non-Gaussian Measurement Noise Research Articles

Optimizing kernel width for new risk-sensitive loss: A generalized algorithmic approach

This paper outlines a novel approach to the development of adaptive filtering algorithms, which minimizes susceptibility to the effects of non-Gaussian measurement noise. Using the generalized Gaussian density (GGD) function as the kernel function, we developed a generalized kernel risk-sensitive loss (GKRSL) criterion by which to derive the generalized minimum kernel risk-sensitive loss (GMKRSL) algorithm. We also developed a variable kernel width algorithm for GMKRSL (VKW-GMKRSL) to address the trade-off between convergence rate and steady-state misalignment resulting from a constant kernel width. In simulations, GMKRSL and VKW-GMKRSL outperformed existing works in system identification performance.

Integrated elastic identification and LOS angular rate extraction for slender rockets: A continuous-discrete maximum correntropy Kalman filter approach

Slender rockets experience significant elastic deformation during flight due to aeroelastic forces, impacting their dynamic behavior and posing challenges for traditional line-of-sight (LOS) angular rate estimation methods. This paper addresses this challenge by proposing a novel and highly accurate line-of-sight angular rate extraction model. This model integrates elastic identification with line-of-sight angular rate extraction, employing estimated generalized coordinates to calculate seeker elastic deformation. After elastic decoupling of the seeker, the slender rocket's line-of-sight angular rate can be estimated accurately. Additionally, the model incorporates a continuous-discrete maximum correntropy Kalman filter (CD-MCKF) to effectively handle the non-Gaussian measurement noise and limitations associated with discretizing the continuous model. Simulations demonstrate that the proposed method achieves significantly higher accuracy compared to existing approaches. The improved accuracy of this method can provide more precise calculations for the design of slender rocket guidance and control systems, ultimately improving the flight stability and control accuracy of rockets, and laying a solid foundation for the integrated guidance and control research of slender rockets.

A robust state estimation method for power systems using generalized correntropy loss function

The accurate estimation of power system states is crucial for effective monitoring and control. However, the performance of conventional state estimators, which assume Gaussian measurement noise and do not account for denial-of-service attacks, can deteriorate significantly in real power systems. To address these issues, this paper proposes a novel robust state estimation method based on the quadratic function (QF) and the generalized correntropy loss function (GCL). The proposed QF-GCL state estimation method can effectively deal with non-Gaussian measurement noise and denial-of-service attacks. To enhance the computational efficiency, an influence function based solving method is developed. To determine the optimal parameters for the proposed QF-GCL state estimation method, a new state estimation error covariance equation is further derived. Simulations are performed on the IEEE 30-bus, 118-bus and 300-bus systems, to demonstrate the accurate and robust performance of the proposed QF-GCL robust state estimation method.

Kalman filtering based on dynamic perception of measurement noise

In this work, we focus on the online state estimation problem for linear systems in non-Gaussian measurement noise. Specifically, the measurement noise is modeled as a Gaussian mixture model (GMM). Then, Kalman innovation is used to approximate the current measurement noise, and dynamically perceive its responsiveness to each sub-model of the GMM. The responsiveness from different Gaussian scales is mapped to a new cost function, while the corresponding Kalman filter algorithm is derived. The theoretical steady-state error and computational complexity analysis of the algorithm are also given. The simulation and real experimental results agree with the theoretical predictions and demonstrate the superior performance of the proposed algorithm.

A Novel Hybrid Model Combining Improved VMD and ELM with Extended Maximum Correntropy Criterion for Prediction of Dissolved Gas in Power Transformer Oil

