Robust GPS Navigation via Centered Error Entropy Variational Bayesian Extended Kalman Filter

Managing unknown, time-varying noise and outliers presents a critical challenge in GPS applications. Variational Bayesian (VB) inference effectively estimates unknown noise statistics but lacks robustness to outliers, while robust filters such as the centered error entropy (CEE) suppress outliers but rely on fixed noise assumptions. To address both limitations, we propose the centered error entropy-based variational Bayesian extended Kalman filter (CEEVB-EKF), which integrates VB inference with the CEE criterion in a unified framework. The method estimates time-varying noise covariance via recursive VB updates and applies the CEE cost function for robustness to heavy-tailed disturbances and outliers. This dual-stage design improves adaptability and reliability, with simulations showing superior, stable state estimation, making CEEVB-EKF suitable for positioning, tracking, and autonomous navigation.