introduces a multi-stage adaptive filtering model wherein the noisy signal is analyzed through a cascade of stages. The proposed signal de-noising scheme utilizes the automatic selection of stages to be cascaded such that the steady-state MSE is minimum. Further, to enhance convergence speed, the LMS adaptive filter's step-size is automatically adjusted at each stage. Hence, by controlling the number of stages to be cascaded automatically and utilizing a different step-size for each stage, we obtain a high convergence speed and minimum steady-state MSE. The proposed filter structure is tested for signal de-noising application to assess its performance concerning MSE, Signal-to-Noise Ratio (SNR), Average Noise Reduction (ANR), and convergence speed. The results attained have shown that the proposed filter structure provides remarkable performance improvement at different input noise levels. Further, the proposed Improved Variable-Stage (IVS) cascaded adaptive filter model employs LMS adaptive algorithm, hence offering a cost-effective and straightforward hardware implementation of ANC. [ABSTRACT FROM AUTHOR]

A prediction model is an indispensable tool in business, helping to make decisions, whether in the short, medium, or long term. In this context, the implementation of machine learning techniques in time series forecasting models has a notorious relevance, as information processing and efficient and dynamic knowledge uncovering are increasingly demanded. This paper develops a model called Variable step-size evolving Participatory Learning with Kernel Recursive Least Squares, VS-ePL-KRLS, applied to the forecast of weekly prices for S500 and S10 diesel oil, at the Brazilian level, for biweekly and monthly horizons. The presented model demonstrates a better accuracy compared with analogous models in the literature, without loss of computational performance for all time series analyzed. [ABSTRACT FROM AUTHOR]

Purpose: To improve fixed filter tap-length and step-size adaptive filtering control algorithm for micro vibration suppression applications using piezoelectric stack actuators, a hybrid DE-Jaya optimized variable step-size and tap-length adaptive filtering control algorithm is proposed to balance the convergence speed and steady-state error. Methods: To describe the rate-dependent hysteresis characteristic of the piezoelectric stack actuator, a Hammerstain model combining discrete time non-symmetrical Bouc–Wen model is proposed. The proposed algorithm (named FX-VSSVFT-LMS algorithm) employs self-optimal tuning variable step-size and variable fractional tap-length. An improved optimization algorithm named hybrid DE-Jaya algorithm is proposed to automatically tune the algorithm parameters of FX-VSSVFT-LMS algorithm to obtain appropriate algorithm parameters, in which a hybrid mutant operator and Jaya operator to balance between convergence speed and solution accuracy. Results: A 3DOF micro-vibration isolation experimental platform is built using piezoelectric stack actuators. Under the same vibration disturbance, experimental tests are done. Conclusion: Comparison experiments show the proposed FX-VSSVFT-LMS algorithm with optimal parameters tuning has better convergence performance and control performance. [ABSTRACT FROM AUTHOR]

Linear and nonlinear numerical techniques are the most popular techniques for finding approximate solutions to initial value problems in numerous scientific fields. Due to the substantial importance of ordinary differential equations, an attempt has been made in the present research study to obtain a new nonlinear hybrid technique based upon contraharmonic and harmonic means having fourth-order accuracy. Theoretical analysis in terms of consistency, stability, asymptotic errors (local and global truncation errors), and convergence has also been carried out. The newly formulated technique is compared with some existing techniques having the same characteristics and observed to be much better because of errors, CPU time, and stability region. The adaptive step-size approach improves the performance of the proposed technique, and strategies to control the errors are developed. Some numerical experiments for scalar and vector initial value problems, including logistic growth, sinusoidal and industrial Robot Arm systems, are presented to show better performance of the proposed technique. [ABSTRACT FROM AUTHOR]

In view of the poor performance of the traditional adaptive filtering algorithm in identifying sparse systems under impulse noise, an affine projection maximum correntropy criterion with compound inverse proportional function (APMCCCIPF) algorithm is proposed in this paper, and the compound inverse proportional function approaching l0 norm is introduced into the traditional affine projection maximum correntropy criterion (APMCC) algorithm. The fixed step‐size APMCCCIPF algorithm cannot obtain faster convergence speed and lower steady‐state error at the same time, and the most effective method to solve this contradiction is to change the fixed step‐size in the algorithm to a variable step‐size. Further, a variable step‐size factor is constructed in the APMCCCIPF algorithm, and a novel variable step‐size APMCCCIPF algorithm is proposed. A modified Gaussian function, which can resist impulse noise interference, is applied to adjust the step‐size change. Besides, the convergence and complexity of the proposed algorithms are analyzed. In the simulation of sparse system identification and echo cancellation under impulsive noise, the proposed algorithms not only achieve a lower and faster convergence rate, but also obtain a lower steady‐state error. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

