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Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with exogenous inputs (NARX) and a process noise adaptive square root cubature Kalman filter (PASCKF) to address this issue. Driven by vehicle acceleration data, an NARX-based road roughness identification system is constructed to mitigate the model uncertainties. Furthermore, a hybrid strategy is proposed. On the one hand, the accurate road roughness estimated by the NARX is converted into process noise covariance, enhancing the estimator's accuracy and convergence rate. Another switching strategy is proposed to optimize the non-convergence issues of the PASCKF. Finally, simulation and actual vehicle experiment data demonstrate that this approach offers superior identification accuracy and adaptability compared to the standalone SCKF algorithm. [ABSTRACT FROM AUTHOR]

The widely linear complex-valued least mean square (WL-CNLMS) algorithm is extensively used for processing complex-valued signals, but it exists performance compromise between convergence rate and steady-state misadjustment. In response to this problem, we incorporate the idea of switching step-size (SSS), that is, selecting an optimal step-size at each iteration by comparing the mean-square deviation trends of the WL-CNLMS algorithm with pre-set different step-sizes and then proposing the SSS based WL-NLMS algorithm. Meanwhile, to keep the robustness of the algorithm in the impulsive noise environment, a robust variant of it is proposed by utilizing the modified Huber function instead of the quadratic function. Through extensive simulations in the contexts of system identification and beamforming, we have verified the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper presents novel and low computational complexity spline adaptive filtering (SAF) algorithms based on partial coefficients selection and adaption. They are addressed partial update SAF normalized least mean squares (PU-SAF-NLMS) algorithms. The PU-SAF-NLMS equations are established via the steepest gradient descent constraint to the proposed cost function. In the proposed algorithms, the filter coefficients are updated based on periodic, sequential, and selective rules, leading to reduction in computational complexity. Furthermore, the convergence speed of PU-SAF-NLMS algorithms is close to the conventional SAF-NLMS. Moreover, the convergence analysis of algorithms is studied. Ultimately, the performance of the presented algorithms is appraised through several experimental results. [ABSTRACT FROM AUTHOR]

While the practical application of adaptive filters has indeed garnered substantial attention, two pressing issues persist that have a profound impact on their performance—system sparsity and the presence of contaminated Gaussian impulsive noise. In this research paper, we propose a novel approach to tackle both of these issues simultaneously by introducing the concept of a proportionate matrix. Specifically, we present a proportionate maximum total complex correntropy algorithm based on the errors-in-variables model. The paper presents a theoretical analysis of the steady-state weight error power under the influence of impulsive noise. Furthermore, it discusses the performance comparison in system identification and highlights the robustness of the proposed algorithm. To validate its effectiveness, a simulation involving stereophonic acoustic echo cancellation is conducted, and the results confirm the clear advantages of the proposed Proportionate Maximum Total Complex Correntropy algorithm. [ABSTRACT FROM AUTHOR]

The projection order of the affine projection algorithm (APA) affects not only the convergence performance but also the steady-state behavior. Therefore, for solving the fixed projection order of the conventional APA, we develop a new scheme of variable projection order (VPO) that enables the evolution from the maximum projection order to the minimum one by resorting to the adaptation of the mixing factor, thereby yielding a novel APA with VPO. Moreover, for dealing with sparse systems with fast convergence, we extend the proposed VPO scheme to proportionate APA and develop a VPO-based memory proportionate APA. Simulation results in the scenarios of system identification and acoustic echo cancellation have shown that the proposed algorithms have a faster convergence rate and lower steady-state error as compared to their original counterparts and the existing VPO algorithms. [ABSTRACT FROM AUTHOR]

