A modified mix-differenced approach for estimating multi-GNSS real-time satellite clock offsets

A modified mixed-differenced approach for estimating multi-GNSS real-time clock offsets is presented. This approach, as compared to the earlier presented mixed-differenced approach which uses epoch-differenced and undifferenced observations, further adds a satellite-differenced process. The proposed approach, based on real-time orbit products and a mix of epoch-differenced and satellite-differenced observations to estimate only satellite clock offsets and tropospheric zenith wet delays, has fewer estimated parameters than other approaches, and thus its implementing procedure is efficient and can be performed and extended easily. To obtain high accuracy, the approach involves three steps. First, the high-accuracy tropospheric zenith wet delay of each station is estimated using mixed-differenced carrier phase observations. Second, satellite clock offset changes between adjacent epochs are estimated using also mixed-differenced carrier phase observations. Third, the satellite clock offsets at the initial epoch are estimated using satellite-differenced pseudorange observations. Finally, the initial epoch clock results and clock offset changes are concatenated to obtain the clock results of the current epoch. To validate the real-time satellite clock results, multi-GNSS post-processing clock products from IGS ACs were selected for comparison. From the comparison, the standard deviations of the GPS, GLONASS, BeiDou and Galileo systems clock results are approximately 0.1–0.4 ns, except for the BeiDou GEO satellites. The root mean squares are about 0.4–2.3 ns, which are similar to those of other international real-time products. When the clock estimates were assessed based on a pseudo-kinematic PPP procedure, the positioning accuracies in the East, North and Up components reach 5.6, 5.5 and 7.6 cm, respectively, which meet the centimeter level and are comparable to the application of other products.