In this paper, a hyperbolic tangent variable step-size convex combination of the least mean square (HTVSCLMS) algorithm is proposed and analyzed. This work avoids the compromise between the convergence speed and the steady-state error for two filters in convex combination of the least mean square (CLMS) algorithm. In the proposed algorithm, the big step-size filter is replaced by a filter whose iteration step-size is a modified function based on hyperbolic tangent function. Thus it constructs hyperbolic tangent nonlinear relationship between step-size and error. At the same time, the small step-size filter remains unchanged but fixed. So, it conquers the slow convergence speed and the weak anti-interference ability of fixed step-size CLMS. Simulation results show that HTVSCLMS algorithm, compared with CLMS algorithm and variable step-size CLMS (VSCLMS) algorithm, not only has superior capability of tracking in the presence of noise and in a stable and even non-stable environment, but also can maintain a better convergence.

Abstract A new variable step-size strategy for the least mean square (LMS) algorithm is presented for distributed estimation in adaptive networks using the diffusion scheme. This approach utilizes the ratio of filtered and windowed versions of the squared instantaneous error for iteratively updating the step-size. The result is that the dependence of the update on the power of the error is reduced. The performance of the algorithm improves even though it is at the cost of added computational complexity. However, the increase in computational complexity can be minimized by careful manipulation of the update equation, resulting in an excellent performance-complexity trade-off. Complete theoretical analysis is presented for the proposed algorithm including stability, transient and steady-state analyses. Extensive experimental analysis is then done to show the performance of the proposed algorithm under various scenarios.

Estimation in a cooperative and distributed manner in wireless sensor networks (WSNs) has considered much attention in recent years. When this distributed estimation is performed adaptively, the concept of adaptive networks will develop. In such networks, proper selection of the unknown parameter length is an issue in itself. A deficient filter length results in an additional steady-state error while selecting a large length will impose a more computational load on the nodes, which is critical in sensor networks due to the lack of energy resources. This motivates the use of variable tap-length adaptive filters in the context of the adaptive networks. This has been achieved in adaptive networks using the distributed fractional tap-length (FT) algorithm. This algorithm requires proper selection of the length adaptation parameters, such as error width and length adaptation step-size. This paper proposes an automatic method for selecting these parameters. In the proposed method, these parameters are adapted based on the estimated gradient vector. The proposed method is fully distributed and presented in a diffusion strategy. Simulation results show that the proposed algorithm has both the advantage of fast length convergence and an unbiased steady-state tap-length. [ABSTRACT FROM AUTHOR]

The widely linear model has attracted much attention due to its good features for non-circular adaptive signal processing in recent years. In this paper, a sparsity-induced augmented complex-valued NLMS algorithm is proposed to promote the performance of the adaptive filter for estimating sparse systems, which is established by incorporating the l 0 -norm regularization into the squared error normalized by the input vector. To address the problem of trade-off between fast convergence rate and low steady-state misalignment, we minimize the variance of the a posteriori error to derive an optimal step-size and then some practical problems are considered. Simulation results are provided to verify the superior performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a novel auto-scaling variable step-size maximum power point tracking (MPPT) method. The novel method solves the problems associated with conventional variable step-size method. Firstly, the conventional variable step-size method use individual scaling factor N adjusted in order to modify the step-size to balance between the precision of tracking and its divergence rate during the design stage. However, this individual scaling factor N causes the dynamic response of the PV system to be slow in the extremely irradiation change condition. To address this issue, the proposed method combines the dual scaling factors N, which are (N1) with a high value and (N2) with a low value. The N1 is used for a faster response at the beginning of the execution. In the meantime, the second N2 value is used to help stabilize the power oscillation. The proposed method can automatically adjust the algorithm's step-size to obtain a fast dynamic response that adapts to weather variations, resulting in reliable steady-state output power. Secondly, the conventional variable step-size, which is based on division of the PV module power change by the PV voltage change, endures from steady-state power oscillations and dynamic problems, particularly when subjected to sudden environmental changes. In this paper, an improvement to the conventional variable step-size method is introduced, in which the step-size of the proposed method is based solely on the change in PV power in order to completely eliminate the division calculations involved in its structure. As a result, the complexity of algorithm implementation is reduced, allowing for the use of low-cost microcontrollers to reduce system costs. Simulation results are provided through MATLAB-SIMULINK to verify the performance of the novel auto-scaling variable step-size maximum power point tracking (MPPT) method. [ABSTRACT FROM AUTHOR]

