Multi-GNSS real-time precise clock estimation considering the correction of inter-satellite code biases

For reasons mostly related to chip shape distortions, global navigation satellite system (GNSS) observations are corrupted by receiver-dependent biases. These are often stable in the long term, though numerically different depending on the signal frequency, satellite system and receiver manufacturer. Based on the mixed-differenced model combining undifferenced pseudorange with epoch-differenced carrier phase observations, we present a multi-GNSS real-time precise clock estimation model considering correction of inter-satellite code biases (ISCBs). Pre-estimated receiver-dependent ISCB corrections are introduced to correct the inter-receiver, inter-satellite and inter-system biases largely. Then the number of estimated parameters is reduced to a manageable level for real-time estimation. Comparisons with post-processed data show that compared to undifferenced, epoch-differenced and non-bias-corrected mixed-differenced models, the proposed bias-corrected model can greatly reduce the precise clock offset systematic biases, especially for GLONASS and BeiDou. The test results show the root mean square data reductions are improved by up to 96% for GLONASS, 78% for BeiDou and 40% for GPS and Galileo.