Steady-state mean-square performance analysis of the block-sparse maximum Versoria criterion

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

Accurate channel-estimation algorithms are critical for enhancing the throughput of wireless communication systems, including millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems, where precise channel knowledge enables reliable signal detection and beamforming. In practical wireless environments, impulsive non-Gaussian noise with unknown statistics often occurs due to electromagnetic interference and harsh propagation conditions, significantly degrading estimation accuracy and overall system performance. In this context, the maximum correntropy criterion (MCC) has emerged as an attractive solution for robust channel estimation that outperforms state-of-the-art algorithms. However, the MCC-based algorithm’s performance is sensitive to the tuning of hyperparameters, which is challenging in the presence of non-Gaussian noise, such as impulsive noise (IN). Furthermore, a recent genre of kernel width sampling methods makes MCC hyperparameter-free and allows for asymptotic convergence to the squared-error performance of MCC with the ideal kernel width. To ensure their practical applicability, convergence analysis is essential to theoretically guarantee stability and performance under various IN scenarios. This study presents convergence analysis of hyperparameter-free MCC-based channel estimation for mmWave MIMO systems considering various IN scenarios. To validate the theoretical analysis, simulations are conducted on practical mmWave MIMO system models. Simulation results closely match the analytical findings, which confirms the accuracy and effectiveness of the analysis we here present.

In vehicle lateral stability control, accurately estimating the vehicle’s lateral state is crucial. Vehicle state estimation is influenced by model accuracy, filter algorithms, and sensor accuracy, which are typically assumed to be affected by Gaussian noise. However, non-Gaussian noise often interferes with sensors in actual driving conditions, leading to decreased estimation accuracy and affecting subsequent stability analysis and control research. Traditional Kalman filters exhibit low accuracy and robustness under non-Gaussian noise conditions. This paper proposes the Maximum Correntropy Criterion Square Root Cubature Kalman Filter algorithm (MCCSCKF). By fusing signals from multiple vehicle sensors, the MCCSCKF processes non-Gaussian noise using the Maximum Correntropy Criterion and integrates it with the Square Root Cubature Kalman Filter to estimate the sideslip angle and yaw rate. The accuracy and robustness of the MCCSCKF algorithm are verified through comparisons with traditional Kalman filter variants under double-shift conditions at high-speed, low-adhesion, and fishhook conditions at medium-speed, low-adhesion in the MATLAB/Simulink co-simulation platform. Under high-speed conditions, the maximum estimation error of the sideslip angle using MCCSCKF is 0.003 rad, with a root mean square error (RMSE) reduction of 38.8%, significantly better than the UKF’s 90.5%. Under medium-speed conditions, the maximum sideslip angle error is 0.002 rad, with an RMSE of 12.2%. Finally, in real-vehicle tests using the VBOX-3iSL, the maximum sideslip angle error of the MCCSCKF is 0.0025 rad, with an RMSE of 9.7%, representing a 20.5% reduction compared to the SCKF, validating its superiority and robustness.

A soft parameter function penalized normalized maximum correntropy criterion (SPF-NMCC) algorithm is proposed for sparse system identification. The proposed SPF-NMCC algorithm is derived on the basis of the normalized adaptive filter theory, the maximum correntropy criterion (MCC) algorithm and zero-attracting techniques. A soft parameter function is incorporated into the cost function of the traditional normalized MCC (NMCC) algorithm to exploit the sparsity properties of the sparse signals. The proposed SPF-NMCC algorithm is mathematically derived in detail. As a result, the proposed SPF-NMCC algorithm can provide an efficient zero attractor term to effectively attract the zero taps and near-zero coefficients to zero, and, hence, it can speed up the convergence. Furthermore, the estimation behaviors are obtained by estimating a sparse system and a sparse acoustic echo channel. Computer simulation results indicate that the proposed SPF-NMCC algorithm can achieve a better performance in comparison with the MCC, NMCC, LMS (least mean square) algorithms and their zero attraction forms in terms of both convergence speed and steady-state performance.

