A NEW ROBUST KALMAN FILTERING ALGORITHM OF UNEQUAL PRECISION OBSERVATIONS BASED ON RESIDUAL VECTORS IN STATIC PRECISE POINT POSITIONING

Precise Point Positioning (PPP), which can achieve high-precision positioning with only a single Global Navigation Satellite System (GNSS) receiver, is a popular but challenging research topic. The traditional Robust Kalman Filter (RKF) based on innovation vectors can effectively resist outliers in certain cases. However, this filter is less effective in treating unequal precision observations for PPP, such as crowded outliers or small outliers in high-precision carrier phase observations. In this study, the residual vector is used to construct a robust factor that is sensitive to outliers. Our strategy is to apply decorrelation to this vector. Firstly, the squared Mahalanobis distances of carrier phase and pseudorange observations are used to evaluate whether measurements contain outliers in the current epoch. Secondly, the residual vector is decorrelated with respect to the residual covariance. Finally, through iteration, the robust factor for the residual vector and the gain matrix are determined, which theoretically eliminates the residual vector correlation for different observations. Our proposed modification of the RKF method has been tested using data from International GNSS Service (IGS) Stations. Results show that our RKF based on residual vectors can effectively reduce the effects of a single outlier. Given many outliers, computations must be iterated to reduce the residual vector correlation, especially for cases where more outliers can effectively be suppressed by filter divergence.