Generally, gross errors exist in observations, and they affect the accuracy of results. We review methods to detect the gross errors by Robust estimation method based on L1-estimation theory and their validity in adjustment of geodetic networks with different condition. In order to detect the gross errors, we transform the weight of accidental model into equivalent one using not standardized residual but residual of observation, and apply this method to adjustment computation of triangulation network, traverse network, satellite geodetic network and so on. In triangulation network, we use a method of transforming into equivalent weight by residual and detect gross error in parameter adjustment without and with condition. The result from proposed method is compared with the one from using standardized residual as equivalent weight. In traverse network, we decide the weight by Helmert variance component estimation, and then detect gross errors and compare by the same way with triangulation network In satellite geodetic network in which observations are correlated, we detect gross errors transforming into equivalent correlation matrix by residual and variance inflation factor and the result is also compared with the result from using standardized residual. The results of detection are shown that it is more convenient and effective to detect gross errors by residual in geodetic network adjustment of various forms than detection by standardized residual.

The accuracy and reliability of Kalman filter are easily affected by the gross errors in observations. Although robust Kalman filter based on equivalent weight function models can reduce the impact of gross errors on filtering results, the conventional equivalent weight function models are more suitable for the observations with the same noise level. For Precise Point Positioning (PPP) with multiple types of observations that have different measuring accuracy and noise levels, the filtering results obtained with conventional robust equivalent weight function models are not the best ones. For this problem, a classification robust equivalent weight function model based on the t-inspection statistics is proposed, which has better performance than the conventional equivalent weight function models in the case of no more than one gross error in a certain type of observations. However, in the case of multiple gross errors in a certain type of observations, the performance of the conventional robust Kalman filter based on the two kinds of equivalent weight function models are barely satisfactory due to the interaction between gross errors. To address this problem, an improved classification robust Kalman filtering method is further proposed in this paper. To verify and evaluate the performance of the proposed method, simulation tests were carried out based on the GPS/BDS data and their results were compared with those obtained with the conventional robust Kalman filtering method. The results show that the improved classification robust Kalman filtering method can effectively reduce the impact of multiple gross errors on the positioning results and significantly improve the positioning accuracy and reliability of PPP.