The prediction of dissolved gas change trends in power transformer oil is very important for the diagnosis of transformer faults and ensuring its safe operation. Considering the time series and nonlinear features of the gas change trend, this paper proposes a novel robust extreme learning machine (ELM) model combining an improved data decomposition method for gas content forecasting. Firstly, the original data with nonlinear and sudden change properties will make the forecasting model unstable, and thus an improved variational modal decomposition (IPVMD) method is developed to decompose the original data to obtain the multiple modal dataset, in which the marine predators algorithm (MPA) optimization method is utilized to optimize the free parameters of the VMD. Second, the ELM as an efficient and easily implemented tool is used as the basic model for dissolved gas forecasting. However, the traditional ELM with mean square error (MSE) criterion is sensitive to the non-Gaussian measurement noise (or outliers). In addition, considering the nonlinear non-Gaussian properties of the dissolved gas, a new learning criterion, called extended maximum correntropy criterion (ExMCC), is defined by using an extended kernel function in the correntropy framework, and the ExMCC as a learning criterion is introduced into the ELM to develop a novel robust regression model (called ExMCC-ELM) to improve the ability of ELM to process mutational data. Third, a gas-in-oil prediction scheme is proposed by using the ExMCC-ELM performed on each modal obtained by the proposed IPVMD. Finally, we conducted several simulation studies on the measured data, and the results show that the proposed method has good predictive performance.

Impact of the non-Gaussian measurement noise on the performance of state-of-the-art state estimators for distribution systems

This paper aims to investigate the impact of non-Gaussian measurement noise on state estimation (SE) results in distribution systems. To this end, the measurement noise is assumed to be distributed according to Gaussian or one of the following non-Gaussian probability distribution functions: Uniform, Laplace, Weibull and Gaussian mixture of two Gaussian components. The influence is investigated on three different state-of-the-art SE methods: weighted least squares (WLS) based static SE method, and two Kalman filter based forecasting-aided SE methods, namely extended Kalman filter (EKF) and unscented Kalman filter (UKF). Analyses are conducted on modified IEEE 37-bus system under different operating conditions, including quasi-steady state, sudden state changes and bad data. Performance of the methods in the presence of non-Gaussian measurement noise is compared against their performance when measurement noise is Gaussian distributed. The main conclusions were drawn, summarizing the impacts non-Gaussian measurement noise has on SE and proposing the solutions for overcoming some of the negative impacts.

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.

Cooperative positioning method of underwater autonomous vehicle formation based on extended Kalman filter

Autonomous Underwater Vehicles (UAVs) have shown significant potential application value in marine environmental surveillance, development, and utilization of resources. However, due to the complex underwater acoustic channel environment and the relative motion between AUVs, this may lead to heavy-tailed non-Gaussian process noise and measurement noise, leading to increased error and the Extended Kalman Filter (EKF) may fail. In prior studies, we propose a multi-AUV formation hierarchical target location algorithm based on the EKF, which can realize multi-AUV self-localization and stationary target localization. The AUV formation consists of one high-precision piloting AUV and several low-precision following AUVs. The following AUVs are divided into two levels, the reference AUVs and the AUVs to be tested. According to the designed positioning period, the reference AUV receives the position parameters from a high-precision piloting AUV and transmits its own position parameters to the AUV to be measured. Then use the EKF to complete the cooperative position correction of the AUV cluster. In this paper, we will study the influence of heavy-tailed noise on this method and study the EKF based on Huber estimation to improve the antijamming capability.

Enhanced square root CKF with mixture correntropy loss for robust state of charge estimation of lithium-ion battery

The measurement data of lithium-ion battery collected in complex operating conditions may be contaminated by non-Gaussian noises (or outliers), a novel robust state of charge (SOC) estimation approach that enhances the robustness of square-root cubature Kalman filter (SRCKF) by incorporating a mixture correntropy loss (MCL) is proposed to overcome the issue of non-Gaussian measurement noise interference. Although the SRCKF can perform non-destructive state estimation for nonlinear system, it is sensitive to the non-Gaussian noises (or outliers) due to the use of mean square error (MSE) loss. To overcome this limitation, the MCL is used as a cost to replace the MSE in CKF framework, which is constructed by mixture of two Gaussian kernel functions with different kernel widths and has outstanding robustness. Moreover, we establish an effective nonlinear regression model that incorporates noise and state error information into the MCL function, and then a fixed-point iteration method is utilized to update the posterior state estimation. Additionally, to further suppress the influence of abnormal noise on the posterior state estimation, we introduce the exponential function of the innovation vector to adjust the measurement covariance matrix in real-time. Accordingly, an enhanced MCL-SRCKF is developed for SOC estimation considering the measurement noises with non-Gaussian distribution. Results from various simulation environments demonstrate that the proposed method achieves high estimation accuracy in different cases.