Recently, an affine-projection-like M-estimate (APLM) algorithm has gained popularity for its ability to effectively handle impulsive background disturbances. Nevertheless, the APLM algorithm's performance is negatively affected by steady-state misalignment. To address this issue while maintaining equivalent computational complexity, a robust cost function based on the Andrew's sine estimator (ASE) is introduced and a corresponding affine-projection Andrew's sine estimator (APASE) algorithm is proposed in this paper. To further enhance the tracking capability and accelerate the convergence rate, we develop the combined-step-size APASE (CSS-APASE) algorithm using a combination of two different step sizes. A series of simulation studies are conducted in system identification and echo cancellation scenarios, which confirms that the proposed algorithms can attain reduced misalignment compared to other currently available algorithms in cases of impulsive noise. Meanwhile, we also establish a bound on the learning rate to ensure the stability of the proposed algorithms. [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 this study, a novel estimation scheme is proposed for identifying extended Wiener–Hammerstein systems with hysteresis nonlinearity subject to quantised measurements. The proposed scheme is established in a self-error learning framework to achieve high-performance parameter estimation compared with classic error feedback learning estimation algorithms. Initially, the useful identification data can be extracted from contaminated system data by introducing an adaptive filter. Then, with the help of the filtered data, the identification error expression used to establish the estimator is derived. Subsequently, an online compensation estimation error variable is proposed to eliminate the effect of the regression vector on the convergence performance. A new adaptive law is designed with adaptive recursive gain, considering the compensation estimation error data and parameter initial error data. Under general persistent excitation (PE) condition, the PE condition of the regressor information is verified online, and the estimator convergence is strictly proven. Finally, the statistical results of two illustrated examples and a real-word example are provided to validate the positive features and effectiveness of the proposed estimation scheme. • Adaptive law is updated by using the self-error information rather than non-self-error data. • Cost function is established by right of the compensated error and initial error data. • The effect of regressor on estimator is remedied by considering a compensation matrix. • Introduced filter takes into account system prior knowledge and the performance is improved. [ABSTRACT FROM AUTHOR]

Distributed inference tasks could be performed by adaptive filtering techniques. Several enhancement strategies for such techniques were proposed, such as sparsity-aware algorithms, coefficients reuse and correntropy-based cost functions in the case of impulsive noise. In this paper, a general framework based on Lagrange multipliers for the derivation of sophisticated algorithms that incorporate most of these improvements is described. A new general identification algorithm is derived as an example of the proposed approach and its performance is assessed in a distributed setting. [ABSTRACT FROM AUTHOR]

In this letter, a normalized frequency‐domain block sign‐error algorithm (NFBSA) is proposed by minimizing the ℓ1$\ell _{1}$‐norm of the posteriori error vector for filter weight. The NFBSA updates the filter weight vector by employing the sign value of the priori error vector, which can mitigate the impact of impulsive noise. Furthermore, a variable step‐size algorithm (VSS) suitable for application in the NFBSA is proposed, which minimizes the ℓ1$\ell _{1}$‐norm of the posteriori error vector with respect to the step‐size. The system identification simulations are conducted using a first‐order autoregressive signal as an input, assuming that impulsive noise occurs. The simulation results demonstrate that the NFBSA exhibits superior misalignment performance compared to the conventional time‐domain sign algorithm, and the NFBSA with the proposed VSS outperformed other VSS‐based sign algorithms. [ABSTRACT FROM AUTHOR]

Summary: Most of the existing adaptive filter algorithms pay more attention to improving performance while ignoring the computational complexity and the impact of the impulsive environment. When encountering the impulsive noise environments, the performance of traditional nonlinear adaptive filter may be significantly reduced and usually needs high computational cost. Therefore, this article proposes a hyperbolic tangent Leclerc robust nonlinear adaptive filter based on the low complexity decomposable Volterra model (HTLNAF‐DVM). The filter is implemented by imposing a rank‐one structure on the full Volterra model to get a product of linear filters, and employs a hyperbolic tangent Leclerc function as a robust norm to effectively improve the robustness against the impulsive noise. In addition, we give the theoretical analyses of the steady‐state mean‐square performance of the proposed HTLNAF‐DVM. Finally, the simulation results prove that the proposed HTLNAF‐DVM algorithm has better performance than the existing algorithms and fit well with the theory. [ABSTRACT FROM AUTHOR]

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

In this paper, a stochastic model is presented for the nonparametric variable step-size normalized least-mean-square (NP-VSS-NLMS) algorithm. This algorithm has demonstrated potential in practical applications and hence a deeper understanding of its behavior becomes crucial. In this context, model expressions are obtained for characterizing the algorithm behavior in the transient phase as well as in the steady state, considering a system identification problem and Gaussian input data. Such expressions reveal interesting algorithm characteristics that are useful for establishing design guidelines and for the advancement of more refined algorithms. Simulation results for various operating scenarios ratified both the model's accuracy and the algorithm's superior performance relative to other recent and relevant algorithms from the literature. [ABSTRACT FROM AUTHOR]

