Maximum Correntropy Criterion Research Articles

A Distributed Robust System-Wide State Estimation Method for Power Systems Based on Maximum Correntropy

The distribution of measurement noise applied in practical power system state estimation (PSSE) can deviate from the assumed Gaussian model and the performance of an estimator becomes bad if the Gaussian model is still used. This paper proposes a new distributed robust PSSE method for multi-area power systems. The non-Gaussian model is utilized to fit the measurement noise distribution to reach high model accuracy. The proposed distributed method is derived based on the maximum correntropy criterion to further reduce the impact of non-Gaussian measurement noise and outliers. The influence function combined with the finite-time average consensus algorithm is used to implement the proposed distributed robust method in a fully distributed manner. Simulations conducted on the IEEE 30-bus, 118-bus and 300-bus systems and the Polish 2383-bus system demonstrate the robustness and effectiveness of the proposed distributed method. Each local area can get the system-wide robust state estimation solution by only using local information and small amounts of data from neighboring areas. Our proposed distributed robust method has at least twelve percent improvement in reducing the mean squared error under Gaussian-Uniform noise. It is verified the communication network applied for the proposed method is fairly flexible while the existing distributed approaches use a fixed communication network when the power systems are partitioned. The simulation results also verify the robustness of the proposed method to bad data and communication failure.

Filtering in Triplet Markov Chain Model in the Presence of Non-Gaussian Noise with Application to Target Tracking

In hidden Markov chain (HMC) models, widely used for target tracking, the process noise and measurement noise are in general assumed to be independent and Gaussian for mathematical simplicity. However, the independence and Gaussian assumptions do not always hold in practice. For instance, in a typical radar tracking application, the measurement noise is correlated over time as the sampling frequency of a radar is generally much higher than the bandwidth of the measurement noise. In addition, target maneuvers and measurement outliers imply that the process noise and measurement noise are non-Gaussian. To solve this problem, we resort to triplet Markov chain (TMC) models to describe stochastic systems with correlated noise and derive a new filter under the maximum correntropy criterion to deal with non-Gaussian noise. By stacking the state vector, measurement vector, and auxiliary vector into a triplet state vector, the TMC model can capture the complete dynamics of stochastic systems, which may be subjected to potential parameter uncertainty, non-stationarity, or error sources. Correntropy is used to measure the similarity of two random variables; unlike the commonly used minimum mean square error criterion, which uses only second-order statistics, correntropy uses second-order and higher-order information, and is more suitable for systems in the presence of non-Gaussian noise, particularly some heavy-tailed noise disturbances. Furthermore, to reduce the influence of round-off errors, a square-root implementation of the new filter is provided using QR decomposition. Instead of the full covariance matrices, corresponding Cholesky factors are recursively calculated in the square-root filtering algorithm. This is more numerically stable for ill-conditioned problems compared to the conventional filter. Finally, the effectiveness of the proposed algorithms is illustrated via three numerical examples.

Robust transformer-based anomaly detection for nuclear power data using maximum correntropy criterion

Due to increasing operational security demands, digital and intelligent condition monitoring of nuclear power plants is becoming more significant. However, establishing an accurate and effective anomaly detection model is still challenging. This is mainly because of data characteristics of nuclear power data, including the lack of clear class labels combined with frequent interference from outliers and anomalies. In this paper, we introduce a Transformer-based unsupervised model for anomaly detection of nuclear power data, a modified loss function based on the maximum correntropy criterion (MCC) is applied in the model training to improve the robustness. Experimental results on simulation datasets demonstrate that the proposed Trans-MCC model achieves equivalent or superior detection performance to the baseline models, and the use of the MCC loss function is proven can obviously alleviate the negative effect of outliers and anomalies in the training procedure, the F1 score is improved by up to 0.31 compared to Trans-MSE on a specific dataset. Further studies on genuine nuclear power data have verified the model's capability to detect anomalies at an earlier stage, which is significant to condition monitoring.

