Assessment of BDS-3 PPP-B2b Service and Its Applications for the Determination of Precipitable Water Vapour

Abstract

The precise point positioning (PPP) service via the B2b signal (PPP-B2b) on the BeiDou Navigation Satellite System (BDS) provides high-accuracy orbit and clock data for global navigation satellite systems (GNSSs), enabling real-time atmospheric data acquisition without internet access. In this study, we assessed the quality of orbit, clock, and differential code bias (DCB) products from the PPP-B2b service, comparing them to post-processed products from various analysis centres. The zenith tropospheric delay (ZTD) and precipitable water vapour (PWV) were computed at 32 stations using the PPP technique with PPP-B2b corrections. These results were compared with post-processed ZTD with final orbit/clock products and ZTD/PWV values derived from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA5) and radiosonde data. For stations between 30° N and 48° N, the mean root mean square error (RMSE) of ZTD for the PPP-B2b solution was approximately 15 mm compared to ZTD from the International GNSS Service (IGS). However, accuracy declined at stations between 30° N and 38° S, with a mean RMSE of about 25 mm, performing worse than ZTD estimates using Centre National d’Études Spatiales (CNES) products. The mean RMSEs of PWV derived from PPP-B2b were 3.7 mm and 4.4 mm when compared to PWV from 11 co-located radiosonde stations and ERA5 reanalysis, respectively, and underperformed relative to CNES solutions. Seasonal variability in GNSS-derived PWV was also noted. This reduction in accuracy limits the global applicability of PPP-B2b. Despite these shortcomings, satellite-based PPP services like PPP-B2b remain viable alternatives for real-time positioning and atmospheric applications without requiring internet connectivity.

1. Introduction

Water vapour and temperature are two key variables in the study of the global climate change and the weather nowcasting [1,2,3]. The global navigation satellite systems (GNSSs), which are designed mainly for positioning, navigation, and timing [4], has also been used to remotely sense the Earth’s atmosphere since the 1990s. In 1992, Bevis et al. [5] introduced the concept of ground-based GNSS meteorology for the first time, which has since prompted extensive academic investigation into the precision and reliability of GNSS-derived zenith total delay (ZTD) and precipitable water vapour (PWV). Due to its high accuracy and all-weather operational capability, GNSS-derived ZTD or PWV has become an indispensable dataset for atmospheric and climate studies [6,7,8,9,10,11,12,13] and weather forecasting [14,15,16,17,18]. In addition, GNSS-derived ZTD or PWV have been used in many studies to evaluate data derived with other techniques [19,20] or for tropospheric corrections for remote sensing techniques, e.g., interferometric synthetic aperture radar [21]. In 2013, the International GNSS Service (IGS) formally launched the IGS real-time service (RTS) to provide GNSS orbit and clock correction products to subscribed users via the internet. With the provided real-time satellite orbit and clock corrections [22,23,24], ZTD or PWV can be estimated in real time and with high accuracy using a precise point positioning (PPP) data processing strategy [25]. As demonstrated by Shi et al. [26], the accuracy of real-time ZTD or PWV estimates using PPP highly depends on the quality of the satellite orbit and clock products. Previous studies [27,28,29,30,31,32,33] have demonstrated that the accuracy of real-time tropospheric estimates using PPP with high-accuracy and real-time satellite orbit and clock products can reach 2–3 mm for PWV or approximately 5–10 mm for ZTD. The real-time orbit and clock products adopted in these studies are disseminated through the internet in the state space representation (SSR) format.