To enhance the performance of the diffusion robust adaptive filtering algorithm, this paper presents a novel loss function framework named the "Tanh cost function framework." By utilizing this framework, we are able to incorporate standard cost functions, devise novel cost functions, and introduce the associated diffusion algorithm. Moreover, the convergence of the algorithm is thoroughly analyzed. Furthermore, the proposed diffusion Tanh algorithm family is simulated in a system identification model to assess its performance, demonstrating superior performance compared to the standard diffusive algorithm. Notably, the DTHLMS within the diffusion tanh algorithm family exhibits superior performance over the mainstream robust diffusion algorithms. [ABSTRACT FROM AUTHOR]

The normalized subband adaptive filtering algorithm provides fast convergence rate for colored input signals as compared to the normalized least mean square algorithm, but it suffers from a poor convergence issue in the α -stable noise. In light of this, the normalized subband p-norm (NSPN) algorithm, which is based on the least mean p-power error (MPE) criterion, is proposed in this study. This technique is not only robust against impulsive noise samples, but it also maintains a fast convergence rate when colored input signals are used. In addition to this, we develop both the steady-state and the transient models of the NSPN algorithm and provide some insights. Then, in order to solve the problem of making a choice regarding the order p in the NSPN algorithm, we design an autonomous system and come up with the NSPN algorithm with a variable p-norm (VP-NSPN). In addition, we offer the TFC-based VP-NSPN algorithm with a fast convergence rate and low steady-state misadjustment simultaneously by making use of the tap-weights feedback-based convex combination (TFC) scheme. In conclusion, simulation results on system identification and acoustic echo cancellation are undertaken in order to validate the superiority of the proposed algorithms and validate the usefulness of the theoretical analysis. [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]

Within the realm of machine learning, kernel methods stand out as a prominent class of algorithms with widespread applications, including but not limited to classification, regression, and identification tasks. Our paper addresses the challenging problem of identifying the finite impulse response (FIR) of single-input single-output nonlinear systems under the influence of perturbations and binary-valued measurements. To overcome this challenge, we exploit two algorithms that leverage the framework of reproducing kernel Hilbert spaces (RKHS) to accurately identify the impulse response of the Proakis C channel. Additionally, we introduce the application of these kernel methods for estimating binary output data of nonlinear systems. We showcase the effectiveness of kernel adaptive filters in identifying nonlinear systems with binary output measurements, as demonstrated through the experimental results presented in this study. [ABSTRACT FROM AUTHOR]

Background and Objectives: In order to improve the performance of normalized subband adaptive filter algorithm (NSAF) for identifying the block-sparse (BS) systems, this paper introduces the novel adaptive algorithm which is called BSNSAF. In the following, an improved multiband structured subband adaptive filter (IMSAF) algorithms for BS system identification is also proposed. The BSIMSAF has faster convergence speed than BS-NSAF. Since the computational complexity of BS-IMSAF is high, the selective regressor (SR) and dynamic selection (DS) approaches are utilized and BS-SR-IMSAF and BS-DS-IMSAF are introduced. Furthermore, the theoretical steady-state performance analysis of the presented algorithms is studied. Methods: All algorithms are established based on the 0-norm constraint to the proposed cost function and the method of Lagrange multipliers is used to optimize the cost function. Results: The good performance of the proposed algorithms is demonstrated through several simulation results in the system identification setup. The algorithms are justified and compared in various scenarios and optimum values of the parameters are obtained. Also, the computational complexity of different algorithms is studied. In addition, the theoretical steady state values of mean square error (MSE) values are compared with simulation values. Conclusion: The BS-NSAF algorithm has better performance than NSAF for BS system identification. The BSIMSAF algorithm has better convergence speed than BS-NSAF. To reduce the computational complexity, the BS-SR-IMSAF and BS-DSRIMSAF algorithms are developed. These algorithms have close performance to BSIMSAF. [ABSTRACT FROM AUTHOR]

