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.
In the classical Kalman filter(KF), the estimated state is a linear combination of the one-step predicted state and measurement state, their confidence level change when the prediction mean square error matrix and covariance matrix of measurement noise vary. The existing student's t based Kalman filter(TKF) works similarly to the way KF works, they both work well with impulse noise, but when it comes to Gaussian noise, TKF encounters an adjustment limit of the confidence level, this can lead to inaccuracies in such situations. This brief optimizes TKF by using the Gaussian mixture model(GMM), which generates a reasonable covariance matrix from the measurement noise to replace the one used in the existing algorithm and breaks the adjustment limit of the confidence level. At the end of the brief, the performance of the covariance adaptive student's t based Kalman filter(TGKF) is verified.
The resolution accuracy of the inertial navigation system/global navigation satellite system (INS/GNSS) integrated system would be degraded in challenging areas. This paper proposed a novel algorithm, which combines the second-order mutual difference method with the maximum correntropy criteria extended Kalman filter to address the following problems (1) the GNSS measurement noise estimation cannot be isolated from the state estimation and suffers from the auto-correlated statistic sequences, and (2) the performance of EKF would be degraded under the non-Gaussian condition. In detail, the proposed algorithm determines the possible distribution of the measurement noise by a kernel density function detection, then depending on the detection result, either the difference sequences–based method or an autoregressive correction algorithm’s result is utilized for calculating the noise covariance. Then, the obtained measurement noise covariance is used in MCEKF instead of EKF to enhance filter adaptiveness. Meanwhile, to enhance the numerical stability of the MCEKF, we adopted the Cholesky decomposition to calculate the matrix inverse in the kernel function. The road experiment verified that our proposed method could achieve more accurate navigation resolutions than the compared ones.
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