Robust Data-Driven Sparse Estimation of Distribution Factors Considering PMU Data Quality and Renewable Energy Uncertainty - Part I: Theory

Data-driven sparse estimation of distribution factors (DFs) facilitates online power flow sensitivity analysis for secure system operation. However, existing methods are vulnerable to time-varying non-Gaussian PMU measurement noise, bad data, and uncertain renewable energy sources (RESs). Moreover, they lack scalability to large-scale systems. This two-part paper proposes a robust and scalable sparse DF estimation framework considering PMU data quality and RES uncertainty. In this Part I, a novel Adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -Lasso estimator with theoretically guaranteed robustness is proposed. It mitigates the impacts of measurement and RES uncertainties to yield accurate dominant DF estimates while promoting sparsity. The key idea is to integrate the robust statistics theory with sparse representation techniques, in particular the Huber loss function, adaptively-weighted <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization, concomitant scale estimate, and pseudo-residuals. Two important robustness properties of this estimator are theoretically proven, i.e., the bounded influence function and the asymptotic consistency of dominant DF estimates given limited samples. The breakdown points of this estimator to measurement and RES uncertainties are derived. Test results validate that the proposed estimator allows accurate estimation without relying on power flow models or massive operating data. It achieves significantly superior robustness over existing methods in multiple scenarios.

Multisensor-Based Maneuvering Target Tracking Algorithm under Non-Gaussian Measurement Noise

The UAVs have become a huge threat in the battlefield. The excellent maneuverability makes them competent for the actual combat operations such as investigation and strike. Therefore, accurate tracking of UAVs is critical. Centralized radar/IR fusion system has been widely concerned to track the UAVs because of the complementary characteristics between these two sensors. The appearance of non-Gaussian measurement noise produces a negative impact on tracking accuracy. This paper proposes a novel IMM-CMCSCKF algorithm which can improve the tracking accuracy of radar/IR fusion system for maneuvering target under non-Gaussian measurement noise. The heterogeneous measurements from radar and IR are firstly fused. Then, CMCSCKF algorithm is presented based on MCC to deal with non-Gaussian measurement noise. To improve maneuvering target tracking accuracy, CMCSCKF is embed into IMM algorithm. Numerical simulation verifies the effectiveness of the proposed IMM-CMCSCKF.

An Agent-Based Distributed State Estimation Approach for Interconnected Power Systems

Phasor measurement units (PMUs) are becoming more popular in power systems and most of the distributed state estimation methods are based on the Gaussian measurement noise assumption. However, the PMU measurement noise has been demonstrated to be non-Gaussian. This article presents a distributed multiarea state estimation approach based on the quadratic and exponential functions for power systems to deal with the non-Gaussian measurement noise efficiently. The matrix splitting technique is utilized to implement a robust estimator in a fully distributed scheme. Based on the local measurements and the limited information exchanged between neighboring areas, each local area only estimates its local states and the computation time needed is further reduced. The effective and robust performance of the proposed distributed multiarea state estimation approach is demonstrated using the IEEE 30-, 118-, and 300-bus systems.

Distributed Maximum Correntropy Cubature Information Filtering for Tracking Unmanned Aerial Vehicle

Aiming at improving the performance of tracking unmanned aerial vehicle in the battlefield, this paper focuses on the algorithm involving tracking the maneuvering target with a distributed sensor network under non-Gaussian measurement noise. A novel distributed maximum correntropy cubature information filtering based on interactive multiple model is proposed. Taking advantage of the correntropy, we design a maximum correntropy cubature information filtering for each node to estimate the target state under non-Gaussian measurement noise. Then, distributed information fusion based on weighted average consensus is conducted to improve the stability of the sensor network. After that, the information pair is changed, so that a distributed state estimation algorithm based on interactive multiple model is developed to increase the accuracy of maneuvering target tracking. Simulation results and comparison with other algorithms in three typical non-Gaussian measurement noise scenarios are given to evaluate the effectiveness of the proposed algorithm.