The relaxed CQ algorithm is a very efficient algorithm for solving the split feasibility problem (SFP) whenever the convex subsets involved are level subsets of given convex functions. It approximates the original convex subset by a sequence of half-spaces that overcomes the difficulties for calculating the projection onto original convex subsets. In this paper, we propose a new inertial relaxed algorithm in which we approximate the original convex subset by a sequence of closed balls instead of half spaces. Moreover, we construct a new variable step-size that does not need any prior information of the norm. We then establish the weak convergence of the proposed algorithm under two different assumptions. Experimental results in the LASSO and elastic net methods show that our algorithm has a better performance than other relaxed algorithms. [ABSTRACT FROM AUTHOR]

This paper addresses the stability issues of the least mean absolute third (LMAT) algorithm using the normalization based on the third order in the estimation error. A novel robust normalized least mean absolute third (RNLMAT) algorithm is therefore proposed to be stable for all statistics of the input, noise, and initial weights. For further improving the filtering performance of RNLMAT in different noises and initial conditions, the variable step-size RNLMAT (VSSRNLMAT) and the switching RNLMAT (SWRNLMAT) algorithms are proposed using the statistics of the estimation error and a switching method, respectively. The filtering performance of RNLMAT is improved by VSSRNLMAT and SWRNLMAT at the expense of affordable computational cost. RNLMAT with less computational complexity than other normalized adaptive filtering algorithms, can provide better filtering accuracy and robustness against impulsive noises. The steady-state performance of RNLMAT and SWRNLMAT in terms of the excess mean-square error is performed for theoretical analysis. Simulations conducted in system identification under different noise environments confirm the theoretical results and the superiorities of the proposed algorithms from the aspects of filtering accuracy and robustness against large outliers.

In compressive sampling matching pursuit algorithm, it requires that the sparsity information of original signal to control the size of the preliminary atomic set and the maximum number of the algorithm iteration. This weakens the reconstruction accuracy, increases the computation complexity and limits its practical application capacity. To overcome the problem, an improved method is proposed. The proposed method firstly sets a fixed step-size as the assumed sparsity to expand the preliminary atomic set at the initial stage when the sparsity information is unknown. Secondly, the proposed algorithm adopts the fuzzy threshold strategy to select the more relevant atoms from the preliminary atomic set to expand the candidate atomic set. Finally, the double threshold control method, multiply stages setting and variable step-size method are used to control the iteration stop condition and adjust the estimated sparsity. When the two threshold iteration stop conditions are simultaneously satisfied, the iteration stops, which shows that the reconstructed signal better approximated the original signal, and the reconstruction performance is the best. Otherwise, if only one of the conditions is satisfied, the size of the estimated sparsity is increased by the variable step size method to reduce the error between the reconstructed signal and original signal. In addition, we extended the proposed algorithm to the multiple measurement vectors scenario for joint sparse signal recovery. Simulation results indicate that the proposed algorithm is better than the other method in terms of the reconstruction performance in single measurement vector and multiple measurement vector cases.

The adaptive algorithms have been widely studied in Gaussian environment. However, the impulsive noise and other non-Gaussian noise may largely deteriorate the performance of algorithm in practical applications. To address this problem, in this paper, we propose two novel adaptive algorithms for system identification problem with mixed noise scenarios. Both proposed algorithms are based on the framework of the affine projection (AP) algorithm. The first proposed algorithm, termed as VS-APMCCA, combines variable step-size (VS) strategy and maximum correntropy criterion (MCC) to obtain improved performance. For further performance improvement, the VC-VS-APMCCA is developed, which is based on the variable center (VC) scheme of MCC. The convergence analysis of the VC-VS-APMCCA is conduced. Finally, simulation results demonstrate the superior performance of the VS-APMCCA and VC-VS-APMCCA.

