A robust filtering mechanism is developed for GNSS navigation processing in this study. A nonlinear system filter employs the maximum correntropy criterion based extended Kalman filter (MCCEKF) by using the maximum correntropy criterion (MCC) as the optimization criterion rather than the MMSE to increase robustness and reduce impulsive disturbances. In information theoretic learning (ITL), correntropy encompasses a wide range of statistical information compared to mean squared error (MSE) algorithms to improve solutions. MCCEKF is a fixed-point technique utilized for updating previous estimations after an initial state estimation. The covariance matrix is obtained by using the state and covariance matrix dispersion equation. We analyzed a nonlinear regression maximum correntropy EKF (NRMCC-EKF) based on MCCEKF. The prediction process is comparable to that of the original EKF and the state mean. Covariance matrix propagation equations are used to resolve the previous estimations of the state and covariance matrix. Additionally, the new fixed-point recursive procedure is used to update the posterior estimates. The algorithm is designed to execute even when the measured noise quality varies over time with non-Gaussian errors or dynamic system nonlinearities. The new filters are based on time-varying iterative solutions. The proposed recursive filter adopts different weights and kernel bandwidths to analyze the filtering, estimation accuracy, and smoothing gains, respectively.