Therefore, to estimate the ZTD or PWV in real time with IGS RTS, one must have stable internet access; this limits the use of this technique in areas without reliable internet connections, for example, island, rural, and mountainous areas. With the launch of the last satellite on 23 June 2020, the third generation of the Beidou Navigation Satellite System (BDS-3) began providing timing and navigation services for global coverage [34]. The main feature of BDS-3 is its PPP service via the B2b signal (PPP-B2b), which provides high-accuracy orbit and clock information for BDS-3 and Global Positioning System (GPS) satellites through three geosynchronous equatorial orbit (GEO) satellites [35]. The BDS GEO satellites operate in orbit at altitudes of 35,786 km and are located at 80° E, 110.5° E, and 140° E. Compared with the IGS RTS, the BDS-3 PPP-B2b service is more convenient for users without a reliable internet connection. Figure 1 shows the coverage areas of three BDS GEO satellites on Earth for different elevation cut-off angles. The PPP-B2b service can be accessed by users in most regions of Asia, Europe, Africa, and Oceania, even with the cut-off angle set to 15°.

The quality of orbit and clock information provided by the PPP-B2b service has been assessed in several recent studies [36,37,38]. For example, Tao et al. [38] investigated the accuracy of PPP-B2b orbit and clock products by comparing them with products provided by Wuhan University. The results indicate that the root mean square errors (RMSEs) of the orbits from PPP-B2b were approximately 6 cm and 21 cm in the radial and cross-track directions, respectively, for both GPS and BDS-3. In the along-track direction, the RMSEs were approximately 24 cm and 34 cm for BDS-3 and GPS, respectively. In terms of the clock products, the standard deviations (STDs) of the PPP-B2b clocks were 0.11 ns and 0.13 ns for BDS-3 and GPS, respectively. Recent studies [36,37] also indicate that the average positioning accuracy of static PPP with PPP-B2b corrections is better than 3 cm in the north, east, and upwards directions. This good positioning performance means that tropospheric information could be accurately estimated in real time using the PPP-B2b service, a feature that would be useful in areas without reliable internet connections for weather forecasting and atmospheric studies. The retrieval performance of ZTD in China has been subject to analysis in several studies. Yang et al. [39] reported a RMS difference of 17.4 mm between ZTD values derived using the PPP-B2b service and those estimated by IGS across nine stations from DOY 195 to DOY 200. Xu et al. [40] conducted an analysis of ZTD values derived from PPP-B2b against those provided by the Wuhan University (WHU) analysis centre at eight stations from DOY 187 to DOY 191 in 2021, finding an RMS within 20 mm for stations located in China. However, these investigations are predominantly constrained by their short temporal scope (e.g., one week) and regional focus on China. Given that the effective coverage area of PPP-B2b is not clearly delineated and considering the crucial importance of its temporal stability for operational applications, a more comprehensive study encompassing a broader spatial distribution and extended temporal duration is warranted.

This study conducted a comprehensive investigation into the performance of PPP-B2b corrections, focusing on their application in ZTD/PWV estimation across 32 widely distributed stations over approximately one year. The accuracy of BDS-3, GPS orbit, and clock correction from PPP-B2b was assessed using geodetic benchmark (GBM) products from Deutsches Geo-ForschungsZentrum (GFZ) as a reference. Previous studies have demonstrated centimetre-level agreement between orbit/clock products from different analysis centres, with static positioning results showing only centimetre-level differences between products from the Center for Orbit Determination in Europe and GFZ [41]. Additionally, GFZ’s GBM products have been widely adopted for the evaluation of real-time orbit and clock products [36,42].