The estimation performance of the standard diffusion affine projection algorithm may be degraded when the distributed network nodes are disturbed by impulsive noise. To overcome the limitation, a diffusion affine projection M-estimate (DAPM) algorithm is proposed for distributed estimation in the adaptive diffusion networks. This algorithm uses a robust cost function based on M-estimate function to eliminate the adverse effects of impulsive noise on distributed diffusion network nodes. In order to further enhance the performance of the DAPM algorithm, namely fast convergence rate and low steady-state error, a variable step-size diffusion affine projection M-estimate (VSS-DAPM) algorithm is presented. In addition, the convergence range of the step-size is deduced to ensure the convergence of the proposed algorithms. Computer simulations show that the proposed DAPM and VSS-DAPM algorithms have good convergence performance for distributed estimation in the adaptive diffusion networks. More importantly, the proposed VSS-DAPM algorithm improves convergence rate and the network mean square deviation (MSD) as compared to the DAPM algorithm in the distributed estimation.

The performance of the traditional second-order statistics based channel estimation methods degrade seriously in the presence of impulsive noises.In order to deal with this problem,a Weibull distribution function based variable step-size sign algorithm for channel estimation under impulsive noises was proposed.The proposed method was robust against impulsive noises and it could improve the convergence speed of the sign algorithm with the Weibull distribution function based variable step-size method.Computational complexity analysis and simulation results demonstrate that the proposed algorithm can achieve the same steady-state estimation error with faster convergence speed and lower computational complexity.

Summary: A fundamental challenge affecting the performance of a system is the undesired effect of noise on the system. Practically, real‐time systems are influenced by Gaussian noise and impulsive noise. Identification of these nonlinear physical systems in the presence of noise offers broader applications than linear system identification. Hence, this article introduces a variable step‐size technique to solve the conflicting requirement of rapid convergence and low mean square error (MSE) in the presence of both Gaussian and impulsive noise. Moreover, to avoid over parameterized equations existing in the variable step‐size equation, this article proposes the nonparametric variable step‐size (NPVSS), which depends on error estimates at instants of time and is used with the least mean square/fourth (LMS/F) algorithm. The computational complexity analysis, computer simulations, and implementation in real‐time setup validate that the proposed NPVSS‐LMS/F algorithm provides superior performance in terms of convergence time and MSE compared to the existing algorithms for both linear and nonlinear system identification in the presence of noise. [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]

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]

A lot of research has been done in the diffusion paradigm for the wireless sensor networks. However, not enough attention has been given to the incremental strategy. Despite having better performance than the diffusion scheme, incremental based algorithms have been generally ignored. This brief presents an incremental variable step-size strategy for distributed estimation. A detailed analysis of the performance of the algorithm is shown. The mean analysis and mean square analysis are given along with steady-state results. The mean square analysis, as presented here, is being performed for the first time and provides closed form results, unlike previous works present in the literature. [ABSTRACT FROM AUTHOR]

Despite its low computational cost, and steady state behavior, some well known drawbacks of the least means squares (LMS) algorithm are: slow rate of convergence and unstable behaviour for ill conditioned autocorrelation matrices of input signals. Several modified algorithms have been presented with better convergence speed, however most of these algorithms are expensive in terms of computational cost and time, and sometimes deviate from optimal Wiener solution that results in a biased solution of online estimation problem. In this paper, the inverse Cholesky factor of the input autocorrelation matrix is optimized to pre-whiten input signals and improve the robustness of the LMS algorithm. Furthermore, in order to have an unbiased solution, mean squares deviation (MSD) is minimized by improving convergence in misalignment. This is done by regularizing step-size adaptively in each iteration that helps in developing a highly efficient optimal preconditioned regularized LMS (OPRLMS) algorithm with adaptive step-size. Comparison of OPRLMS algorithm with other LMS based algorithms is given for unknown system identification and noise cancelation from ECG signal, that results in preference of the proposed algorithm over the other variants of LMS algorithm. [ABSTRACT FROM AUTHOR]