Maximum correntropy criterion (MCC) based adaptive filters are found to be robust against impulsive interference. This paper proposes a novel MCC based adaptive filter with variable step size in order to obtain improved performance in terms of both convergence rate and steady state error with robustness against impulsive interference. The optimal variable step size is obtained by minimizing the Mean Square Deviation (MSD) error from one iteration to the other. Simulation results in the context of a highly impulsive system identification scenario show that the proposed algorithm has faster convergence and lesser steady state error than the conventional MCC based adaptive filters.

Unsupervised feature learning with deep networks has been widely studied in the recent years. Despite the progress, most existing models would be fragile to non-Gaussian noises and outliers due to the criterion of mean square error (MSE). In this paper, we propose a robust stacked autoencoder (R-SAE) based on maximum correntropy criterion (MCC) to deal with the data containing non-Gaussian noises and outliers. By replacing MSE with MCC, the anti-noise ability of stacked autoencoder is improved. The proposed method is evaluated using the MNIST benchmark dataset. Experimental results show that, compared with the ordinary stacked autoencoder, the R-SAE improves classification accuracy by 14% and reduces the reconstruction error by 39%, which demonstrates that R-SAE is capable of learning robust features on noisy data.

To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.

Autonomous Underwater Vehicles (AUVs) need accurate navigation and positioning data to carry out their operations in challenging marine environments. However, non-Gaussian environmental noise and sensor outliers in underwater environments degrade the positioning accuracy and stability of traditional algorithms. In such circumstances, the typical Unscented Kalman Filter (UKF) performs worse according to the Minimum Mean Square Error (MMSE) criteria. To reduce non-Gaussian environmental disturbances, a Maximum Correntropy Criterion (MCC) is created. This study extends the MCUKF by utilizing a mixture correntropy framework and an effective iterative optimization technique, and an improved Sage-Husa filtering mechanism is integrated into the iterative algorithm to address time-varying noise dynamics in complex scenarios. These changes increase the algorithm's resilience and flexibility in demanding underwater conditions. The algorithm's capability is confirmed using simulation and sea experiments, which show notable gains in Root Mean Square Error and navigation accuracy. Experimental results show that the proposed method outperforms other existing algorithms in terms of navigation accuracy performance in our simulations and experiments. To guarantee algorithm performance and resilience for the non-Gaussian time-varying measurement noise issue that AUVs encounter in intricate maritime settings, and to additionally enhance the precision and dependability of localization, this study uses the MCC-UKF to combat the environment's non-Gaussian noise, and the Levenberg-Marguardt iterative method to improve reliability of numbers and estimation precision, while the Maximum Mixture Correntropy Criterion (MMCC) serves the purpose of improve the filter flexibility and convergence speed, and finally, the improved Sage-Husa algorithm is combined to improve the robustness to time-varying noise. The following are the study's primary contributions. (1) In our study, we suggest an enhanced UKF algorithm that combines the MCC and iterated cost function, and adopt a Levenberg-Marquardt optimization strategy to accelerate the convergence. The mixture correntropy criterion was added in the construction of the LMIMC-UKF framework in order to achieve the synergistic enhancement of convergence performance and calculate accuracy. (2) Targeting the issue of time-varying environment noise interference, a fusion approach of iterative tuning and improved Sage-Husa filtering is suggested to achieve the systematic improvement of algorithm robustness. (3) By combining the Monte Carlo simulation with maritime measurement data, the algorithm's technical viability is confirmed, and the parameter sensitivity is quantitatively examined by methodical simulation tests. According to the results, the suggested algorithm performs noticeably better than the current maximum correntropy filtering techniques in terms of anti-interference capability, iteration speed, and navigation accuracy.

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.

