Research on Robust Kalman Filter of Observations with Unequal Precision in Precise Point Positioning

The robust Kalman filter principle of precise point positioning is deduced. The standard deviation of residuals is used to construct robust factor based on IGGⅢ function by equivalent weight matrix, which is very sensitive to the outliers, because the residual covariance is smaller than the innovation covariance. The correlation of residuals and robust factor of carrier phase among satellites is greatly weakened by iterating. The robust factor of carrier phase and code are independently calculated, because of the unequal accuracy and irrelevant between carrier phase and code observations. Four models are used to test and analyze by the GPS dual-frequency observations, which included the standard Kalman filter, the robust Kalman filter (RKF) based on innovation, the RKF based on robust residuals and gain matrix, and the RKF based on robust residuals and equivalent weight matrix. Results show that it is insensitive to the outliers of accurate carrier phase observations, which the RKF based on innovation. The smaller carrier phase outliers are difficult to be detected via the RKF based on robust residuals and equivalent weight matrix, and the estimated coordinates has a large deviation from the true value in the epoch of outliers occurred. The RKF based on robust residuals and equivalent weight matrix can efficiently and accurately resist outliers, and the deviations between the estimated coordinates and true value is 1 mm smaller for the outliers of single satellite.