Global Navigation Satellite Systems (GNSSs) observables, such as those of the Global Positioning System (GPS), are frequently affected by multipath effects that cause unpredictable signal interference at the receiver, posing significant challenges for accurate state estimation in complex environments with non-Gaussian noise or outliers. The traditional extended Kalman filter (EKF), based on the minimum mean square error (MMSE) criterion, assumes Gaussian noise distributions and exhibits degraded performance under non-Gaussian conditions. To overcome this limitation, the minimum error entropy (MEE) criterion was proposed to reduce random uncertainty in estimation error distributions; however, due to its translation invariance property, MEE may inadvertently increase bias when errors contain systematic offsets, leading to poor convergence. In contrast, the maximum correntropy criterion (MCC) concentrates the error probability density function (PDF) around zero, enabling effective entropy adjustment even in the presence of bias and achieving superior error convergence. This paper presents the centered error entropy (CEE) extended Kalman filter (CEE-EKF) that integrates the complementary merits of both MEE and MCC approaches to overcome their individual limitations. Experimental validation in complex nonlinear GPS environments with non-Gaussian noise demonstrates that the CEE-EKF significantly outperforms individual algorithms in noise suppression, particularly exhibiting enhanced robustness and accuracy when handling outliers. These results offer an effective approach to enhancing the reliability of GPS navigation in challenging real-world environments, and the algorithm can be readily extended to other GNSS applications.
Chang et al. (Tue,) studied this question.