Purpose: Real-time systems are affected by nonlinearities which might be due to the use of passive devices. To model these nonlinearities, a combined split adaptive exponential functional link network (cSAEFLN) architecture is proposed which uses the AEFLN-based modeling that enhances the architecture's capability for nonlinear system identification. Method: The cSAEFLN architecture consists of one linear adaptive filter and a convex combination of two nonlinear adaptive filters. To address the sparsity issue and deal with the nonlinearities resulting from the functional expansion of the input signal, a novel improved proportionate least mean square/fourth (IPLMS/F) algorithm is introduced for updating the nonlinear adaptive filter coefficients. Results: Different experiments related to the system identification problem are examined to analyze the robustness of the proposed architecture. The testified outcome indicates the efficiency of the cSAEFLN architecture in terms of mean square error and convergence rate for different systems. [ABSTRACT FROM AUTHOR]

To further improve the performance of the kernel adaptive filtering algorithm in a non-Gaussian environment, a robust kernel least mean square algorithm is proposed, and the effectiveness of the root cost function and the convergence of the algorithm is theoretically analyzed. An improved online vector quantization criterion is then applied to the proposed algorithm to suppress the linearly growing network size. Finally, the different performances of the algorithm of this paper and other kernel adaptive filtering algorithms as well as this paper's algorithm before and after quantization are compared in Mackey Glass chaotic time series as well as in system identification, confirming the superiority of the algorithm of this paper and the improved online vector quantization criterion. [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 address the contradiction between the convergence error and convergence rate in the LMS algorithm, this study proposes a variable-step-size adaptive filter algorithm with a momentum term based on the logistic function. First, the normalization LMS algorithm is obtained by seeking the extremum under the Lagrange function constraint. Second, to reduce the convergence error of the algorithm, the logistic model is used as a function model of step size variation with error, resulting in a variable-step normalization LMS algorithm. Our experimental results demonstrate that this algorithm achieves smaller convergence errors compared to those of the traditional LMS algorithm. Finally, to further improve the convergence rate of the algorithm, a momentum term is introduced into the weight coefficient update process of the LMS algorithm. This leads to the development of a variable-step adaptive filter algorithm with a momentum term based on the logistic function. The impact of different parameters on the algorithm performance is also investigated. In order to verify the rationality of the proposed algorithm, a dynamic system mathematical model was identified using the proposed algorithm. The results showed that the proposed algorithm had an identification accuracy of over 97% for the mathematical model parameters and a suppression of over 99% for noise. In order to verify the engineering application value of the proposed algorithm, real-time vibration data fitting experiments were conducted in the Aeroelasticity Laboratory of the China Aerodynamics Research and Development Center, and their results were compared with three algorithms: ARMAX, N4SID, and LMS. The results showed that the proposed algorithm had a higher fitting accuracy than the three others. Through simulations and experiments, it is demonstrated that this study has value both theoretically and in engineering applications, promoting engineering applications of adaptive filtering algorithms and providing strong support for the research of adaptive control. [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 work focuses on linear system identification problems in the framework of the Wiener filter. Specifically, it addresses the challenging identification of systems characterized by impulse responses of long length, which poses significant difficulties due to the existence of large parameter space. The proposed solution targets a dimensionality reduction of the problem by involving the decomposition of a fourth-order tensor, using low-rank approximations in conjunction with the nearest Kronecker product. In addition, the rank of the tensor is controlled and limited to a known value without involving any approximation technique. The final estimate is obtained based on a combination of four (shorter) optimal filters, which are alternatively iterated. As a result, the designed iterative Wiener filter outperforms the traditional counterpart, being more robust to the accuracy of the statistics' estimates and/or noisy conditions. In addition, simulations performed in the context of acoustic echo cancellation indicate that the proposed iterative Wiener filter that exploits this fourth-order tensor decomposition achieves better performance as compared to some previously developed solutions based on lower decomposition levels. This study could further lead to the development of computationally efficient tensor-based adaptive filtering algorithms. [ABSTRACT FROM AUTHOR]

