A study on the model of robust fractional-order extended Kalman filtering with gross error

The global navigation satellite system (GNSS) is widely employed in location-based services (LBS) as a pivotal technology for high-precision navigation and positioning. However, measurement errors cannot be fully eliminated in practical applications, potentially impacting positioning accuracy and reliability. Based on robust estimation and fractional calculus, we construct a robust fractional-order extended Kalman filter (RFEKF) model with a Huber function model. First, we introduce a fractional-order extended Kalman filter (FEKF) model. Second, the RFEKF is constructed by incorporating an equivalence weight matrix that introduces redundancy and the statistical properties of predicted residuals. The RFEKF model adapts the gain matrix through iterative adjustment, obtaining optimal solutions and enhancing the operational efficiency of the model. Finally, simulation experiment and practical implementation are carried out to verify the proposed RFEKF model in GNSS navigation and positioning. The results demonstrate that the RFEKF significantly improves the accuracy of navigation and positioning in the presence of gross errors, surpassing the performance of the REKF.