The Random Data-Reusing GMCC Adaptive Filtering Algorithm for System Identification Under Impulsive Noise Environments

Nonlinear system identification in noisy environments presents a significant challenge in adaptive filtering, particularly when dealing with impulsive noise, non-Gaussian distributions, and complex system dynamics. Traditional filtering approaches, including Least Mean Squares (LMS) and Recursive Least Squares (RLS), often exhibit performance degradation due to their reliance on second-order statistical assumptions. The Maximum Correntropy Criterion (MCC) has shown promise in improving robustness; however, it suffers from limitations in capturing highly nonlinear system behaviors. This study proposes a Generalized Maximum Correntropy Criterion (GMCC) with Spline Adaptive Filtering, leveraging B-spline basis functions to enhance function approximation and noise resilience. The GMCC framework was evaluated against LMS, RLS, and conventional MCC-based adaptive filtering methods across Gaussian, Laplacian, and impulsive noise environments. Experimental results demonstrate that GMCC consistently achieves lower Mean Squared Error (MSE) values across all noise scenarios, outperforming conventional approaches in both accuracy and convergence stability. Statistical analysis using ANOVA confirmed performance consistency, though differences were not statistically significant at the 95% confidence level. Practical applications include biomedical signal processing, financial modeling, radar tracking, and autonomous systems, where robust nonlinear filtering is essential. Future research should focus on optimizing computational efficiency, incorporating deep learning enhancements, and extending real-time implementations for IoT and edge computing applications.

Under Gaussian assumption, online sequential extreme learning machine (OS-ELM) can achieve optimal performance. However, OS-ELM is based on the mean square error (MSE) criterion which is not a good choice for non-Gaussian signals. In this paper, a novel OS-ELM algorithm based on the generalized maximum correntropy criterion (OS-ELM-GMCC) is derived. Since the maximum correntropy criterion (MCC) can be generalized by the generalized maximum correntropy criterion (GMCC), the GMCC-based adaptive filtering algorithms with an appropriate shape parameter achieve better filtering performance than the MCC-based ones in the presence of non-Gaussian noise. As the important parameters, the number of hidden node, the shape parameter and scale parameter are discussed by simulations. Simulations in the context of the two examples including the system identification and Mackey-Glass (MG) chaotic time series demonstrate the superiority of OS-ELM-GMCC over OS-ELM and OS-ELM-MC.

Robust adaptive signal processing algorithms based on a generalized maximum correntropy criterion (GMCC) suffers from high steady state misalignment. In an endeavour to achieve lower steady state misalignment, in this letter we propose a generalized hyperbolic secant function (GHSF) as a robust norm and derive the generalized hyperbolic secant adaptive filter (GHSAF). The new algorithm is seen to offer robust system identification performance over the conventional GMCC algorithm. To further improve the convergence performance under non-Gaussian noise environments, we propose the nearest Kronecker product decomposition based GMCC and GHSAF algorithms. Extensive simulation study show the improved convergence performance provided by the proposed algorithms for system identification.

This paper first reviews Correlation Phase Algorithm (CPhiA) for adaptive filters in the complex-number domain with colored Gaussian reference inputs. Stochastic models are presented for two types of impulse noise intruding adaptive filters: one in observation noise and another at filter input. To improve the filter convergence speed for a strongly correlated filter reference input, we combine the CPhiA with simple recurrent calculation of the inverse covariance matrix of the filter input using the Newton's method (CPhi-Newton algorithm). We further propose a new adaptive step-size (ASS) control algorithm to be combined with the CPhi-Newton algorithm. We develop performance analysis of the ASS-CPhi-Newton algorithm to derive difference equations for theoretically calculating transient and steady-state convergence behavior. Through experiment with some examples, it is demonstrated that faster convergence and high robustness are realized with the proposed ASS-CPhi-Newton algorithm in impulsive noise environments. Good agreement between simulated and theoretical convergence validates the analysis.