In the underwater domain where Autonomous Underwater Vehicles (AUVs) operate, measurements may suffer from the impact of outliers and non-Gaussian noise. These factors can potentially undermine the efficacy of integrated navigation algorithms. The Maximum Correntropy Criterion (MCC) can be utilized to enhance the robustness of AUV integrated navigation algorithms through the construction and maximization of the correntropy function. Notwithstanding, the underwater environment occasionally presents unknown time-varying noise, a situation for which the MCC lacks adaptability. In response to this issue, our study introduces a novel integrated navigation algorithm that synergizes the MCC and the Variational Bayesian approach, thereby augmenting both the robustness and adaptability of the system. Initially, we implement the MCC along with a mixture kernel function in an Unscented Kalman Filter (UKF) to strengthen the robustness of the AUV integrated navigation algorithms amidst the complexities inherent to underwater environmental conditions. Additionally, we utilize the Variational Bayesian method to refine the approximation of measurement noise covariance, thereby boosting the algorithm’s adaptability to fluctuating scenarios. We evaluate the performance of our proposed algorithm using both simulation and sea trial datasets. The experimental results reveal a significant enhancement in the Root Mean Square Error (RMSE) and navigation accuracy of our proposed algorithm. Notably, in a complex noise environment, our algorithm achieves, approximately, a 50% improvement in navigation accuracy over other established algorithms.

A blocked proportionate normalized maximum correntropy criterion (PNMCC) is presented to improve the estimation behavior of the traditional maximum correntropy criterion (MCC) algorithm for identifying the blocked sparse systems. The proposed blocked MCC is implemented by constructing a new cost function based on a hybrid-norm constraint (HNC) of the filter coefficient vector to adaptively utilize the cluster-sparse characteristic of unknown systems, denoting as hybrid-norm constrained PNMCC (HNC-PNMCC). The proposed HNC-PNMCC algorithm is achieved by using the basis pursuit. Various simulations are brought out to confirm the validity of the HNC-PNMCC. Simulation results indicate that the HNC-PNMCC is better than the PNMCC, MCC, and sparse MCC with respect to the estimation performance for the cluster-sparse system identification under the impulsive noises.

In this paper, an adaptive and robust Kalman filter algorithm based on the maximum correntropy criterion (MCC) is proposed to solve the problem of integrated navigation accuracy reduction, which is caused by the non-Gaussian noise and time-varying noise of GPS measurement in complex environment. Firstly, the Grubbs criterion was used to remove outliers, which are contained in the GPS measurement. Then, a fixed-length sliding window was used to estimate the decay factor adaptively. Based on the fixed-length sliding window method, the time-varying noises, which are considered in integrated navigation system, are addressed. Moreover, a MCC method is used to suppress the non-Gaussian noises, which are generated with external corruption. Finally, the method, which is proposed in this paper, is verified by the designed simulation and field tests. The results show that the influence of the non-Gaussian noise and time-varying noise of the GPS measurement is detected and isolated by the proposed algorithm, effectively. The navigation accuracy and stability are improved.

The maximum correntropy criterion (MCC) algorithm has attracted much attention due to its capability of combating impulsive noise. However, its performance depends on choice of the kernel width, which is a hard issue. Several variable kernel width schemes based on various error functions have been proposed to address this problem. Nevertheless, these methods may not provide an optimal kernel width because they do not contain any knowledge of the background noise that actually has influence on the optimization of the kernel width. This brief proposes an improved variable kernel width MCC algorithm, which is derived by minimizing the squared deviation at each iteration. We also design a reset mechanism for the proposed algorithm to improve its tracking capability when the estimated vector encounters a sudden change. Simulations for system identification and echo cancellation scenarios show that the proposed scheme outperforms other variable kernel width algorithms.

Non-orthogonal multiple access (NOMA) has emerged as a promising multiple-access technique capable of accommodating many users over limited time-frequency resources. Among several NOMA techniques, sparse code multiple access (SCMA) has emerged as viable due to its promise of high coding-gain by appropriate codebook-design and simplistic detection using message-passing algorithm (MPA). However, the performance of classic SCMA based systems are severely impaired by impulsive noise (IN), which causes outages and therefore non-negligible degradations to the bit-error-rate (BER) performance. Exploiting the robustness of the maximum correntropy criterion (MCC) to non-Gaussian noise processes, an MPA based detector is formulated with message-functions derived from the MCC criterion. Based on the said MCC criterion, concurrent-adaptation of the MCC’s spread-parameter is proposed in this letter. Lastly, analytical results for the proposed approach’s BER performance are presented with corresponding validation by computer-simulations.

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.