Characterising underwater acoustic transducers is essential to optimal signal processing in sound navigation and ranging systems. Precise characterisation allows for equalisation of the input and output hardware, resulting in improved performance of the overall system. A critical quantity of the characterisation is the impulse response of the underwater transducers, which are usually measured in a special low‐noise water tank. An established method in other fields to estimate impulse responses of unknown systems is using adaptive filters and include an inherent quality measure. Such approaches allow for very fast and very reliable measurements. However, when using fixed control parameters, a trade‐off between convergence speed and final mismatch needs to be found, which can be eliminated using variable control parameters. In this article, a method for determining an optimal step size for adaptive algorithms based on the normalised least mean square method is derived based on a theoretical analysis of the convergence process by taking the reverberation parameters of such measurement tanks into account. The new method is specialised on the application of underwater transducer characterisation and allows a very reliable approximation of the optimal step size and thus a maximally fast adaption behaviour—leading to a very short measurement time. This is firstly shown in simulations and afterwards demonstrated in a real measurement with unknown transducers in a measurement water tank. [ABSTRACT FROM AUTHOR]

The grid-connected inverter is the key component for the reliable and safe operation of grid-interconnected renewable energy systems. In order to ensure that the inverter output current is in-phase synchronized with the grid voltage, a highly efficient and fast control strategy is required. This paper proposes an algorithmically driven approach for designing the adaptive controller for a grid-connected DC/AC inverter. The controller consists of two adaptive IIR filters based on the LMS algorithm and has two modes of operation. During the learning mode, the controller uses the filters to estimate the coefficients of the inverse transfer function of the PWM-driven inverter at several grid frequencies within a specific range. During the online mode, the controller generates the driving signal for the inverter block using a set of learned coefficients corresponding to the current grid frequency. By constantly monitoring the grid voltage and reconfiguring the controller accordingly, a fast adaptation of the inverter output current to grid frequency variations is achieved. For grid frequency variations in the range of 48 to 52 Hz, the MATLAB simulation results show that the phase difference between the grid voltage and inverter output current waveforms becomes less than 1 degree after at most four periods. [ABSTRACT FROM AUTHOR]

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]

A novel kernel recursive second-order sine adaptive (KRSOSA) algorithm was devised for identifying non-linear systems, which was constructed using a symmetry squared sine function to develop a novel kernel loss function and recursive scheme. In the proposed KRSOSA algorithm, the squared sine function provides resistance to impulsive noise due to the sine operation, which was well-derived and investigated in the framework of kernel adaptive filtering (KAF). The behavior of the proposed KRSOSA algorithm was investigated and analyzed using computer simulations, which provided good performance for identifying non-linear systems under impulsive noises. [ABSTRACT FROM AUTHOR]

To improve the performance of identifying the block-sparse systems, firstly, a new sparsity aware block-sparse proportionate affine projection algorithm (BS-PAPA) with a fixed zero attractor is proposed in this paper. The proposed algorithm is obtained by integrating a weighted l 0 -norm penalty into the cost function of the BS-PAPA. Adding the penalty results in zero attraction terms in the weight update recursive equation of the BS-PAPA, which helps in the shrinkage of inactive coefficients. The proposed algorithm is named l 0 -block-sparse proportionate affine projection algorithm ( l 0 -BS-PAPA). The convergence analysis in the mean is derived for the l 0 -BS-PAPA. Secondly, for applications having time varying measurement noise, an adaptive zero attractor l 0 -BS-PAPA is also developed by adaptive optimisation of the zero attractor. This one is more robust to the varying degree of measurement noise than the former. A variable step-size l 0 -BS-PAPA is also introduced to further enhance the performance of the l 0 -BS-PAPA. Computer simulation experiments reveal that the l 0 -BS-PAPA outperforms the existing algorithms in block-sparse systems in terms of convergence rate, normalised misalignment, and tracking ability. [ABSTRACT FROM AUTHOR]

