Thanks to the international GNSS service (IGS), which has provided multi-GNSS precise products, multi-GNSS precise point positioning (PPP) time and frequency transfer has of great interest in the timing community. Currently, multi-GNSS PPP time transfer is not investigated with different precise products. In addition, the correlation of the receiver clock offsets between adjacent epochs has not been studied in multi-GNSS PPP. In this work, multi-GNSS PPP time and frequency with different precise products is first compared in detail. A receiver clock offset model, considering the correlation of the receiver clock offsets between adjacent epochs using an a priori value, is then employed to improve multi-GNSS PPP time and frequency (scheme2). Our numerical analysis clarify how the approach performs for multi-GNSS PPP time and frequency transfer. Based on two commonly used multi-GNSS products and six GNSS stations, three conclusions are obtained straightforwardly. First, the GPS-only, Galileo-only, and multi-GNSS PPP solutions show similar performances using GBM and COD products, while BDS-only PPP using GBM products is better than that using COD products. Second, multi-GNSS time transfer outperforms single GNSS by increasing the number of available satellites and improving the time dilution of precision. For single-system and multi-GNSS PPP with GBM products, the maximum improvement in root mean square (RMS) values for multi-GNSS solutions are up to 7.4%, 94.0%, and 57.3% compared to GPS-only, BDS-only, and Galileo-only solutions, respectively. For stability, the maximum improvement of multi-GNSS is 20.3%, 84%, and 45.4% compared to GPS-only, BDS-only and Galileo-only solutions. Third, our approach contains less noise compared to the solutions with the white noise model, both for the single-system model and the multi-GNSS model. The RMS values of our approach are improved by 37.8–91.9%, 10.5–65.8%, 2.7–43.1%, and 26.6–86.0% for GPS-only, BDS-only, Galileo-only, and multi-GNSS solutions. For frequency stability, the improvement of scheme2 ranges from 0.2 to 51.6%, from 3 to 80.0%, from 0.2 to 70.8%, and from 0.1 to 51.5% for GPS-only, BDS-only, Galileo-only, and multi-GNSS PPP solutions compared to the solutions with the white noise model in the Eurasia links.

The augmentation of the Global Navigation Satellite System (GNSS) by Low Earth Orbit (LEO) satellites is proposed as an effective method to improve the precision and shorten the convergence time of Precise Point Positioning (PPP). Serving as navigation satellites in the future, LEO satellites need to be provided with their high-accuracy orbits in real-time. This would potentially enable the high-accuracy real-time LEO satellite clock determination, and eventually facilitate the high-accuracy ground-based positioning. Studies have been performed to achieve such real-time orbits using a Kalman filter in both the kinematic and reduced-dynamic modes. Batch Least-Squares (BLS) adjustment delivers more stable orbits in near-real-time, as it performs better phase screening. However, it suffers from longer delays compared to the Kalman filter. With the LEO satellite orbit prediction strategies improved over time, this latency can be bridged by short-term orbit prediction. In this study, using real-time GNSS satellite products, the real-time LEO satellite orbits are obtained based on the batch least-squares adjustment and short-term prediction. LEO ephemeris parameters are generated within specific prediction time windows. Using real data from the 500 km GRACE C satellite and 810 km Sentinel-3B satellite, the near-real-time BLS Precise Orbit Determination (POD) results exhibit good accuracy with an Orbital User Range Error (OURE) of 2–4 cm using different real-time GNSS products. A range of delays of the BLS POD processes are assumed, based on tests performed on different processing machines, leading to various prediction windows, from 3–8 min to 12–17 min that correspond to the real-time usage. The orbital prediction errors are shown to be highly correlated with the orbital height and the prediction time. The computational efficiency thus becomes essential to reduce the prediction errors for a certain LEO satellite. For advanced processing units leading to a prediction window shorter or equal to 6–11 min, one can expect a total real-time orbital error budget of 3–5 cm, provided that an appropriate prediction strategy is applied and high-quality GNSS products are used. For a given fitting interval, the ephemeris fitting errors are generally related to the number of ephemeris parameters and the orbital height. Compared with the prediction errors, the ephemeris fitting errors do not play a significant role in the total error budget when using 22 ephemeris parameters.

Nowadays, integrity monitoring (IM) is required for diverse safety-related applications using intelligent transport systems (ITS). To ensure high availability for road transport users for in-lane positioning, a sub-meter horizontal protection level (HPL) is expected, which normally requires a much higher horizontal positioning precision of, e.g., a few centimeters. Precise point positioning-real-time kinematic (PPP-RTK) is a positioning method that could achieve high accuracy without long convergence time and strong dependency on nearby infrastructure. As the first part of a series of papers, this contribution proposes an IM strategy for multi-constellation PPP-RTK positioning based on global navigation satellite system (GNSS) signals. It analytically studies the form of the variance-covariance (V-C) matrix of ionosphere interpolation errors for both accuracy and integrity purposes, which considers the processing noise, the ionosphere activities and the network scale. In addition, this contribution analyzes the impacts of diverse factors on the size and convergence of the HPLs, including the user multipath environment, the ionosphere activity, the network scale and the horizontal probability of misleading information (PMI). It is found that the user multipath environment generally has the largest influence on the size of the converged HPLs, while the ionosphere interpolation and the multipath environments have joint impacts on the convergence of the HPL. Making use of 1 Hz data of Global Positioning System (GPS)/Galileo/Beidou Navigation Satellite System (BDS) signals on L1 and L5 frequencies, for small- to mid-scaled networks, under nominal multipath environments and for a horizontal PMI down to $2\times {10}^{-6}$, the ambiguity-float HPLs can converge to 1.5 m within or around 50 epochs under quiet to medium ionosphere activities. Under nominal multipath conditions for small- to mid-scaled networks, with the partial ambiguity resolution enabled, the HPLs can converge to 0.3 m within 10 epochs even under active ionosphere activities.

