Maximum Correntropy Criterion Kalman Filter for α-Jerk Tracking Model with Non-Gaussian Noise

Bowen Hou, Zhangming He, Xuanying Zhou, Haiyin Zhou, Dong Li, Jiongqi Wang
2017 Entropy  
As one of the most critical issues for target track, α-jerk model is an effective maneuver target track model. Non-Gaussian noises always exist in the track process, which usually lead to inconsistency and divergence of the track filter. A novel Kalman filter is derived and applied on α-jerk tracking model to handle non-Gaussian noise. The weighted least square solution is presented and the standard Kalman filter is deduced firstly. A novel Kalman filter with the weighted least square based on
more » ... he maximum correntropy criterion is deduced. The robustness of the maximum correntropy criterion is also analyzed with the influence function and compared with the Huber-based filter, and, moreover, the kernel size of Gaussian kernel plays an important role in the filter algorithm. A new adaptive kernel method is proposed in this paper to adjust the parameter in real time. Finally, simulation results indicate the validity and the efficiency of the proposed filter. The comparison study shows that the proposed filter can significantly reduce the noise influence for α-jerk model. For the nonlinear filter design, a lot of techniques were proposed according to the different optimization rules, including the function approximation, the posteriori probability density approximation and the stochastic model approximation [8] [9] [10] [11] . Extended Kalman Filter (EKF) is a typical technique of the function approximation based on Taylor series expansion. Unscented Kalman Filter (UKF) is the most common way of the sampling-based moment approximation [12, 13] . The stochastic model approximation [14] can approximate the nonlinear function in some probabilistic senses. However, it has not gained popularity mainly because the expectations involved are not easy to evaluate. No matter what nonlinear filter methods are used, they are applied on the state estimation with Gaussian white noises in most time. However, in practical applications, especially in the maneuver target track system, non-Gaussian noises do exist and have substantial effects on the state estimation. Up to now, some practical models are proposed, such as Gaussian mixture noise model [15] , glint noise model [16] and so on. In a non-Gaussian process, the performance of many nonlinear filters can break down [17] . However, the filter robustness against non-Gaussian noises can be improved by the following approaches: 1. The first approach is to develop filters for the systems with non-Gaussian noises directly. Noise distributions such as heavy-tailed distributions and t-distributions are considered in these filters [18, 19] . However, it is difficult to handle more than one dimension, which limits its applicability [20]. 2. Approximating the posteriori probability density is another practical approach to handle the non-Gaussian noises. The unscented Kalman filter (UKF) uses the unscented transformation (UT) technique to capture the mean and the covariance of the state estimation with sigma points [21] . The ensemble Kalman filter (EnKF) is a method to approximate the state estimation with a set of samples to handle non-Gaussian noises [22] . Gaussian sum filter (GSF) is an algorithm to obtain the filtering distribution and the predictive distribution recursively approximated as Gaussian mixtures [23-25]. 3. Huber-based robust filter is a classical method to handle the non-Gaussian noises and outliers [26] . It has become the research focus these past several years and been applied in the field of the navigation and the target track [27] [28] [29] [30] . 4. A new robust Kalman filter is proposed by Chang [31] in recent years. It handles the outliers based on the hypothesis testing theory, which defines a judging index as the square of the Mahalanobis distance from the observation to its prediction. It can effectively resist the heavy-tailed distribution of the observation noises and the outliers in the actual observations. 5. Multi-sensor data fusion Kalman filter is a fuzzy logical method proposed by Rodger [32] . It can effectively improve the computational burden and the robustness of Kalman filter. Furthermore, it has been applied on the vehicle health maintenance system. 6. Maximum correntropy criterion is the latest optimization criterion that is used for improving Kalman filter. Maximum correntropy Kalman filter (MCKF) is a newly proposed filter to process the non-Gaussian noises [33] . In addition, several improved MCKF algorithms have been proposed and applied on state estimation [34] [35] [36] [37] .
doi:10.3390/e19120648 fatcat:avzwdumrp5enrcogulznn2r6b4