Improved Differential Positioning Algorithm for GBAS Based on Fuzzy Adaptive Kalman Filter

Abstract

In order to improve the airborne terminal positioning accuracy of the ground based augmentation system (GBAS), the mathematical model of differential position calculation is established, and the Kalman filter algorithm is used to obtain optimal position solution. Aiming at the problem that the measurement noise covariance matrix of the Kalman filter algorithm cannot be determined beforehand, a new adaptive Kalman filter (ADKF) algorithm is proposed. After calculating the ratio between actual covariance of innovation sequence and theoretical covariance of innovation sequence, fuzzy inference system (FIS) is used to modify the Kalman’s measurement noise covariance matrix adaptively. The static and dynamic positioning verification experiments are carried out using the GBAS developed by the laboratory. Experimental results show that under static conditions, the position accuracy of the three positioning methods is nearly the same. However, under vehicle dynamic conditions, the FIS-ADKF algorithm has the highest position resolution accuracy and the corresponding root mean square error (RMSE) is the smallest, which verifies the effectiveness of the proposed algorithm and has engineering application values.