Abstract
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.
Highlights
The unscented Kalman filter (UKF) utilizes the unscented transformation (UT) technique to achieve the nonlinear propagation of the mean and covariance of the system state, which avoids the derivation of the Jacobian matrices
Gaussian kernel function in the definition of correntropy to better utilize the heavy-tailed features of noises when the underlying system is disturbed by heavy-tailed non-Gaussian noise
The performance of the proposed filter is verified through comparative simulations with Kalman filter (KF), Huber-based Kalman filter (HKF), and Maximum correntropy Kalman filter (MCKF)
Summary
The state estimation problem is ubiquitous in various applications, such as navigation [1], target tracking [2], and so on [3,4]. Most of the above filters are based on the mean square error (MSE) criterion and can achieve satisfying state estimation accuracy when the system noises are Gaussian. Various nonlinear filters based on these information-theoretic learning criteria were proposed, such as the maximum correntropy unscented filter [24], minimum error entropy unscented Kalman filter [25], and so forth [26,27,28]. The performance of the filters based on the information learning criterion heavily depends on the kernel function and its parameters. A novel Cauchy kernel-based maximum correntropy Kalman filter (CKKF) was proposed in the Ref. The comparative simulations show that with the proper parameters of the kernel function, the accuracy of state estimation of the STKKF outperforms that of conventional algorithms when the noises are heavy-tailed non-Gaussian.
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