A Robust GPS Navigation Filter Based on Maximum Correntropy Criterion with Adaptive Kernel Bandwidth

Multiple forms of interference and noise that impact the receiver’s capacity to receive and interpret satellite signals, and consequently the preciseness of positioning and navigation, may be present during the processing of Global Positioning System (GPS) navigation. The non-Gaussian noise predominates in the signal owing to the fluctuating character of both natural and artificial electromagnetic interference, and the algorithm based on the minimum mean-square error (MMSE) criterion performs well when assuming Gaussian noise, but drops when assuming non-Gaussian noise. The maximum correntropy criteria (MCC) adaptive filtering technique efficiently reduces pulse noise and has adequate performance in heavy-tailed noise, which addresses the issue of filter performance caused by the presence of non-Gaussian or heavy-tailed unusual noise values in the localizing measurement noise. The adaptive kernel bandwidth (AKB) technique employed in this paper applies the calculated adaptive variables to generate the kernel function matrix, in which the adaptive factor can modify the size of the kernel width across a reasonably appropriate spectrum, substituting the fixed kernel width for the conventional MCC to enhance the performance. The conventional maximum correntropy criterion-based extended Kalman filter (MCCEKF) algorithm’s performance is significantly impacted by the value of the kernel width, and there are certain predetermined conditions in the selection based on experience. The MCCEKF with a fixed adaptive kernel bandwidth (MCCEKF-AKB) has several advantages due to its novel concept and computational simplicity, and gives a qualitative solution for the study of random structures for generalized noise. Additionally, it can effectively achieve the robust state estimation of outliers with anomalous values while guaranteeing the accuracy of the filtering.

New robust state‐estimation frameworks for angles‐only underwater target tracking problems

SummaryTracking a moving target using only angle measurements is a challenging and complex problem. This is because the measurements received from a sensor on a moving observer provide very little information about the target's movements. Additionally, there are uncertainties regarding the target's initial range and speed, which can further complicate the estimation process. The angle measurements themselves carry a lot of uncertainties as they can be affected by significant outliers, which do not fit the standard Gaussian distribution that estimation algorithms typically assume. Furthermore, the observer's position can also be uncertain due to various environmental factors. To address these challenges and to propose a robust, unified and accurate solution, two new estimation frameworks are proposed. They involve making use of a range and speed parametrization approach to compensate for the initial uncertainty in the target's range and speed. They also involve using a maximum correntropy (MC) criterion and a numerically stable centered error entropy (CEE) criterion to deal with measurement outliers and the observer motion uncertainties. The performance of the proposed frameworks is evaluated by comparing them to the traditional unscented Kalman filter (UKF) and its parametrized versions using different performance metrics. The simulations conducted showed that the developed algorithms perform better in terms of estimation accuracy than conventional methods. Specifically, the second framework based on the CEE criterion outperformed MC‐based estimators.

Nonlinear active noise control with tap-decomposed robust volterra filter

The Volterra filter is proven to be a structurally simple method for nonlinear active noise control (NLANC). However, its wide application is deeply constrained by computational complexity. This paper proposes a tap-decomposed Volterra filter, in which a long-tap Volterra filter is approximated as multiple short-tap filters by the nearest Kronecker decomposition. Since the number of taps of decomposed filters is much less than that of the original counterpart, the proposed method greatly reduces the implementation cost of the Volterra filter. Moreover, for impulsive noise sources in NLANC, decomposed filters are updated using the maximum correntropy criterion derived from information theory. Simulation experiments with different noise source types highlight the noise control performance of the proposed approach.

Sparsity-Constrained Kernel Generalized Maximum Versoria Criterion With Variable Center

Sparsity-aware kernel adaptive filtering algorithms using maximum correntropy criterion (MCC) and maximum Versoria criterion (MVC) have emerged as a promising candidate for nonlinear sparse parameter estimation under non-Gaussian distortions. However, the existing zero-attracting (ZA) kernel-MCC (ZA-KMCC) and ZA-kernel-MVC (ZA-KMVC) algorithms deliver suboptimal performance for non-zero-mean noise distributions due to the fixed center located at origin. In this brief, first we propose a novel generalized MVC with variable center (GMVC-VC) based learning paradigm by introducing a center at any location, which consists of higher order central moments of error. Next, we propose a novel generalized Versoria zero-attracting kernel GMVC-VC (GVZA-KGMVC-VC) algorithm, which is robust for nonlinear sparse systems under non-Gaussian noise having non-zero-mean. Furthermore, the detailed convergence analysis in both mean and mean-square sense is performed for the proposed algorithm. Simulations demonstrate that the proposed GVZA-KGMVC-VC approach delivers lower mean square deviation over the existing state-of-art benchmarks.