Stereophonic audio devices employ two loudspeakers and two microphones in order to create a bidirectional sound effect. In this context, the stereophonic acoustic echo cancellation (SAEC) setup requires the estimation of four echo paths, each one corresponding to a loudspeaker-to-microphone pair. The widely linear (WL) model was proposed in recent literature in order to simplify the handling of the SAEC mathematical model. Moreover, low complexity recursive least- squares (RLS) adaptive algorithms were developed within the WL framework and successfully tested for SAEC scenarios. This paper proposes to apply a data-reuse (DR) approach for the combination between the RLS algorithm and the dichotomous coordinate descent (DCD) iterative method. The resulting WL-DR-RLS-DCD algorithm inherits the convergence properties of the RLS family and requires an amount of mathematical operations attractive for practical implementations. Simulation results show that the DR approach improves the tracking capabilities of the RLS-DCD algorithm, with an acceptable surplus in terms of computational workload. [ABSTRACT FROM AUTHOR]

A novel sparse LMS algorithm for the sparse system identification is proposed to reduce the complexity of the existing algorithms. The proposed algorithm discards W(n) when the value of the current weight vector is within a certain range. The algorithm also optimizes the iterative update equation by using only the product term to calculate the value of W(n+1). The hardware implementation shows that the total logic elements number of the proposed algorithm is 60.06% less than the latest l0-ILMS algorithm, while the performance is nearly the same. [ABSTRACT FROM AUTHOR]

The Least Mean Square (LMS) algorithm has a slow convergence rate as it is dependent on the eigenvalue spread of the input correlation matrix. In this research, we solved this problem by introducing a novel adaptive filtering algorithm for complex domain signal processing based on q-derivative. The proposed algorithm is based on Wirtinger calculus and is called as q- Complex Least Mean Square (q-CLMS) algorithm. The proposed algorithm could be considered as an extension of the q-LMS algorithm for the complex domain. Transient and steady-state analyses of the proposed q-CLMS algorithm are performed and exact analytical expressions for mean analysis, mean square error (MSE), excess mean square error (EMSE), mean square deviation (MSD) and misadjustment are presented. Extensive experiments have been conducted and a good match between the simulation results and theoretical findings is reported. The proposed q-CLMS algorithm is also explored for whitening applications with satisfactory performance. A modification of the proposed q-CLMS algorithm called Enhanced q-CLMS (Eq-CLMS) is also proposed. The Eq-CLMS algorithm eliminates the need for a pre-coded value of the q-parameter thereby automatically adapting to the best value. Extensive experiments are performed on system identification and channel equalization tasks and the proposed algorithm is shown to outperform several benchmark and state-of-the-art approaches namely Complex Least Mean Square (CLMS), Normalized Complex Least Mean Square (NCLMS), Variable Step Size Complex Least Mean Square (VSS-CLMS), Complex FLMS (CFLMS) and Fractional-ordered-CLMS (FoCLMS) algorithms. [ABSTRACT FROM AUTHOR]

This study aims to identify parametric models to estimate track irregularities in high-speed railways with simple acceleration measurements. The primary contribution of current research is the development of effective parametric models with smaller parameters. These parameters are derived from the measured data via a specialized track geometry inspection system. An adaptive Kalman filter algorithm, using the displacement estimated from the acceleration signals as the input and measured track irregularities as the output, is applied to obtain the model's unknown parameters. These models are applied to acceleration measured from high-speed rail vehicles in operation, and track irregularities are estimated in spatial and wavelength domains. The estimated irregularities are compared to the track geometry inspection system's results. [ABSTRACT FROM AUTHOR]

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For system identification under impulsive-noise environments, the gradient-based generalized maximum correntropy criterion (GB-GMCC) algorithm can achieve a desirable filtering performance. However, the gradient method only uses the information of the first-order derivative, and the corresponding stagnation point of the method can be a maximum point, a minimum point or a saddle point, and thus the gradient method may not always be a good selection. Furthermore, GB-GMCC merely uses the current input signal to update the weight vector; facing the highly correlated input signal, the convergence rate of GB-GMCC will be dramatically damaged. To overcome these problems, based on the Newton recursion method and the data-reusing method, this paper proposes a robust adaptive filtering algorithm, which is called the Newton recursion-based data-reusing GMCC (NR-DR-GMCC). On the one hand, based on the Newton recursion method, NR-DR-GMCC can use the information of the second-order derivative to update the weight vector. On the other hand, by using the data-reusing method, our proposal uses the information of the latest M input vectors to improve the convergence performance of GB-GMCC. In addition, to further enhance the filtering performance of NR-DR-GMCC, a random strategy can be used to extract more information from the past M input vectors, and thus we obtain an enhanced NR-DR-GMCC algorithm, which is called the Newton recursion-based random data-reusing GMCC (NR-RDR-GMCC) algorithm. Compared with existing algorithms, simulation results under system identification and acoustic echo cancellation are conducted and validate that NR-RDR-GMCC can provide a better filtering performance in terms of filtering accuracy and convergence rate. [ABSTRACT FROM AUTHOR]

