Global Positioning System (GPS) observables are often affected by non-Gaussian errors caused by multipath propagation and environmental interference. The Extended Kalman Filter (EKF) can account for system nonlinearity, but its minimum mean square error (MMSE) formulation is less suitable when the measurement errors depart from the Gaussian assumption. Among information-theoretic alternatives, the minimum error entropy-based EKF (MEE-EKF) provides greater robustness by reducing uncertainty in the error distribution, yet remains prone to bias owing to the translation invariance of entropy. The maximum correntropy criterion-based EKF (MCC-EKF) improves outlier suppression by concentrating the error probability density around zero, yet its adaptability to varying noise conditions remains limited. This study therefore adopts a centred error entropy EKF (CEE-EKF) to combine the desirable properties of these two information-theoretic criteria. Its performance is compared with the Student’s t-based EKF (ST-EKF) and Variational Bayesian EKF (VB-EKF). The results indicate that the CEE-EKF provides more effective outlier mitigation and consistently improves positioning accuracy under non-Gaussian measurement errors.