An anti-noise algorithm based on locally linear embedding and weighted XGBoost for fault diagnosis of T/R module

Due to the noise accompanied with fault signals, it is challenging to identify the discriminant information and the local geometric feature from the complex fault data for enhancing fault diagnosis accuracy. To address this challenge, this work proposed an anti-noise algorithm based on locally linear embedding integrated with diffusion distance and maximum correntropy criterion (DMLLE). In DMLLE, diffusion distance was adopted instead of the Euclidean distance for neighborhood construction. Meanwhile, the optimal weights were updated to reveal local geometry information based on the loss function of the maximum correntropy criterion. Subsequently, DMLLE is eventually developed to further restrain noise embedding into raw signals and obtain low dimensional features. Furthermore, weighted extreme gradient boosting is used to map the low dimensional features to the types of faults, which easily implements fault pattern recognition. Finally, two synthetic manifold datasets and fault data acquired from the transmit/receive (T/R) module are used to validate the performance of the proposed diagnosis methodology. Compared with the existing methods, the proposed diagnosis methodology generates a smoother flow structure by preserving the local neighborhood of the dataset with noises and realizes a higher accuracy of 94.41% on the T/R module dataset, which outperforms 3%–9% better than other classification models. Therefore, it can be concluded that the proposed diagnosis methodology can effectively extract intrinsic fault features by weakening the influence aroused by noise and achieve superior accuracy in fault diagnosis by addressing the problem of small sample size.

An outlier-robust Rao–Blackwellized particle filter for underwater terrain-aided navigation

Terrain-aided navigation (TAN) is one of the key techniques for autonomous navigation and positioning of AUVs. This paper develops a novel integrated navigation system that combines the inertial navigation system (INS) and TAN into one filter, in contrast to the conventional INS/TAN model. This method not only provides a position estimate for the carrier but also the INS error, which increases the filtering dimension significantly. Thus, the Rao-Blackwellized particle filter (RBPF) technique is introduced to address the “dimensional disaster” problem. A three-dimensional (3-D) model is established to estimate the horizontal position while compensating for the tidal inaccuracy by extending the tidal depth bias to the state space. Furthermore, the variable and complex underwater environment can potentially result in outlier interference in depth measurements, which significantly degrades the performance of the RBPF-based estimation algorithm. This paper thus presents a 3-D adaptive RBPF method based on the maximum correntropy criterion (MCC) to suppress the influence of measurement outliers on positioning precision. Simulations and experimental tests verify the effectiveness of the proposed algorithm. The results demonstrated that the 3-D model-based AMCCRBPF method can effectively improve robustness to outliers and provide an accurate estimate of the tidal depth bias.

Generalized kernel maximum correntropy criterion with variable center: Formulation and performance analysis

Recently, the kernel adaptive filtering algorithm with the generalized maximum correntropy criterion (GMCC) has gained attention due to its excellent nonlinear system modeling ability and robustness to non-Gaussian noise. However, since the default center of the GMCC is located at zero, it hampers its performance in the non-zero mean noise environment. To overcome the problem, this paper proposes a kernel adaptive filtering algorithm based on the GMCC with variable center (GMCC-VC) called generalized kernel maximum correntropy criterion with variable center (GKMCC-VC). In addition, the online vector quantization (VQ) method is introduced to the GKMCC-VC algorithm for suppressing the increasing network size. The probability of divergence, the mean-square steady-state behavior, and the convergence condition of the GKMCC-VC algorithm are also obtained under some assumptions. The potential relationship between the GMCC-VC and the generalized minimum error entropy (GMEE) criteria is discussed in the paper. Finally, the simulation results verify the superiority of the proposed algorithm in modeling nonlinear systems and the correctness of the theoretical model.

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.