Low Earth orbit (LEO) satellites benefit future ground-based positioning with their high number, strong signal strength and high speed. The rapid geometry change with the LEO augmentation offers acceleration of the convergence of the precision point positioning (PPP) solution. This contribution discusses the influences of the LEO augmentation on the precise point positioning—real-time kinematic (PPP-RTK) positioning and its integrity monitoring. Using 1 Hz simulated data around Beijing for global positioning system (GPS)/Galileo/Beidou navigation satellite system (BDS)-3 and the tested LEO constellation with 150 satellites on L1/L5, it was found that the convergence of the formal horizontal precision can be significantly shortened in the ambiguity-float case, especially for the single-constellation scenarios with low precision of the interpolated ionospheric delays. The LEO augmentation also improves the efficiency of the user ambiguity resolution and the formal horizontal precision with the ambiguities fixed. Using the integrity monitoring (IM) procedure introduced in the first part of this series of papers, the ambiguity-float horizontal protection levels (HPLs) are sharply reduced in various tested scenarios, with an improvement of more than 60% from 5 to 30 min after the processing start. The ambiguity-fixed HPLs can generally be improved by 10% to 60% with the LEO augmentation, depending on the global navigation satellite system (GNSS) constellations used and the precision of the ionospheric interpolation.

International time transfer based on Global Navigation Satellite System (GLONASS) precise point positioning (PPP) is influenced by inter-frequency code biases (IFCBs) because of the application of frequency division multiple access technique. This work seeks to gain insight into the influence of GLONASS IFCBs on international time transfer based on GLONASS-only PPP. With a re-parameterization process, three IFCB handling schemes are proposed: neglecting IFCBs, estimating IFCB for each GLONASS frequency number, and estimating IFCB for each GLONASS satellite. Observation data collected from 39 globally distributed stations in a 71-day period (DOY 227–297, 2017) was exclusively processed. For the comparison reason, Global Positioning System (GPS)-only PPP solutions were regarded as reference values. The clock differences derived from GPS- and GLONASS-only PPP solutions were then analyzed. The experimental results demonstrated that considering GLONASS IFCBs could reduce standard deviation (STD) of the clock differences for both identical receiver types and mixed receiver types, of which reduction was from 3.3% to 62.6%. Furthermore, compared with neglecting IFCBs, STD of the clock differences with estimating IFCB for each GLONASS satellite in coordinate-fixed mode was reduced by more than 30% from 0.30 to 0.20 ns, and by 10% from 0.40 to 0.35 ns, for 1-day arc solutions and 10-day arc solutions, respectively. Moreover, different precise products from three International GNSS Service (IGS) analysis centers were also evaluated. Even though different IFCB handling schemes were adopted in GLONASS satellite clock estimation, our numerical results showed that international time transfer on the basis of estimating IFCB for each GLONASS satellite better than the other two processing schemes. To achieve high-precision GLONASS-only PPP-based international time transfer, it is highly recommended to estimate IFCB for each GLONASS satellite.

The components of EAM are strongly correlated with LOD and play an important role in UT1-UTC and LOD prediction. However, the EAM dataset is prone to be noisy. In this study, we propose a hybrid method to reduce the noise of the EAM data and improve the accuracy of UT1-UTC and LOD predictions. We use the EOP data to denoise the EAM data, and use Kalman filtering to denoise the 1–6 days forecast of EAM. Then, we use the denoised EAM dataset to improve the UT1-UTC and LOD prediction. The denoised EAM dataset improved the prediction of UT1-UTC within 10 days by 20%. In addition, we found that by introducing two additional periodic (23.9 days and 91.3 days) components for the least-squares fitting, the accuracy of UT1-UTC and LOD prediction in the range of 30–80 days is significantly improved. In more than 430 UT1-UTC and LOD prediction experiments conducted during 2021–2022, the improvements in the 1–6 days forecast were significant. For the 6th day, 30th day, and 60th day, the MAE of UT1-UTC was 0.1592, 2.9169, and 6.7857 ms, respectively, corresponding to improvements of 31.35, 12.60, and 12.93%, respectively, when compared to predictions of Bulletin A. The MAE of LOD predictions on the 1st day, 6th day, 30th day, and 90th day was 0.0255, 0.0432, 0.1694, and 0.2505 ms, respectively, which improved by 26.09, 14.29, 6.36, and 3.76% when compared with our second EOPPCC method.