Noise and interference are the two most common and basic problems in wireless communication systems. The noise in wireless communication channels has the characteristics of randomness and impulsivity, so the performance of adaptive filtering algorithms based on geometric algebra (GA) and second-order statistics is greatly reduced in the wireless communication systems. In order to improve the performance of adaptive filtering algorithms in wireless communication systems, this paper proposes two novel GA-based adaptive filtering algorithms, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion (MSEMEE) of the MEE and the mean square error (MSE) with the help of GA theory. The noise interference in wireless communication is modeled by alpha-stable distribution which is in good agreement with the actual data in this paper. Simulation results show that for the mean square deviation (MSD) learning curve, the GA-based MEE (GA-MEE) algorithm has faster convergence rate and better steady-state accuracy compared to the GA-based maximum correntropy criterion algorithm (GA-MCC) under the same generalized signal-to-noise ratio (GSNR). The GA-MEE algorithm reduces the convergence rate, but improves the steady-state accuracy by 10–15 dB compared to the adaptive filtering algorithms based on GA and second-order statistics. For GA-based MSEMEE (GA-MSEMEE) algorithm, when GA-MSEMEE and the adaptive filtering algorithms based on GA and second-order statistics keep the same convergence rate, its steady-state accuracy is improved by 10–15 dB, and when GA-MSEMEE and GA-MEE maintain approximately steady-state accuracy, its convergence rate is improved by nearly 100 iterations. In addition, when the algorithms are applied to noise cancellation, the average recovery error of the two proposed algorithms is 7 points lower than that of other GA-based adaptive filtering algorithms. The results validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in the alpha-stable noise environment, providing new methods to deal with multi-channel interference in wireless networks.

The purpose of adaptive filter is to solve the dilemma of fast convergence rate and low mean square error. In the past two decades many adaptive filter algorithms have been presented and have claimed that they have good convergence speed and tracking properties. This paper describes the concept of adaptive noise cancellation, an alternative method of estimating signals corrupted by additive noise or interference. This paper summarizes three promising algorithms and gives a performance comparision via extensive simulation. Step size is the main parameter for the convergence rate and mean square error. The simulation analysis showed that RLS algorithm had faster convergence speed and smaller steady state error compared with basic LMS algorithm.The results shown, for convergence rate with less no of taps is the most difficult phase in signal processing applications for the perfect working of any system.

A Robust Generalized Maximum Correntropy Criterion Algorithm for Active Noise Control

The reweighted zero-attracting least mean square (RZA-LMS) algorithm has good performance in sparse system identification. However, the convergence performance of the RZA-LMS algorithm degrades in the impulsive noise environment. In this brief, a reweighted zero-attracting least mean M-estimate (RZA-LMM) algorithm is proposed to address the issue. The RZA-LMM algorithm employs the M-estimate cost function with a sparsity-aware penalty term and is derived by using the unconstrained minimization method. In order to further enhance the convergence speed and reduce the steady-state error of the RZA-LMM algorithm, a variable step-size reweighted zero-attracting least mean M-estimate (VSSRZA-LMM) algorithm is proposed. The variable step-size scheme, which adopts the M-estimate cost function with a sparsity-aware penalty term and a constrained term of the step-size, is obtained by using the constrained minimization method. Besides, the mean-square stability is analyzed to obtain the range of the step-size, which guarantees the stabilization of the proposed algorithms. The computer simulation results show that the proposed RZA-LMM algorithm achieves better convergence performance than the RZA-LMS algorithm, and the proposed VSSRZA-LMM algorithm exhibits better convergence performance in terms of convergence speed and steady-state normalized mean square deviation (NMSD) than the RZA-LMM algorithm for sparse system identification in the impulsive noise environment.

State of charge estimation of Li-ion batteries based on strong tracking adaptive square root unscented Kalman filter with generalized maximum correntropy criterion

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of the adaptive robust filtering to the unscented particle filter. This algorithm adaptively determines the equivalent weight function and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise, thus preventing particles from degeneracy. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of adaptive robust filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, and the filtering accuracy is much higher than the extended Kalman filter, unscented Kalman filter, standard particle filter and unscented particle filter.

Sparse constraint Least Mean Square (LMS) is a recently proposed efficient adaptive algorithm for sparse system identification. However, its computational complexity is quite high especially when the filter length is long and convergence is slow for colored input signal. This paper extends the idea of sparse constraint into multidelay frequency adaptive filter (MDF) algorithm and proposes the sparse MDF algorithm for echo cancellation. The proposed algorithm perserves both the advantage of sparse LMS which has fast convergence performance for sparse system and MDF algorithm which has temporal decorrelation effect with lower implementation complexity. Two typical sparse constraints, l 1 -norm and an approximate l 0 -norm, are employed. And their performances of various aspects are simulated. Experiments show they have better performance than existing algorithms.