Multiple similarity measure-based maximum correntropy criterion Kalman filter with adaptive kernel width for GPS/INS integration navigation

The filter based on the maximum correntropy criterion (MCC) has low sensitivity to non-Gaussian noise, which can effectively improve the robustness of the filter. However, the uncertainty of kernel width restricted the application of the maximum correntropy criterion Kalman filter (MCCKF) in the integrated navigation system. In order to overcome the above difficulty, this paper proposes a multiple similarity measure-based maximum correntropy criterion Kalman filter with adaptive kernel width (ABMCCKF). ABMCCKF uses the MORKF framework and distinguishes the noise polluted by outliers through a designed protecting window, which also ensures that the kernel width is compatible with the noise pollution level. Through the window, ABMCCKF utilizes the optimality of both MCC and the minimum mean square error criterion (MMSE). Simulations and vehicular experiments are used to verify the effectiveness of the method. The results show that the ABMCCKF have a good performance when the optimal kernel width is uncertain.

Adaptive filtering under multi-peak noise

In this paper, we assume the multi-peak noise in adaptive filtering follows a multimodal probability distribution (MPD), and model it as a Gaussian mixture model (GMM). Then a new gradient ascent algorithm is proposed based on the maximum likelihood function. Under the MPD assumption, multiple means and variances of the modes can be estimated by the expectation-maximization (EM) algorithm, and a corresponding closed-form solution can be obtained. Since the GMM can exactly approximate multi-peak probability density function (PDF), the closed-form solution of the proposed MPD algorithm can approximate the optimal solution of the adaptive filtering problem under multi-peak additive noise. According to the interaction between the distance and magnitudes of adjacent peaks, multi-peak noise can be divided into significant multi-peak (SMP) noise, hidden multi-peak (HMP) noise (e.g., Rayleigh), and invisible multi-peak (IMP) noise (e.g., Uniform). Simulations demonstrate that the proposed MPD algorithm outperforms the maximum correntropy criterion (MCC) and minimum error entropy (MEE) under SMP and HMP noise, and outperforms the least mean fourth (LMF) under IMP noise. The experimental steady-state errors align well with the theoretical values.

Hierarchical One-Class Model With Subnetwork for Representation Learning and Outlier Detection.

The multilayer one-class classification (OCC) frameworks have gained great traction in research on anomaly and outlier detection. However, most multilayer OCC algorithms suffer from loosely connected feature coding, affecting the ability of generated latent space to properly generate a highly discriminative representation between object classes. To alleviate this deficiency, two novel OCC frameworks, namely: 1) OCC structure using the subnetwork neural network (OC-SNN) and 2) maximum correntropy-based OC-SNN (MCOC-SNN), are proposed in this article. The novelties of this article are as follows: 1) the subnetwork is used to build the discriminative latent space; 2) the proposed models are one-step learning networks, instead of stacking feature learning blocks and final classification layer to recognize the input pattern; 3) unlike existing works which utilize mean square error (MSE) to learn low-dimensional features, the MCOC-SNN uses maximum correntropy criterion (MCC) for discriminative feature encoding; and 4) a brand-new OCC dataset, called CO-Mask, is built for this research. Experimental results on the visual classification domain with a varying number of training samples from 6131 to 513 061 demonstrate that the proposed OC-SNN and MCOC-SNN achieve superior performance compared to the existing multilayer OCC models. For reproducibility, the source codes are available at https://github.com/W1AE/OCC.

AMCC-Based Power Management Scheme With Full Ancillary Services Support for a Wind–Solar Renewable Power Generation System

This paper introduces a power management scheme (PMS) for an integrated wind-solar renewable power generation system (RPGS). The PMS takes advantage of time of use electricity pricing mechanism to manage the net power exchange between the grid and the RPGS. A battery energy storage (BES) is utilized for enabling the system price arbitrage functionality. Meanwhile, the system control is performed through a novel application of the adaptive kernel width maximum correntropy criterion (AMCC) strategy. Apart from utilizing the electricity price volatility to maximize returns, the RPGS is also equipped to offer ancillary services support to the utility grid in the form of, (i) grid reactive current injection considering system constraints and (ii) grid power quality conditioning through local compensation of load reactive power, harmonics and unbalance. Moreover, for reduced system losses and minimized ripples in the grid currents amidst variations in grid voltages, a self-adjustable DC voltage reference technique is accommodated in the control strategy. An RPGS, employing a solar photovoltaic array and a doubly-fed induction generator for wind power generation, is utilized to experimentally demonstrate the effective operation of the overall control strategy.

