Accurate positioning in global navigation satellite systems (GNSS) is often compromised when the measurement noise departs from Gaussian assumptions, particularly in environments with multipath interference or dynamic signal conditions. To enhance robustness under such uncertainties, this work introduces a modified extended Kalman filter framework that integrates the maximum correntropy criterion with variational Bayesian inference. The proposed method adaptively estimates the time-varying noise covariance from incoming measurements, while simultaneously mitigating the effect of outliers and impulsive errors through a correntropy-based cost function. The filter, implemented without relying on fixed noise assumptions, continuously updates its statistical model in response to changes in the measurement environment. This enables accurate state tracking even under heavy-tailed or unpredictable noise conditions. Simulation results show that the proposed method achieves improved estimation accuracy and robustness compared to conventional EKF-based techniques, particularly in scenarios with irregular noise patterns. The approach provides a reliable and adaptive solution for robust navigation in complex GNSS applications.