Non-negative constraints arise in certain system identification problems when the systems to be identified have only positive coefficients. This paper studies the stochastic behavior of modified LMS and NLMS algorithms, modified so as to only allow adaptation with positive coefficients. The mean and second moment behavior of these algorithms are analyzed for Gaussian inputs. Excellent agreement is demonstrated between the theory and Monte Carlo simulations for the LMS algorithm. • Convergence of LMS and NLMS algorithms under non-negative weight constraints. • At each iteration, the weight vector is projected onto the feasible space. • The new algorithm optimally projects the weight vector onto the feasible set. • Models are derived for the mean and mean-square behavior of the adaptive weights. • Simulation results are in excellent agreement with theoretical predictions. [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]

Echo cancellation has been effectively achieved through the successful application of subband adaptive filtering (SAF) algorithms. However, the performance of these algorithms may significantly deteriorate when the system exhibits nonlinear distortion. The Van der Pol–Duffing oscillator (VDPDO) system is widely recognized as a complex nonlinear system that displays intricate dynamical behaviors, emphasizing the importance of identifying this nonlinear model. This paper proposes a novel SAF, termed nonlinear SAF (NLSAF) for VDPDO system identification. The NLSAF is based on the functional link artificial neural network (FLANN) to achieve superior nonlinear modeling capability. In particular, the Andrew's sine estimator is integrated into the NLSAF, generating NLSAF-ASE algorithm for performance improvement. The simulation results provide evidence of the accurate identification of the Van der Pol system through the effective utilization of the NLSAF-ASE algorithm. [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]

Conventional affine projection (AP) algorithm with a fixed order is subject to a tradeoff between convergence speed and steady-state misalignment. In order to address such problem, a switching mechanism on the order of AP algorithm is proposed by comparing the performance of two AP algorithms with different orders. Firstly, the mean square deviations (MSD) behavior of the AP algorithm is analyzed, and a calculation formula for computing MSD at each iteration is derived. Secondly, we design a switching mechanism to select the better order of the two AP algorithms by comparing the MSDs of them; the MSD of the chosen order is smaller than that of the other. We also give the theoretical analysis, including steady-state mean square error (MSE) and computational complexity. Finally, the experiments in system identification and echo-cancellation scenarios demonstrate that the proposed algorithm has good performance not only in a stationary environment but also in a non-stationary environment. [ABSTRACT FROM AUTHOR]

This paper presents a novel variable matrix-type step-size affine projection sign algorithm (VMSS-APSA) characterized by robustness against impulsive noise. To mathematically derive a matrix-type step size, VMSS-APSA utilizes mean-square deviation (MSD) for the modified version of the original APSA. Accurately establishing the MSD of APSA is impossible. Therefore, the proposed VMSS-APSA derives the upper bound of the MSD using the upper bound of the L 1 -norm of the measurement noise. The optimal matrix-type step size is calculated at each iteration by minimizing the upper bound of the MSD, thereby improving the filter performance in terms of convergence rate and steady-state estimation error. Because a novel cost function of the proposed VMSS-APSA was designed to maintain a form similar to the original APSA, they have symmetric characteristics. Simulation results demonstrate that the proposed VMSS-APSA improves filter performance in a system-identification scenario in the presence of impulsive noise. [ABSTRACT FROM AUTHOR]

This paper presents a stochastic model for the least-mean-square algorithm with symmetric/antisymmetric properties (LMS-SAS), operating in a system identification setup with Gaussian input data. Specifically, model expressions are derived to describe the mean weight behavior of the (global and virtual) adaptive filters, learning curves, and evolution of some correlation-like matrices, which allow predicting the algorithm behavior. Simulation results are shown and discussed, confirming the accuracy of the proposed model for both transient and steady-state phases. [ABSTRACT FROM AUTHOR]

