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

Abstract

Abstract Based on the Huber function, this paper constructs a model of the robust fractional order extended system (RFEKF), which effectively reduces the influence of the gross error. Firstly, by analyzing the abnormal observation characteristics of gross error in fractional order system, the RFEKF is constructed by an equivalence weight matrix of introducing redundancy and the statistical characteristics of predicted residuals, and thus it adjusts the gain matrix and obtains the optimal solution through iteration. Secondly, combined with the RFEKF, the robust estimation of the observed values with gross error is carried out, which further improves the real-time operational efficiency of the model. Finally, simulation experiment and practical implementation are carried out to verify the proposed RFEKF model in GNSS positioning and navigation field, the results show that the RFEKF can still navigate correctly in the case of gross error, compared with EKF, the accuracy of navigation positioning can be significantly improved.