<p>In complex urban environments, global navigation satellite systems (GNSS) signals are affected by multipath and non-line-of-sight effects, leading to non-Gaussian error distribution and extreme anomalies, which degrades the robustness and accuracy of Kalman filter solutions. To address this issue, we derive an iterative adaptive robustness filter framework and propose an adaptive robust maximum correntropy extended Kalman filter (ARMCKF) to improve GNSS positioning performance. Firstly, an adaptive kernel bandwidth strategy based on GNSS pseudorange measurements, dynamic system models, and noise parameters is proposed to address the uncertainty of kernel bandwidth in maximum correntropy Kalman filter (MCKF). Secondly, to reduce the impact of GNSS anomalies, the algorithm combines the maximum entropy criterion and robust estimation theory, deriving and using iterative variance inflation factors and adaptive classification factors to dynamically update the measurement and state covariance matrices. The urban experimental results show that ARMCKF has the highest robustness, followed by robust maximum correntropy extended Kalman filter (RMCKF), then adaptive robust iterative extended Kalman filter (AREKF), robust iterative extended Kalman filter (REKF), MCKF, and iterative extended Kalman filter (IEKF), and weighted least squares (WLS) has the lowest robustness. The improved algorithm based on MCKF is superior to the improved algorithm based on IEKF. In Wuhan and Tokyo, ARMCKF improves the horizontal positioning accuracy by 73.0 and 46.3% over IEKF, and by 10.1 and 12.3% over AREKF, respectively. It has the smallest error and fluctuation, reducing the maximum errors by 53.58 and 57.45% compared to IEKF, and 55.2% and 39.8% compared to AREKF, respectively.</p>