Robust State Estimation via Maximum Correntropy EKF on Matrix Lie Groups With Application to Low-Cost INS/GPS-Integrated Navigation System

This paper focuses on solving state estimation problems of nonlinear systems whose states evolve on matrix Lie groups and measurements live in the Euclidean space under non-Gaussian measurement noise. Building upon the maximum correntropy criterion and the invariant Kalman filtering theory, a generalized robust extended Kalman filtering algorithm on matrix Lie groups is derived from maximizing a novel optimization cost function. This cost function is introduced by considering the correntropy and the system geometry structure. Then, two alternative versions of the proposed filtering algorithm are provided according to the distinct processing approaches of the nonlinear measurement function in the cost function. A Gaussian-Newton method on Lie groups and a fixed-point iterative method are applied to update the posterior estimation. In addition, sufficient conditions are given to ensure the convergence of fixed-point iterative steps. Extensive Monte-Carlo simulations on an INS/GPS integrated navigation system and experiments on open-source datasets validate the theoretical analysis and illustrate the effectiveness and robustness of the proposed filter.

GMM-Based Adaptive Extended Kalman Filter Design for Satellite Attitude Estimation under Thruster-Induced Disturbances.

Star images from star trackers are usually defocused to capture stars over an exposure time for better centroid measurements. While a satellite is maneuvering, the star point on the screen of the camera is affected by the satellite, which results in the degradation of centroid measurement accuracy. Additionally, this could result in a worse star vector outcome. For geostationary satellites, onboard thrusters are used to maintain or change orbit parameters under orbit disturbances. Since there is misalignment in the thruster and torque is generated by an impulsive shape signal from the torque command, it is difficult to generate target torque; in addition, it also impacts the star image because the impulsive torque creates a sudden change in the angular velocity in the satellite dynamics. This makes the noise of the star image non-Gaussian, which may require introducing a method for dealing with non-Gaussian measurement noise. To meet this goal, in this study, an adaptive extended Kalman filter is implemented to predict measurement vectors with predicted states. The GMM (Gaussian mixture model) is connected in this sequence, giving weighting parameters to each Gaussian density and resulting in the better prediction of measurement vectors. Simulation results show that the GMM-EKF exhibits a better performance than the EKF for attitude estimation, with 30% improvement in performance. Therefore, the GMM-EKF could be a more attractive approach for use with geostationary satellites during station-keeping maneuvers.

A Background-Impulse Kalman Filter With Non-Gaussian Measurement Noises

In the Kalman filter (KF), the estimated state is a linear combination of the one-step prediction and measurement. The two combination weights depend on the prediction mean-square error matrix and the covariances matrix of measurement noise (CMMN), respectively. When the measurement noise values are small (large), the corresponding measurement is close to (far from) the real value, and the weight should be large (small). If there is non-Gaussian measurement noise, especially heavy-tailed noise, most of the noise values are small, and a few of them are large. The occasional impulses cause the overall noise variance to be much greater than the noise without impulses. Since the overall CMMN is adopted in the KF, its performance will deteriorate. In this article, we divide the measurement noise into two parts: 1) the background noise with small variance and 2) the impulse noise with large variance. Then, we use the expectation–maximization algorithm to dynamically calculate the parameters and propose a new KF algorithm to process them separately, which is called background-impulse KF (BIKF). It can dynamically determine whether there is an impulse and eliminate its impact as much as possible. Compared with the recent maximum correntropy criterion and minimum error entropy criterion-based KFs, simulations show that the proposed BIKF works better than them with lower computational complexity.

Dynamic data reconciliation to enhance the performance of model free adaptive control

As a novel data-driven control method, model-free adaptive control (MFAC) has a high requirement for the accuracy of the feedback signal. However, the sensor used to obtain the output inevitably contains measurement noise due to its own error or external interference, which may lead to an adverse effect on the control performance. The dynamic data reconciliation (DDR) is proposed and combined with MFAC to improve the control performance in this paper, which uses predicted output and measured data to suppress measurement noise considering Gaussian and non-Gaussian distributed measurement noise. The effectiveness of the DDR combined with MFAC (DDR-MFAC) is illustrated in the single-input single-output and multiple-input multiple-output systems with Gaussian and non-Gaussian distributed measurement noise. DDR-MFAC is also successfully applied to DC–AC converter, which improves its conversion precision.

