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.

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.

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 development of the BeiDou navigation system (BDS) is divided into three phases: The demonstration system (BDS-1), the regional system (BDS-2) and the global BeiDou navigation system (BDS-3). At present, the construction of the global BeiDou navigation system (BDS-3) constellation network is progressing very smoothly. The signal design and functionality of BDS-3 are different from those of BDS-1 and BDS-2. The BDS-3 satellite not only broadcasts B1I (1561.098 MHz) and B3I (1268.52 MHz) signals but also broadcasts new signals B1C (1575.42 MHz) and B2a (1176.45 MHz). In this work, six tracking stations of the international GNSS monitoring and assessment system (iGMAS) were selected, and 41 consecutive days of observation data, were collected. To fully exploit the code observations of BDS-2 and BDS-3, the time group delay (TGD) correction model of BDS-2 and BDS-3 are described in detail. To further verify the efficacy of the broadcast TGD parameters in the broadcast ephemeris, the standard point positioning (SPP) of all the signals from BDS-2 and BDS-3 with and without TGD correction was studied. The experiments showed that the B1I SPP accuracy of BDS-2 was increased by approximately 50% in both the horizontal and vertical components, and B1I/B3I were improved by approximately 70% in the horizontal component and 47.4% in the vertical component with TGD correction. The root mean square (RMS) value of B1I and B1C from BDS-3 with TGD correction was enhanced by approximately 60%–70% in the horizontal component and by approximately 50% in the vertical component. The B2a-based SPP was increased by 60.2% and 64.4% in the east and north components, respectively, and the up component was increased by approximately 19.8%. For the B1I/B3I and B1C/B2a dual-frequency positioning accuracy with TGD correction, the improvement in the horizontal component ranges from 62.1% to 75.0%, and the vertical component was improved by approximately 45%. Furthermore, the positioning accuracy of the BDS-2 + BDS-3 combination constellation was obviously higher than that of BDS-2 or BDS-3.

To resolve the dilemma in any post-processing strategy, i.e., the difficulty of monitoring the real-time time and frequency signals in a timely manner, real-time GPS time and the frequency transfer have recently become trending topics. Unfortunately, data interruption occurs when conducting real-time time transfer, sometimes from unexpected reasons. In this study, to ensure the stability and precision of real-time time transfer, an adaptive prediction model and a between-epoch constraint receiver clock model are applied as the mathematic models. The purpose of prediction is to solve the ambiguity from re-convergence when the data reappear. Moreover, compared to the conventional method, the between-epoch constraint receiver clock model is employed in this study to consider the correlation of epoch-wise clock parameters to avoid wasting useful information. The simulation data and real data are compared to verify the performance of the new approach. The simulation data for 165 days are designed with random daily interruptions of 10, 30, 60 and 90 min. Real data from 12 days is captured from the incomplete data in routine observation records. Ignoring the simulation data and real data, the investigation of six stations shows that the results with the between-epoch constraint receiver clock model were smoother than those with a white noise model. With an adaptive prediction model and the between-epoch constraint receiver clock model, the simulation results illustrate that the average root mean squares (RMS) values of all the stations are significantly reduced, i.e., by 66.03% from 0.43 to 0.14 ns, by 64.91% from 0.44 to 0.15 ns, by 57.47% from 0.43 to 0.18 ns, and by 51.67% from 0.44 to 0.21 ns for the 10, 30, 60 and 90 min data interruptions, respectively. The stability of all the stations is improved by at least 50%. The improvement increases to 100% for short-term stability. The real results show that the stability of four links is boosted by at least 5%. The model proposed in this paper is more effective in producing short-term stability than long-term stability.

The timing group delay parameter (TGD) or differential code bias parameter (DCB) is an important factor that affects the performance of GNSS basic services; therefore, TGD and DCB must be taken seriously. Moreover, the TGD parameter is modulated in the navigation message, taking into account the impact of TGD on the performance of the basic service. International GNSS Monitoring and Assessment System (iGMAS) provides the broadcast ephemeris with TGD parameter and the Chinese Academy of Science (CAS) provides DCB products. In this paper, the current available BDS-3 TGD and DCB parameters are firstly described in detail, and the relationship of TGD and DCB for BDS-3 is figured out. Then, correction models of BDS-3 TGD and DCB in standard point positioning (SPP) or precise point positioning (PPP) are given, which can be applied in various situations. For the effects of TGD and DCB in the SPP and PPP solution processes, all the signals from BDS-3 were researched, and the validity of TGD and DCB has been further verified. The experimental results show that the accuracy of B1I, B1C and B2a single-frequency SPP with TGD or DCB correction was improved by approximately 12–60%. TGD will not be considered for B3I single-frequency, because the broadcast satellite clock offset is based on the B3I as the reference signal. The positioning accuracy of B1I/B3I and B1C/B2a dual-frequency SPP showed that the improvement range for horizontal components is 60.2% to 74.4%, and the vertical components improved by about 50% after the modification of TGD and DCB. In addition, most of the uncorrected code biases are mostly absorbed into the receiver clock bias and other parameters for PPP, resulting in longer convergence time. The convergence time can be max increased by up to 50% when the DCB parameters are corrected. Consequently, the positioning accuracy can reach the centimeter level after convergence, but it is critical for PPP convergence time and receiver clock bias that the TGD and DCB correction be considered seriously.