Generalized reliability measures of Kalman filtering for precise point positioning

To deal with the adverse influence of model failures on Kalman filtering (KF) estimation, it is necessary to investigate the generalized reliability theory, including the model failure detection and identification method as well as the separability and reliability theories. Although the generalized reliability theory for the least square has been discussed for many decades, the generalized reliability theory of KF is not widely discussed. Compared with the least square, KF includes not only the measurement model, but also the dynamic model. In KF, the predicted value of the state parameters from the dynamic model is considered as pseudo-measurements and combined with the observed measurements to compose the form of the least square. According to the reliability of the least square, the generalized reliability of KF is derived. Then, the dynamic model failure of precise point positioning is simulated to demonstrate the usage of the generalized reliability theory. The results show that the adverse influence of the dynamic model failure is more severe than that of the measurement model. Moreover, it is recommended that the model failure identification should always be used even if the overall model test passes. It is shown that the derived generalized reliability measures are suitable for the generalized KF estimation.