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.

Multipath error is an important factor restricting the relative positioning accuracy of the Beidou Navigation Satellite System (BDS). Because of the complexity of the reflection environment, the mathematical modeling of multipath errors is quite difficult. The sidereal filtering algorithm corrects multipath errors by using the feature of period repetition, which can greatly reduce its influence and improve the accuracy of positioning and attitude measurement. In view of the constellation heterogeneity of BDS, it is more complicated to apply sideral filtering. Based on the reconstructed single-difference residual of the carrier phase, the multipath repetition time of the Beidou satellite is estimated using the idea of segmentation. The Tikhonov regularization method and the classical wavelet method are used to extract the multipath of the single-difference residual of the carrier phase, and the “clean” sequence of the single-difference residual is obtained. The experimental results show that it is feasible to extract the multipath error correctly by Tikhonov regularization, and the multipath error is smoother than the original residual measurement. Furthermore, the estimation method of the regularization parameter is further optimized. After using the optimized Tikhonov regularization method with sidereal filtering, the mean RMS improvements of GEO, IGSO, and MEO satellites are 45.9%, 38.2%, and 37.5%, respectively. The positioning accuracy on E, N, and U components is improved by 24.8%, 26.3%, and 42.7%, respectively. The attitude resolution accuracy is improved by 22.9% in the yaw angle and 12.6% in the pitch angle. The proposed method can be an alternative BDS multipath error modeling and mitigation approach.

The fast and accurate solution of integer ambiguity is the key to achieve GNSS high-precision positioning. Based on the lattice theory of high-dimensional ambiguity solving, the reduction time consumption is much larger than the search time consumption, and it is especially important to improve the efficiency of the lattice basis reduction algorithm. The Householder QR decomposition with minimal column pivoting is utilized to pre-sort the basis vectors and reduce the number of basis vector exchanges during the reduction process by partial size reduction and relaxing the basis vector exchange condition to improve the reduction efficiency of the LLL algorithm. The improved algorithm is validated using simulated and measured data, respectively, and the performance advantages and disadvantages of the improved algorithm are evaluated from the perspectives of the extent of reduction basis orthogonality and the quality of reduction basis size reduction. The results show that the improved LLL algorithm can significantly reduce the number of basis vector exchanges and the reduction time consumption. The HSLLL and PSLLL algorithms with the Siegel condition as the basis vector exchange condition have a better reduction effect, but are slightly less stable. The PLLLR algorithm significantly improves the search ambiguity resolution efficiency, which is conducive to the rapid realization of ambiguity resolution.

Fengyun-3C (FY-3C) is a Global Navigation Satellite Systems (GNSS) Radio Occultation (RO) mission founded which was by China on 23 September 2013. In this study, under a specific temporal and spatial domain, we systematically compare FY-3C refractivity profiles with Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) refractivity profiles for the year 2015. The COSMIC profiles used in this study contain reflections, as identified in the Radio Occultation Meteorology Satellite Application Facility (ROM SAF) flag database. From 0 to 25 km altitude, the mean biases and relative standard deviations of the comparisons between FY-3C and COSMIC are less than 1% and 2% when COSMIC profiles present reflected signals. Radio holographic analysis is used to visualize and identify the spectra of FY-3C-reflected signals in the time-frequency domain. It is confirmed that the reflected signals in the lower troposphere and near the surface can be tracked by an FY-3C receiver. Further, most of the FY-3C events that matched with COSMIC reflected events show reflection patterns at a lower height, especially above the ocean’s surface. Under Bouguer’s rule and spherical symmetry assumptions, we reconstructed the reflected bending angle models by Abel transformation, which are valuable for reducing N-bias in the ducting layer. Three examples of FY-3C events show that the reflected bending branch is near the surface. Overall, the reflected signal of FY-3C could be used as a supplementary data portion for FY-3C atmospheric products.

The main purpose of this article is to evaluate the comprehensive performance of two inter-frequency code bias (IFCB) models using undifferenced and uncombined observations. These two IFCB models estimate IFCB parameters for each GLONASS satellite (EG model) and IFCB parameters using a quadratic function of frequency channels K (K = −7…6) (QF model). The data sampled in 30 s from 140 stations of the IGS network on 1–7 September 2021, are used for this study. We analyze all the combinations, including the GLONASS data, from the perspective of positioning accuracy, convergence time, and data utilization. The results show that the positioning accuracy of these two IFCB models for the same combination is comparable in three directions in both static and kinematic modes under long-term observation; the positioning accuracies of each IFCB model for all the combinations are almost the same in three directions in static mode, and the positioning accuracy of the combinations including the GPS data in three directions is better than that of the combinations not including the GPS data for kinematic mode. For some combinations, such as GLONSS-only and GPS/GLONASS, the convergence time of the EG model is better than that of the QF model, but the improvement rate does not exceed 22%. However, for other combinations, such as GLONASS/BDS and GLONASS/BDS/GALILEO, the convergence time of the QF model is better than that of the EG model, and the improvement rate in some directions is more than 50%. For the combinations including GPS data, the data utilization of the EG and QF models are almost the same for both static and kinematic modes; however, for combinations without GPS data, the data utilization of the QF model is better than that of the EG model. For these two IFCB models (EG and QF models), all combinations can achieve the set accuracy thresholds in three directions, but the EG model has more parameters to estimate than the QF model. From the perspectives of positioning accuracy, solution convergence time, data utilization, and the number of estimated parameters for each IFCB model, we suggest that the IFCB should be estimated using the QF model when performing combined PPP for different combinations.