Jointly Distributed Filtering Based on Generalized Maximum Correntropy Criterion: Memory-Based Event-Triggered Cases

This article addresses jointly distributed entropy filtering issues based on the generalized maximum correntropy criterion (GMCC) for discrete-time stochastic parameter systems with fault and non-Gaussian noise effects. By taking current and historical triggered information, a memory-based event-triggered scheme with a time-varying threshold is put forward to govern the network communication. According to the constructed jointly distributed entropy filter with a two-step form, the upper bounds of the filtering error covariance matrices are derived and an ideal filter gain is obtained to maximize GMCC. Furthermore, an accessible gain is received via fixed-point iterative rules and the corresponding convergence is disclosed in theory. Finally, an application of the proposed distributed filter in ballistic object tracking is provided to show its effectiveness under non-Gaussian environments.

Application of Adaptive Robust Kalman Filter Base on MCC for SINS/GPS Integrated Navigation.

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.

An improved multi-state constraint kalman filter based on maximum correntropy criterion

In recent years, the multi-state constraint Kalman filter has been widely used in the visual-inertial navigation of unmanned systems. However, in most previous studies, the measurement noise of the navigation system was assumed to be Gaussian noise, but this is not the case in practice. In this paper, the maximum correntropy criterion is introduced into the multi-state constraint Kalman filter to improve the robustness of the visual-inertial system. First, the new maximum correntropy criterion-based Kalman filter is introduced, it uses the maximum correntropy criterion to replace the minimum mean square error criterion to suppress the interference of measurement outliers on the filtering results, and it has no numerical problem in the presence of large measurements outliers. Then, an improved multi-state constraint Kalman filter is designed by applying the new maximum correntropy criterion-based Kalman filter to the multi-state constraint Kalman filter, which improved the robustness of the multi-state constraint Kalman filter. The results of numerical simulation and dataset experiments show that the proposed filter improves the accuracy and robustness of the visual-inertial system.

Weighted Maximum Correntropy Criterion-Based Interacting Multiple-Model Filter for Maneuvering Target Tracking

During the process of maneuvering target tracking, the measurement may be disturbed by outliers, which leads to a decrease in the state estimation performance of the classic interacting multiple-model (IMM) filter. To solve this problem, a weighted maximum correntropy criterion (WMCC)-based IMM filter is proposed. In the proposed filter, the fusion state is used as the input of each sub-model to reduce the computational complexity of state interaction and the WMCC is adopted to derive the sub-model state update and state fusion to improve the state estimation performance under outlier interference. Through principal analysis, the superiority of the proposed filter over the classic IMM filter in fusion strategy is revealed. The specific form of the proposed filter in radar maneuvering target tracking is provided. Two experimental cases of maneuvering target tracking are tested to illustrate the effectiveness of the proposed filter.

Enhanced state of charge estimation for Li-ion batteries through adaptive maximum correntropy Kalman filter with open circuit voltage correction

Due to the possible interference of non-Gaussian noise in Li-ion battery management systems, there is no guarantee of reliable accuracy when using the extended Kalman filter (EKF) algorithm for battery state of charge (SOC) estimation. A novel EKF algorithm based on the adaptive maximum correntropy criterion (AMCCEKF) is proposed to enhance the robustness of SOC estimation in the paper. The Gaussian kernel function is chosen as the cost function to reconstruct the state error variance and the measurement noise variance. And a kernel width adaptive update strategy is designed to address the constraints of fixed kernel width on SOC estimation performance. In addition, an open circuit voltage (OCV) correction strategy based on terminal voltage innovation and OCV-SOC curve gradient is designed to reduce the impact of OCV error caused by non-Gaussian noise on SOC estimation. Incorporating the AMCCEKF method and the OCV correction strategy, a novel estimation method based on the dOCV-AMCCEKF is offered to perform the SOC estimation. Simulation results under different operating conditions and temperatures show that the maximum absolute error of the dOCV-AMCCEKF method is close to 0.5%, which verifies it can reduce the SOC estimation error in a non-Gaussian noisy interference environment compared with the EKF based method.