Because of the frequency division multiple access (FDMA) technique, Russian global navigation satellite system (GLONASS) observations suffer from pseudo-range inter-channel biases (ICBs), which adversely affect satellite clock offset estimation. In this study, the GLONASS pseudo-range ICB is treated in four different ways: as ignorable parameters (ICB-NONE), polynomial functions of frequency (ICB-FPOL), frequency-specific parameters (ICB-RF), and satellite-specific parameters (ICB-RS). Data from 110 international global navigation satellite system (GNSS) service stations were chosen to obtain the ICBs and were used for satellite clock offset estimation. The ICBs from the different schemes varied from −20 ns to 80 ns. The ICB-RS model yielded the best results, improving the clock offset accuracy from 300 ps to about 100 ps; it could improve the GLONASS precise point positioning (PPP) accuracy and the converging time by approximately 50% and 30%, respectively. Along similar lines, we introduced the GPS-ICB parameters in the process of GPS satellite clock estimation and GPS/GLONASS PPP, as ICBs may exist for GPS because of different chip shape distortions among GPS satellites. This possibility was found to be the case. Further, the GPS-ICB magnitude ranged from −2 ns to 2 ns, and the estimated satellite clock offsets could improve the accuracy of the GPS and combined GPS/GLONASS PPP by 10%; it also accelerated the converging time by more than 15% thanks to the GPS-ICB calibration.

The precise point positioning real-time kinematic (PPP-RTK) technique enables a single receiver to achieve high-precision and real-time positioning services, mainly relying on integer ambiguity resolution based on satellite phase bias (SPB) information. For the PPP-RTK technique based on uncombined observations, the SPBs of basic frequencies are available only at low precision because of high correlation and therefore need to be updated frequently. Thus, the most appropriate linear combinations of BeiDou triple-frequency SPBs with low update rates for transmission to users must be identified. To acquire combinations of BeiDou triple-frequency SPBs, we use the Z -transformation to process the covariance matrixes corresponding to SPB estimates to generate decorrelated SPB combinations. To meet different circumstances, geometry-free, geometry-fixed and geometry-plus-satellite-clock-fixed variants of PPP-RTK are applied to process data from the regional network. The computed results indicate that the primary stable, secondary and tertiary stable SPB combinations of B1, B2 and B3 frequencies are (0, −1, 1), (1, 2, −3), and (−33, −129, 163) for the geometry-free variant, (0, −1, 1), (1, 2, −3), and (−21, −95, 117) for the geometry-fixed variant, and (0, −1, 1), (1, 3, −4), and (−18, −84, 103) for the geometry-plus-satellite-clock-fixed variant. Furthermore, the statistical results of the SPB series provide stable periods of the primary stable combinations of longer than 7 d. For the secondary and tertiary stable combinations, the stable periods for the geometry-free variant are 12 h and 5 h, for the geometry-fixed variant 12 h and 8 h, and for geometry-plus-satellite-clock-offset variant 12 h and 10 h. These stable periods suggest how often the SPB information should be updated and provide meaningful insight for the allocation of the computing resources of the PPP-RTK server.

The BeiDou-3 Navigation Satellite System (BDS-3) transmit new frequency signals, B1C and B2A, achieving good interoperability with code division multiple access (CDMA) systems such as GPS and Galileo. These new signals feature significant improvements in modulation design and frequency planning, providing a more stable observation foundation for multi-system high-precision positioning. Focusing on resolving observation loss and observation noise amplification in traditional precise point positioning (PPP) and real-time kinematic (RTK) models, this study proposes an undifferenced and uncombined PPP-RTK models based on multi-frequency CDMA signals and analyses its rank-deficiency characteristics and optimization strategies. First we analyze the linear correlations among clock, phase bias, ionospheric delay ambiguity and other parameters, the S-basis linear transformation method is employed to eliminate rank deficiency, furthermore derive the full-rank equations of the multi-frequency CDMA-based PPP-RTK system and complete the product generation based on the new frequencies of the BDS-3 system. Utilizing data from 13 continuous observation stations in the Northern China region, this study conducts a comparative analysis of GPS, GALILEO, and the new (B1C/B2A) and legacy (B1I/B3I) frequencies of BDS-3 in terms of satellite clock offsets, phase biases, and ionospheric products. The results indicate that after convergence the GPS, GALILEO BDS-3 new frequency satellite clock standard deviation can reaches 0.03 ns; uncalibrated phase delays for the L1 frequency is approximately 0.02 cycles; the products of BDS-3 new frequency outperform the old ones. In terms of ionospheric products, data from 4 stations in the survey area over 5 d are selected, the slant delay derived from the geometry-free combination of phase observations is taken as the true value, by calculating the difference between the slant delay derived from model coefficients and the true value, the (root mean square) values of GPS, GAL (Galileo), BDS-3 (B1C & B2A), and BDS-3 (B1I & B3AI) are better than 0.232 m, 0.176 m, 0.164 m, and 0.536 m.