Maximum Correntropy Derivative-Free Robust Kalman Filter and Smoother

Wang, Hongwei; Li, Hongbin; Zhang, Wei; Zuo, Jiakuo; Wang, Heping

doi:10.1109/access.2018.2880618

Cited by 25 publications

(7 citation statements)

References 53 publications

(108 reference statements)

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“…In this section, we analysis the proposed algorithm by investigating the state estimation for a Van der Pol oscillator (VPO). For comparison, we also consider the conventional CKF and some existing robust filters, including the maximum correntropy derivative-free robust CKF (MCC-CKF) [24], linear regression and maximum correntropy based CKF (RMCC-CKF) [22] and Huber's cost function based CKF (Huber-CKF) [13]. We use two different set in the MCC-CKF, i.e., the MCC-CKF1 with {σ = 100, η = 4} and MCC-CKF2 with {σ = 100, η = 5} (setting σ = 100 is to deal with the Gaussian process noise).…”

Section: Simulations and Resultsmentioning

confidence: 99%

Outlier-robust Kalman filters with mixture correntropy

Wang

Zhang

Zuo

et al. 2020

Journal of the Franklin Institute

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We consider the robust filtering problem for a nonlinear state-space model with outliers in measurements. A novel robust cubature Kalman filtering algorithm is proposed based on mixture correntropy with two Gaussian kernels. We have formulated the robust filtering problem by employing the mixture correntropy induced cost to replace the quadratic one in the conventional Gaussian approximation filter for the measurement fitting error. In addition, a tradeoff weighting coefficient is introduced to make sure the proposed approach can provide reasonable state estimates in scenarios with small measurement fitting errors. The robust filtering problem is iteratively solved by using the cubature Kalman filtering framework with a reweighted measurement covariance. Numerical results show that the proposed method can achieve a performance improvement over existing robust solutions.State estimation for stochastic discrete-time dynamic systems is one of the vital issues in control engineering, and it has broad applications in various areas, such as target tracking , sparse signal processing, fault detection and diagnose, information fusion, and many others [1][2][3][4][5]. The state estimates of a linear system with Gaussian noises is provided by the celebrated Kalman filter [6]. For nonlinear systems with a Gaussian assumption (i.e., both the process and measurement noises are Gaussian), several Kalman-liked Gaussian approximation filters (GKF) were investigated, e.g., the unscented Kalman filter [7], cubature Kalman filter [8,9], to name a few. These solutions have shown good performance when the Gaussian assumption meets in systems. In some applications, however, the Gaussian assumption for the measurement noise may fail since outliers may contaminate measurements due to unreliable sensors. Outliers lead to the measurement noise having a heavy tail and becoming non-Gaussian, resulting in a substantial degradation of the existing GKFs.The sequential Monte-Carlo sampling/particle filter (PF) [10] and the Gaussian sum filter (GSM) are two general strategies to deal with non-Gaussian noises caused by measurement outliers. In the PF, a massive number of particles are involved to approximate the posterior probability density function to obtain a reasonable estimation results. In the GSM, the state estimates are obtained by combining the results from several parallelly implemented filters via an interacting procedure. Therefore, both the PF and GSM suffer from a great computational burden, which prevents them from being widely used in applications. In addition, a computationally economical approach, i.e., integrating the robust cost from M-estimation (e.g., Huber's cost) into the GKF framework [11][12][13], has also been studied. This type of robust filters were developed by interpreting the GKF filtering problem as a linear or nonlinear regression. Other approaches for robust filtering such as the heavy-tailed distribution based solution [14] and the H ∞ filter [15] were also reported in literatures.Recently, a novel local simila...

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Section: Simulations and Resultsmentioning

confidence: 99%

Outlier-robust Kalman filters with mixture correntropy

Wang

Zhang

Zuo

et al. 2020

Journal of the Franklin Institute

Self Cite

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“…In the following, a few discussions are added for the practical implementation of the proposed method Like the traditional Kalman filter (KF) and its suboptimal extensions (e.g., EKF, UKF, and CKF), the proposed SSGQKF is also developed under the Gaussian assumption and the minimum mean square error (MMSE) criterion. To deal with non-Gaussian noises and for further improvement, the proposed filter can be combined with other techniques such as the extended H ∞ filtering (EH ∞ F) [29], Huber's Mathematical Problems in Engineering M-estimation theory [30], maximum correntropy criterion (MCC) [31], and global linearization method to get better and more robust performance. (1) Since the extended H ∞ filter does not make any assumptions about the statistics of the process or measurement noise but does require Jacobian matrices during the state estimation of nonlinear systems, by using the derivative-free property of SSGQKF and the linear propagation property, it is possible to embed the EH ∞ F in the SSGQKF framework.…”

Section: E Spherical Simplex Gauss-laguerre Quadrature Cubature Kalman Filter (Ssgqkf)mentioning

confidence: 99%

Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System

Cao

Gao

Sun

et al. 2020

Mathematical Problems in Engineering

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A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is derived. A high-dimensional nonlinear state estimation problem and a target tracking problem are utilized to demonstrate the effectiveness of the proposed spherical simplex Gauss–Laguerre cubature quadrature rule to improve the performance.

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“…Kalman filter is widely adopted in system states estimation and RUL prediction due to its low computational requirement and high accuracy. However, conventional Kalman filters, such as extended Kalman filter and unscented Kalman filter, are of the optimal state estimation based on the LMS criterion, which merely perform well under the Gaussian assumption [37]. However, the non-Gaussian noises (e.g.…”

Section: Robust Kalman Filter Algorithm For Rul Predictionmentioning

confidence: 99%

A Robust Hybrid Filtering Method for Accurate Battery Remaining Useful Life Prediction

Peng

Gao

et al. 2019

IEEE Access

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Accurate remaining useful life (RUL) prediction under the noisy environment is a big challenge for the health management of modern industrial systems since the extraction of the accurate data structure from heavily corrupted data is difficult. In recent years, the kernel adaptive filter (KAF) has been widely adopted to solve the robust regression problem due to its low-complexity and high-approximation capability and robustness while the applications in battery RUL prediction are still few and far between. Thus, this paper is concerned with long-term RUL prediction using the KAF method. At first, concretely speaking, a robust KAF algorithm is derived based on the double-Gaussian-mixture (DGM) cost function, which is used to learn the capacity degradation mechanism from contaminated capacity data and so as to build the long-term prediction model. Second, a robust unscented Kalman filter (UKF) algorithm employing the DGM-based cost function is developed, which is then combined with the KAF-based prediction model to realize a more accurate and reliable prediction. Under the hybrid prognostic framework, the proposed UKF algorithm is applied to filter the noisy observations. When the observation data are inaccessible, the predicted data from the off-line trained KAF-based prediction model are adopted as the approximated value of the real observations for the UKF algorithm to optimize the prediction results and to provide the uncertainty representation. The experimental results reveal that the proposed method has great robustness when the measurements contain noise and large outliers, which makes it possible to get satisfactory prediction performance without preprocessing the data manually.INDEX TERMS Kernel adaptive filter, battery, unscented kalman filter, remaining useful life (RUL), robustness.

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Maximum Correntropy Derivative-Free Robust Kalman Filter and Smoother

Cited by 25 publications

References 53 publications

Outlier-robust Kalman filters with mixture correntropy

Outlier-robust Kalman filters with mixture correntropy

Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System

A Robust Hybrid Filtering Method for Accurate Battery Remaining Useful Life Prediction

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