Since the observation precision of the Global Navigation Satellite System (GNSS) carrier phase is on the order of millimeters, if the phase ambiguity is correctly solved, while calibrating the receiver inter-frequency bias, time synchronization on the order of tens of picoseconds is expected. In this contribution, a method that considers the prior constraints of the between-receiver inter-frequency bias (IFB) and its random variation characteristics is proposed for the estimation of the between-receiver clock difference, based on the uncombined GNSS carrier phase and pseudorange observations of the zero and short baselines. The proposed method can rapidly achieve the single-difference ambiguity resolution of the zero and short baselines, and then obtain the high-precision relative clock offset, by using only the carrier phase observations, along with the between-receiver IFBs being simultaneously determined. Our numerical tests, carried out using GNSS observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, show that the method can fix the between-receiver single-difference ambiguity successfully within an average of fewer than 2 epochs (interval 30 s). Then, a clock difference between two receivers with millimeter precision is obtained, achieving time synchronization on tens of picoseconds level, and deriving a frequency stability of 5 × 10⁻¹⁴ for averaging times of 30,000 s. Furthermore, the proposed approach is compared with the precise point positioning (PPP) time transfer method. The results show that, for different types of receivers, the agreement between the two methods is between −6.7 ns and 0.2 ns.

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.