The Swarm mission aims to study the principle and change regularities of the Earth’s magnetic field. Precise orbit determination is essential to the successful implementation of the mission and relevant scientific research. This article focuses on using two different double-difference methods to improve the accuracy of Swarm kinematic orbit determination. The accuracy of the kinematic orbit determination relies entirely on the space-borne observation data, independent of any dynamic parameters. The article analyzes the data quality of the Swarm space-borne global positioning system (GPS) receiver and presents a detailed introduction to the data pre-processing algorithms. The double-difference observation gathering and the applied orbit determination strategy using two different double-difference methods are discussed. The results of the kinematic orbits under different solar cycle conditions are presented, along with an evaluation based on analysis of GPS carrier phase residuals, subtracting from the post-processed orbits, and assessment with satellite laser ranging (SLR) measurements. The results show that the accuracy of the kinematic orbit determination is at the centimeter level for the three Swarm satellites’ orbit solutions. The daily root mean square (RMS) values of the three satellites’ phase residuals remain at around the 6 mm level. The RMS values of the position residuals between the kinematic orbits and the reduced dynamic orbits released by the European Space Agency (ESA) are at about the 2–3 cm level. The external evaluation with SLR measurements shows a good agreement with the ESA level, with the RMS values of the SLR residuals for kinematic orbits around 2 cm.

In global navigation satellite systems (GNSSs)-based positioning, user receiver clock jump is a common phenomenon on the low-cost receiver clocks and can break the continuity of observation time tag, carrier phase and pseudo range. The discontinuity may affect precise point positioning-related parameter estimation, including receiver clock error, position, troposphere and ionosphere parameters. It is important to note that these parameters can be used for timing, positioning, atmospheric inversion and so on. In response to this problem, the receiver clock jumps are divided into two types. The first one can be expressed by the carrier phase and pseudo range having the same scale jump, and the second one is that they are having different scale jumps. For the first type, if a small priori variance of receiver clock error is provided, it can affect the accuracy of ionospheric delay estimation both in static and kinematic mode, while in the latter mode, it also affects position estimation. However, if large process noise is provided, numerical problems may arise since other parameters’ process noises are usually small, it is proposed to use the single point positioning with pseudo ranges to provide a priori value of receiver clock error, and an empiric value is assigned to its prior variance, this handle can avoid the above problems. For the second type, instead of compensating so many raw observations in the traditional methods, it is proposed to compensate the ambiguities at the clock jump epochs only in a new method. The new method corrects the Melbourne–Wubbena (MW) combination firstly in order to avoid the misjudging of cycle slips for current epoch, and the second step is to compensate the corresponding ambiguities, then, after Kalman filtering, the MW and its mean should be corrected back in order to avoid the misjudging of cycle slips at the next epoch. This approach has the advantage of handling the clock jump epoch-wise and can avoid correcting the rest of the observations as the traditional methods used to. With the numerical validation examples both in static and kinematic modes, it shows the new method is simple but efficient for real time precise point positioning (PPP).