Regularized Maximum Correntropy Criterion Kalman Filter for Uncalibrated Visual Servoing in the Presence of Non-Gaussian Feature Tracking Noise

Some advantages of using cameras as sensor devices on feedback systems are the flexibility of the data it represents, the possibility to extract real-time information, and the fact that it does not require contact to operate. However, in unstructured scenarios, Image-Based Visual Servoing (IBVS) robot tasks are challenging. Camera calibration and robot kinematics can approximate a jacobian that maps the image features space to the robot actuation space, but they can become error-prone or require online changes. Uncalibrated visual servoing (UVS) aims at executing visual servoing tasks without previous camera calibration or through camera model uncertainties. One way to accomplish that is through jacobian identification using environment information in an estimator, such as the Kalman filter. The Kalman filter is optimal with Gaussian noise, but unstructured environments may present target occlusion, reflection, and other characteristics that confuse feature extraction algorithms, generating outliers. This work proposes RMCKF, a correntropy-induced estimator based on the Kalman Filter and the Maximum Correntropy Criterion that can handle non-Gaussian feature extraction noise. Unlike other approaches, we designed RMCKF for particularities in UVS, to deal with independent features, the IBVS control action, and simulated annealing. We designed Monte Carlo experiments to test RMCKF with non-Gaussian Kalman Filter-based techniques. The results showed that the proposed technique could outperform its relatives, especially in impulsive noise scenarios and various starting configurations.

Student's t-Kernel-Based Maximum Correntropy Kalman Filter

The state estimation problem is ubiquitous in many fields, and the common state estimation method is the Kalman filter. However, the Kalman filter is based on the mean square error criterion, which can only capture the second-order statistics of the noise and is sensitive to large outliers. In many areas of engineering, the noise may be non-Gaussian and outliers may arise naturally. Therefore, the performance of the Kalman filter may deteriorate significantly in non-Gaussian noise environments. To improve the accuracy of the state estimation in this case, a novel filter named Student’s t kernel-based maximum correntropy Kalman filter is proposed in this paper. In addition, considering that the fixed-point iteration method is used to solve the optimal estimated state in the filtering algorithm, the convergence of the algorithm is also analyzed. Finally, comparative simulations are conducted and the results demonstrate that with the proper parameters of the kernel function, the proposed filter outperforms the other conventional filters, such as the Kalman filter, Huber-based filter, and maximum correntropy Kalman filter.

Newtonian-Type Adaptive Filtering Based on the Maximum Correntropy Criterion

This paper provides a novel Newtonian-type optimization method for robust adaptive filtering inspired by information theory learning. With the traditional minimum mean square error (MMSE) criterion replaced by criteria like the maximum correntropy criterion (MCC) or generalized maximum correntropy criterion (GMCC), adaptive filters assign less emphasis on the outlier data, thus become more robust against impulsive noises. The optimization methods adopted in current MCC-based LMS-type and RLS-type adaptive filters are gradient descent method and fixed point iteration, respectively. However, in this paper, a Newtonian-type method is introduced as a novel method for enhancing the existing body of knowledge of MCC-based adaptive filtering and providing a fast convergence rate. Theoretical analysis of the steady-state performance of the algorithm is carried out and verified by simulations. The experimental results show that, compared to the conventional MCC adaptive filter, the MCC-based Newtonian-type method converges faster and still maintains a good steady-state performance under impulsive noise. The practicability of the algorithm is also verified in the experiment of acoustic echo cancellation.

Online Gradient Descent for Kernel-Based Maximum Correntropy Criterion

In the framework of statistical learning, we study the online gradient descent algorithm generated by the correntropy-induced losses in Reproducing kernel Hilbert spaces (RKHS). As a generalized correlation measurement, correntropy has been widely applied in practice, owing to its prominent merits on robustness. Although the online gradient descent method is an efficient way to deal with the maximum correntropy criterion (MCC) in non-parameter estimation, there has been no consistency in analysis or rigorous error bounds. We provide a theoretical understanding of the online algorithm for MCC, and show that, with a suitable chosen scaling parameter, its convergence rate can be min-max optimal (up to a logarithmic factor) in the regression analysis. Our results show that the scaling parameter plays an essential role in both robustness and consistency.

A Correntropy-Based Proportionate Affine Projection Algorithm for Estimating Sparse Channels with Impulsive Noise

A novel robust proportionate affine projection (AP) algorithm is devised for estimating sparse channels, which often occur in network echo and wireless communication channels. The newly proposed algorithm is realized by using the maximum correntropy criterion (MCC) and the data reusing scheme used in AP to overcome the identification performance degradation of the traditional PAP algorithm in impulsive noise environments. The proposed algorithm is referred to as the proportionate affine projection maximum correntropy criterion (PAPMCC) algorithm, which is derived in the context of channel estimation framework. Many simulation results were obtained to verify that the PAPMCC algorithm is superior to early reported AP algorithms with different input signals under impulsive noise environments.

