Maximum correntropy unscented Kalman and information filters for non-Gaussian measurement noise

et al. 2018

IEEE Access

We consider the problem of robust estimation involving filtering and smoothing for nonlinear state space models which are disturbed by heavy-tailed impulsive noises. To deal with heavy-tailed noises and improve the robustness of the traditional nonlinear Gaussian Kalman filter and smoother, we propose in this work a general framework of robust filtering and smoothing, which adopts a new maximum correntropy criterion to replace the minimum mean square error for state estimation. To facilitate understanding, we present our robust framework in conjunction with the cubature Kalman filter and smoother. A half-quadratic optimization method is utilized to solve the formulated robust estimation problems, which leads to a new maximum correntropy derivative-free robust Kalman filter and smoother. Simulation results show that the proposed methods achieve a substantial performance improvement over the conventional and existing robust ones with slight computational time increase. IntroductionIn recent years, estimation problems involving filtering and smoothing based on dynamic state space models (SSMs) have received significant attentions. These problems are frequently encountered in many areas, such as target tracking, fault detection and diagnosis, parameter estimation, navigation, and many others. The celebrated Kalman filter (KF) [1] offers optimal estimation with the minimum mean square error (MMSE) for a linear SSM when both the process and measurement noises are Gaussian. Nevertheless, most applications in practice inherently have nonlinear SSMs, for which an optimal nonlinear filter or smoother is typically intractable. Several sub-optimal solutions were proposed for nonlinear SSMs, including the extended KF [2], unscented KF [3], cubature Kalman filter (CKF) [4], and others. Some interesting relations among these solutions can be found in [5,6]. Meanwhile, for smoothing, the Rauch-Tung-Striebel (RTS) smoother was introduced in [7] for linear Gaussian SSMs. A general framework of Gaussian optimal smoothing for nonlinear SSMs was proposed in [8], following which several sub-optimal nonlinear RTS smoothers were developed, such as the extended RTS smoother, unscented RTS smoother, cubature Kalman smoother (CKS), and others.Although the aforementioned filtering and smoothing methods in general perform well under the Gaussian assumption, they can potentially break down in the presence of heavy-tailed non-Gaussian noises, which may appear in either the process procedure or measurement procedure. This happens in, for instance, tracking a maneuvering target with outliers in observations [9]. A primary reason behind the degradation is that the traditional KF/RTS and their sub-optimal extensions were derived from the MMSE criterion, and the resulting estimates are sensitive to heavy-tailed noises [10]. * H. Wang is with the Persistent efforts have been devoted to tackling heavy-tailed noises in order to obtain more robust state estimates. Multiple models based techniques and sequential Monte Carlo sampling methods can be used ...

Section: Related Workmentioning

confidence: 99%

Maximum Correntropy Derivative-Free Robust Kalman Filter and Smoother

Wang

et al. 2018

IEEE Access

“…To address the filtering problems with process uncertainty effectively, a large number of fruitful algorithms have been investigated, such as the particle filter (PF) [ 10 ], the variational Bayesian-based adaptive Kalman filter (VB-AKF) [ 11 , 12 , 13 , 14 ], the maximum correntropy-based Kalman filter (MC-KF) [ 15 , 16 , 17 , 18 , 19 ] and the Huber’s M-Estimation-based Kalman filter (HKF) [ 8 ]. The particle filter is based on the sequence Monte Carlo sampling technique and can solve the nonlinear non-Gaussian system state estimation problem effectively [ 10 ].…”

Section: Introductionmentioning

confidence: 99%

An Improved Strong Tracking Cubature Kalman Filter for GPS/INS Integrated Navigation Systems

Feng

et al. 2018

Sensors

The cubature Kalman filter (CKF) is widely used in the application of GPS/INS integrated navigation systems. However, its performance may decline in accuracy and even diverge in the presence of process uncertainties. To solve the problem, a new algorithm named improved strong tracking seventh-degree spherical simplex-radial cubature Kalman filter (IST-7thSSRCKF) is proposed in this paper. In the proposed algorithm, the effect of process uncertainty is mitigated by using the improved strong tracking Kalman filter technique, in which the hypothesis testing method is adopted to identify the process uncertainty and the prior state estimate covariance in the CKF is further modified online according to the change in vehicle dynamics. In addition, a new seventh-degree spherical simplex-radial rule is employed to further improve the estimation accuracy of the strong tracking cubature Kalman filter. In this way, the proposed comprehensive algorithm integrates the advantage of 7thSSRCKF’s high accuracy and strong tracking filter’s strong robustness against process uncertainties. The GPS/INS integrated navigation problem with significant dynamic model errors is utilized to validate the performance of proposed IST-7thSSRCKF. Results demonstrate that the improved strong tracking cubature Kalman filter can achieve higher accuracy than the existing CKF and ST-CKF, and is more robust for the GPS/INS integrated navigation system.

“…The Huber’s M-estimation is a combined

and

norm filter that can effectively suppress the non-Gaussian noise [ 18 , 19 , 20 ]. Recently, the information theoretical measure correntropy has been used to incorporate the non-Gaussian noise [ 23 , 24 , 25 , 26 , 27 , 28 ]. According to the maximum correntropy criterion (MCC), a new robust filter known as the maximum correntropy Kalman filter (MCKF) has been proposed in [ 24 ], and it is also extended to nonlinear systems using EKF [ 27 ] and UKF [ 25 , 26 , 28 ].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the information theoretical measure correntropy has been used to incorporate the non-Gaussian noise [ 23 , 24 , 25 , 26 , 27 , 28 ]. According to the maximum correntropy criterion (MCC), a new robust filter known as the maximum correntropy Kalman filter (MCKF) has been proposed in [ 24 ], and it is also extended to nonlinear systems using EKF [ 27 ] and UKF [ 25 , 26 , 28 ]. Simulation results show that an MCC based GF (MCGF) may obtain better estimation accuracy than M-estimation when choosing a proper kernel bandwidth [ 23 , 24 , 25 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Maximum Correntropy Gaussian Filter Based on Variational Bayes

Wang

Gao

et al. 2018

Sensors

Self Cite

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.