A family of adaptive filtering algorithms for processing signals which have energy concentrated in a relatively small number of component subspaces in the spectral domain is introduced. The approach is based on transform domain signal decomposition and linear least squares filtering of the selected subset of transform domain signal components. The derivation is based on the linear least squares adaptive filtering framework introduced in previous work (1997). Fast convergence and computational efficiency are the main characteristics of the resulting algorithms. The method is applied to the problem of adaptive line enhancement comb filtering and DFT is used as a transform method. It is also shown that the resulting adaptive structure is capable of handling the case of non-coinciding frequencies. The performance of the algorithm is evaluated through a series of simulation experiments.

In this paper, a new robust adaptive FIR filter algorithm with variable forgetting factor for time-varying parameters estimation in the presence of impulsive noise is discussed. The proposed algorithm is based on the robust recursive least square and extended prediction error variable forgetting factor adaptation algorithms. The feasibility of the approach is demonstrated in a system identification simulation using a FIR filter application.

Improved proportionate-type sparse adaptive filtering under maximum correntropy criterion in impulsive noise environments

In this paper, an efficient Fast Block LMS (FBLMS) algorithm is proposed for removing artifacts preserving the low frequency components and tiny features of the ECG. The proposed implementation is suitable for applications requiring large signal to noise ratios with fast convergence rate. The FBLMS algorithm, being the solution of the steepest descent strategy for minimizing the mean squared error in a complete signal occurrence, is shown to be steady-state unbiased and with a lower variance than the LMS algorithm. Finally, we have applied this algorithm on ECG signals from the MIT-BIH data base and compared its performance with the conventional LMS algorithm. The results show that the performance of the FBLMS algorithm is superior than the LMS algorithm. I. INTRODUCTION The extraction of high-resolution ECG signals from record- ings contaminated with background noise is an important issue to investigate. The goal for ECG signal enhancement is to separate the valid signal components from the undesired artifacts, so as to present an ECG that facilitates easy and accurate interpretation. Many approaches have been reported in the literature to address ECG enhancement using adaptive filters (2)-(3), which permit to detect time varying potentials and to track the dynamic variations of the signals. In (3), Thakor et al. proposed an LMS based adaptive recurrent filter to acquire the impulse response of normal QRS complexes, and then applied it for arrhythmia detection in ambulatory ECG recordings. The reference inputs to the LMS algorithm are deterministic functions and are defined by a periodically extended, truncated set of orthonormal basis functions. In these papers, the LMS algorithm operates on an instantaneous basis such that the weight vector is updated every new sample within the occurrence, based on an instantaneous gradient estimate. There are certain clinical applications of ECG signal processing that require adaptive filters with large number of taps. In such applications the conventional LMS algorithm is computationally expensive to implement. The block processing of data samples can significantly reduce the computational complexity. By applying this strategy, a special implementa- tion of the LMS algorithm is called the block LMS algorithm. In a recent study, however, a steady state convergence analysis for the LMS algorithm with deterministic reference inputs showed that the steady-state weight vector is biased, and thus, the adaptive estimate does not approach the Wiener solution. To handle this drawback another strategy was considered for estimating the coefficients of the linear expansion, ie., the BLMS algorithm (8), in which the coefficient vector is updated only once every occurrence based on a block gradient estimation. The BLMS algorithm has been proposed in the case of random reference inputs and has, when the input is stationary, the same steady state misadjustment and convergence speed as the LMS algorithm. A major advantage of the block, or the transform domain, LMS algorithm is that the input signals are approximately uncorrelated. Moreover, the filter output and the weight update terms can be evaluated faster using FFT-based fast BLMS (FBLMS) algorithm. The advantage of this algorithm is less computational complexity and good filtering capability. These characteristics may plays a vital role in biotelemetry, where extraction of noise free ECG signal for efficient diagnosis and fast computations, high data transfer rate are needed to avoid overlapping of pulses and to resolve ambiguities. To the best of our knowledge, transform domain has not been considered previously within the context of filtering artifacts in ECG signals. In this paper, we present a FBLMS algorithm to remove the artifacts from ECG. Such a realization is intrinsically less complex than its BLMS based counterpart. This algorithm enjoys less compu- tational complexity and good filtering capability. To study the performance of the proposed algorithm to effectively remove the noise from the ECG signal, we carried out simulations on MIT-BIH database for different artifacts. The simulation results shows that the proposed algorithm performs better than the LMS counterpart to eliminate the noise from ECG.