Robust Variable Selection and Estimation Based on Kernel Modal Regression

Model-free variable selection has attracted increasing interest recently due to its flexibility in algorithmic design and outstanding performance in real-world applications. However, most of the existing statistical methods are formulated under the mean square error (MSE) criterion, and susceptible to non-Gaussian noise and outliers. As the MSE criterion requires the data to satisfy Gaussian noise condition, it potentially hampers the effectiveness of model-free methods in complex circumstances. To circumvent this issue, we present a new model-free variable selection algorithm by integrating kernel modal regression and gradient-based variable identification together. The derived modal regression estimator is related closely to information theoretic learning under the maximum correntropy criterion, and assures algorithmic robustness to complex noise by replacing learning of the conditional mean with the conditional mode. The gradient information of estimator offers a model-free metric to screen the key variables. In theory, we investigate the theoretical foundations of our new model on generalization-bound and variable selection consistency. In applications, the effectiveness of the proposed method is verified by data experiments.

Maximum Correntropy Based Unscented Particle Filter for Cooperative Navigation with Heavy-Tailed Measurement Noises

In this paper, a novel robust particle filter is proposed to address the measurement outliers occurring in the multiple autonomous underwater vehicles (AUVs) based cooperative navigation (CN). As compared with the classic unscented particle filter (UPF) based on Gaussian assumption of measurement noise, the proposed robust particle filter based on the maximum correntropy criterion (MCC) exhibits better robustness against heavy-tailed measurement noises that are often induced by measurement outliers in CN systems. Furthermore, the proposed robust particle filter is computationally much more efficient than existing robust UPF due to the use of a Kullback-Leibler distance-resampling to adjust the number of particles online. Experimental results based on actual lake trial show that the proposed maximum correntropy based unscented particle filter (MCUPF) has better estimation accuracy than existing state-of-the-art robust filters for CN systems with heavy-tailed measurement noises, and the proposed MCUPF has lower computational complexity than existing robust particle filters.

Adaptive Robust Unscented Kalman Filter via Fading Factor and Maximum Correntropy Criterion

In most practical applications, the tracking process needs to update the data constantly. However, outliers may occur frequently in the process of sensors’ data collection and sending, which affects the performance of the system state estimate. In order to suppress the impact of observation outliers in the process of target tracking, a novel filtering algorithm, namely a robust adaptive unscented Kalman filter, is proposed. The cost function of the proposed filtering algorithm is derived based on fading factor and maximum correntropy criterion. In this paper, the derivations of cost function and fading factor are given in detail, which enables the proposed algorithm to be robust. Finally, the simulation results show that the presented algorithm has good performance, and it improves the robustness of a general unscented Kalman filter and solves the problem of outliers in system.

Adaptive Maximum Correntropy Gaussian Filter Based on Variational Bayes

In this paper, we investigate the state estimation of systems with unknown covariance non-Gaussian measurement noise. A novel improved Gaussian filter (GF) is proposed, where the maximum correntropy criterion (MCC) is used to suppress the pollution of non-Gaussian measurement noise and its covariance is online estimated through the variational Bayes (VB) approximation. MCC and VB are integrated through the fixed-point iteration to modify the estimated measurement noise covariance. As a general framework, the proposed algorithm is applicable to both linear and nonlinear systems with different rules being used to calculate the Gaussian integrals. Experimental results show that the proposed algorithm has better estimation accuracy than related robust and adaptive algorithms through a target tracking simulation example and the field test of an INS/DVL integrated navigation system.

Sparse-Aware Bias-Compensated Adaptive Filtering Algorithms Using the Maximum Correntropy Criterion for Sparse System Identification with Noisy Input

To address the sparse system identification problem under noisy input and non-Gaussian output measurement noise, two novel types of sparse bias-compensated normalized maximum correntropy criterion algorithms are developed, which are capable of eliminating the impact of non-Gaussian measurement noise and noisy input. The first is developed by using the correntropy-induced metric as the sparsity penalty constraint, which is a smoothed approximation of the ℓ 0 norm. The second is designed using the proportionate update scheme, which facilitates the close tracking of system parameter change. Simulation results confirm that the proposed algorithms can effectively improve the identification performance compared with other algorithms presented in the literature for the sparse system identification problem.

Electricity Consumption Forecasting Scheme via Improved LSSVM with Maximum Correntropy Criterion

In recent years, with the deepening of China’s electricity sales side reform and electricity market opening up gradually, the forecasting of electricity consumption (FoEC) becomes an extremely important technique for the electricity market. At present, how to forecast the electricity accurately and make an evaluation of results scientifically are still key research topics. In this paper, we propose a novel prediction scheme based on the least-square support vector machine (LSSVM) model with a maximum correntropy criterion (MCC) to forecast the electricity consumption (EC). Firstly, the electricity characteristics of various industries are analyzed to determine the factors that mainly affect the changes in electricity, such as the gross domestic product (GDP), temperature, and so on. Secondly, according to the statistics of the status quo of the small sample data, the LSSVM model is employed as the prediction model. In order to optimize the parameters of the LSSVM model, we further use the local similarity function MCC as the evaluation criterion. Thirdly, we employ the K-fold cross-validation and grid searching methods to improve the learning ability. In the experiments, we have used the EC data of Shaanxi Province in China to evaluate the proposed prediction scheme, and the results show that the proposed prediction scheme outperforms the method based on the traditional LSSVM model.