A Stochastic Event-Triggered Robust Cubature Kalman Filtering Approach to Power System Dynamic State Estimation With Non-Gaussian Measurement Noises

In power system communication and control, the wide-area measurement system (WAMS) is usually adversely affected by noisy measurements and data congestion, posing great challenges to the stability and functionality of modern power grids. This study proposes a stochastic event-triggered robust dynamic state estimation (DSE) method for non-Gaussian measurement noises, using the cubature Kalman filter (CKF) technique. To reduce the computational burden and data transmission congestion resulting from centrally processing the measurement data, the proposed event-triggered robust CKF (ET-RCKF) is deployed at a local level with appropriate system formulation. The proposition of the novel robust DSE strategy is detailed in this brief, with its stability mathematically analyzed and proven, and simulation study on the IEEE 39-bus benchmark test system verifies the effectiveness of the proposed ET-RCKF approach. This novel DSE method is able to cope with non-Gaussian measurement noises and produce highly satisfactory estimation results, leading to wide applicability in real-world power system applications.

Kullback–Leibler divergence based sensor placement in linear processes for efficient data reconciliation

Kullback–Leibler divergence (KLD) based sensor placement design (SPD) has been recently proposed for accurate estimation of variables using data reconciliation for steady-state linear processes. Use of KLD enables SPD for both Gaussian and non-Gaussian measurement noise cases. Additionally, it enables direct incorporation of the end-user specified estimation accuracies in the SPD procedure. In the current work, we establish several useful properties of the KLD based objective. We establish its invariance to the choice of primary variables. For the case when measurement noises are uncorrelated and Gaussian, we also establish its non-decreasing and submodular behavior. To solve the NP-hard SPD problem, we design a computationally efficient greedy algorithm. For the uncorrelated Gaussian measurement noise case, the algorithm finds provably near-optimal solution to the SPD problem. We also provide bounds for sensor placement obtained using any algorithm. We demonstrate the proposed approach on a phasor measurement unit, and a water distribution network.

Robust state of charge estimation of lithium-ion battery via mixture kernel mean p-power error loss LSTM with heap-based-optimizer

The state of charge (SOC) estimation of lithium-ion battery is an important function in the battery management system (BMS) of electric vehicles. The long short term memory (LSTM) model can be employed for SOC estimation, which is capable of estimating the future changing states of a nonlinear system. Since the BMS usually works under complicated operating conditions, i.e the real measurement data used for model training may be corrupted by non-Gaussian noise, and thus the performance of the original LSTM with the mean square error (MSE) loss may deteriorate. Therefore, a novel LSTM with mixture kernel mean p-power error (MKMPE) loss, called MKMPE-LSTM, is developed by using the MKMPE loss to replace the MSE as the learning criterion in LSTM framework, which can achieve robust SOC estimation under the measurement data contaminated with non-Gaussian noises (or outliers) because of the MKMPE containing the p-order moments of the error distribution. In addition, a meta-heuristic algorithm, called heap-based-optimizer (HBO), is employed to optimize the hyper-parameters (mainly including learning rate, number of hidden layer neuron and value of p in MKMPE) of the proposed MKMPE-LSTM model to further improve its flexibility and generalization performance, and a novel hybrid model (HBO-MKMPE-LSTM) is established for SOC estimation under non-Gaussian noise cases. Finally, several tests are performed under various cases through a benchmark to evaluate the performance of the proposed HBO-MKMPE-LSTM model, and the results demonstrate that the proposed hybrid method can provide a good robustness and accuracy under different non-Gaussian measurement noises, and the SOC estimation results in terms of mean square error (MSE), root MSE(RMSE), mean absolute relative error (MARE), and determination coefficient R2 are less than 0.05%, 3%, 3%,and above 99.8% at 25℃, respectively.