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

Augmented IIR filter adaptive algorithms have been considered in many studies, which are suitable for proper and improper complex-valued signals. However, lots of augmented IIR filter adaptive algorithms are developed under the mean square error (MSE) criterion. It is an ideal optimality criterion under Gaussian noises but fails to model the behavior of non-Gaussian noise found in practice. Complex correntropy has shown robustness under non-Gaussian noises in the design of adaptive filters as a similarity measure for the complex random variables. In this paper, we propose a new augmented IIR filter adaptive algorithm based on the generalized maximum complex correntropy criterion (GMCCC-AIIR), which employs the complex generalized Gaussian density function as the kernel function. Stability analysis provides the bound of learning rate. Simulation results verify its superiority. [ABSTRACT FROM AUTHOR]

Sparsity-induced kernel adaptive filters have emerged as a promising candidate for a nonlinear sparse system identification (SSI) problem. The existing zero-attracting kernel least mean square (ZA-KLMS) algorithm relies on minimum mean square error criterion, which considers only second order statistics of error, thereby resulting in suboptimal performance in the presence of non-Gaussian/impulsive distortions. In this letter, we propose a novel random Fourier features (RFF) based ZA kernel maximum Versoria criterion (ZA-KMVC) algorithm, and their variants, which are robust for nonlinear SSI in the presence of non-Gaussian distortions over both stationary and time-varying environments. Furthermore, the mean-square convergence analysis of the proposed RFF-ZA-KMVC algorithm is performed. It has been observed from the simulation results that the proposed algorithm delivers better convergence performance as compared to the existing state-of-art approaches. [ABSTRACT FROM AUTHOR]

Traditional recursive least squares (RLS) adaptive filtering is widely used to estimate the impulse responses (IR) of an unknown system. Nevertheless, the RLS estimator shows poor performance when tracking rapidly time-varying systems. In this paper, we propose a multi-layered RLS (m-RLS) estimator to address this concern. The m-RLS estimator is composed of multiple RLS estimators, each of which is employed to estimate and eliminate the misadjustment of the previous layer. It is shown that the mean squared error (MSE) of the m-RLS estimate can be minimized by selecting the optimum number of layers. We provide a method to determine the optimum number of layers. A low-complexity implementation of m-RLS is discussed and it is indicated that the complexity order of the proposed estimator can be reduced to ${\mathcal O}(M)$ , where $M$ is the IR length. Through simulations, we show that m-RLS outperforms the classic RLS and the RLS methods with a variable forgetting factor. [ABSTRACT FROM AUTHOR]

Hammerstein model with a static nonlinearity followed by a linear filter is commonly used in numerous applications. This paper focuses on adaptive filtering techniques for parameter identification of Hammerstein systems and output prediction of nonlinear systems. By formulating the underlying filtering problem as a recursive bilinear least-squares optimization with the non-convex feasible region constraint, we develop a recursive non-convex projected least-squares (RncPLS) algorithm based on alternating direction method of multipliers (ADMM). The RncPLS algorithm alternates between implementing ridge regression and projecting on the non-convex feasible set, which successively refines the system parameters. The convergence and accuracy properties of the proposed RncPLS algorithm are theoretically investigated. Moreover, extensive simulation results in the context of system identification, nonlinear predication, and acoustic echo cancellation, are also included to demonstrate the performance characteristics of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The multikernel least mean square (MKLMS) algorithm is a classical algorithm of multikernel adaptive filters due to its simplicity. However, the linear growth network structure is a main challenge of MKLMS. To address this issue, a novel multiple random features least mean square (MRFLMS) algorithm is proposed by approximating multiple Gaussian kernels with the multiple random features method. In addition, a combined weight transfer strategy is adopted in MRFLMS to develop another combined multiple random features least mean square (CMRFLMS) algorithm to alleviate the influence of step‐size on filtering performance and convergence rate. CMRFLMS with a fixed dimensional network structure can provide comparable performance and faster convergence rate than MKLMS. Simulations on prediction of synthetic and real non‐linear system identification illustrate the superiorities of the proposed CMRFLMS algorithm from the aspects of filtering accuracy, convergence rate, and tracking performance. [ABSTRACT FROM AUTHOR]