The differential code bias (DCB) for BDS-3 from the PPP-B2b service was assessed using data from the German Aerospace Center (DLR) and the Chinese Academy of Sciences (CAS). The ZTD values estimated with the PPP-B2b and Centre National d’Etudes Spatiales (CNES) real-time streams are investigated via comparison with those derived from the final clock and orbit products retrieved from the GBM and ZTD data provided by the IGS. Because it is a well-established method to estimate ZTD/PWV using RTS services, such as CNES RTS, comparing the performance of CNES and PPP-B2b allows us to evaluate the level of accuracy PPP-B2b currently achieves for the real-time applications. As indicated by Yu et al. [43], the orbit accuracy of GNSS products for GPS has been reported to be better than 5 cm in all three directions, with clock errors under 0.1 ns. For BDS, the orbit accuracy is approximately 10 cm, with clock errors around 0.66 ns. The latency of these products is approximately 18 s. The GNSS-derived ZTD and PWV data are compared with those determined from the European Centre for Medium-Range Weather Forecasting (ECMWF) Reanalysis fifth generation (ERA5) and radiosonde observations from the Integrated Global Radiosonde Archive (IGRA). Radiosonde data offer high accuracy through direct atmospheric measurements but are spatially and temporally limited. ERA5, though model-based, provides continuous global coverage and high temporal resolution. Utilizing both datasets allowed us to achieve precise validation where radiosonde data were available, while ensuring broader spatial and temporal analysis with ERA5, offering a more comprehensive assessment of GNSS-derived ZTD and PWV. The investigation, utilizing widely distributed stations and data spanning one year, provides valuable insights into the service’s performance and stability across diverse regions over an extended period.

2. Data and Methodologies

2.1. PPP-B2b Message and GNSS Observations

Using our custom-developed GNSS receiver and self-developed decoding software, the PPP-B2b corrections were received and decoded in real time at station BJ01 (40.07° N, 116.27° E) in Beijing, China. These corrections were then stored for further study. The receiver is equipped with a K803 GNSS OEM module provided by GomNav Technology Ltd. (ShangHai, China), designed to support the PPP-B2b signal with a centre frequency of 1207.14 MHz and a bandwidth of 20.46 MHz. The PPP-B2b data are acquired and transmitted to an Advanced RISC Machine (ARM) processor via the RS-232 communication standard in binary format. Our in-house developed software on the ARM processor then converts these binary data into ASCII format, enabling the real-time estimation of ZTD and coordinates using the PPP software running on the ARM processor. Furthermore, the software includes functionality for storing PPP-B2b data and transmitting the real-time stream to a Linux server, which broadcasts these corrections to users via the Internet. This capability facilitates broader access to real-time corrections for researchers and practitioners. Additional technical details regarding the structure and processing of PPP-B2b information are provided in the Appendix. Researchers interested in utilizing these corrections can request access by contacting the authors directly via email. The performances of the clock, orbit, and DCB broadcast on the PPP-B2b signal between DOY 069-311 in 2022 were compared with the final clock and orbit products from GBM and DCB from the Multi-GNSS Experiment (MGEX) project. It should be noted that our GNSS receiver could not continuously record the PPP-B2b information in May and June 2022 due to a power supply issue. The GNSS observations were available at 32 stations in RINEX format and were downloaded from the Crustal Dynamics Data Information System (CDDIS) (Noll 2010) or from our own observation network.

2.2. ERA5 Data

The production of the ERA5 dataset was based on the operational use of the Integrated Forecasting System (IFS) Cycle 41r2, with the advanced four-dimensional data assimilation technique and modelling, which provides estimates of atmospheric parameters on an hourly basis from 1950 onwards. More information regarding the ERA5 configuration, how it was produced, and how it fits into the framework of other reanalysis activities in the ECMWF can be found in the study by Hersbach et al. [44].

With the hourly temperature T (in Kelvin), specific humidity q (in kg kg⁻¹), and pressure P (in hPa) at 37 pressure levels provided by ERA5, the ZTD (in meters) was calculated with Equation (1) [45].

$${ZTD=10}^{-6}{k}_1{R}_d{\int }_0^{P_{ant}} {\displaystyle \frac{1}{g\left(z\right)}}·dP+{10}^{-6}{R}_w {\int }_0^{P_{ant}} q{\displaystyle \frac{1}{g\left(z\right)}}\left(k_2^{\prime }+{\displaystyle \frac{k_3}{T·}}\right) dP$$

(1)

where $R_d=287.053 \mathrm{J}·{\mathrm{K}}^{-1}·{\mathrm{K}\mathrm{g}}^{-1}$ and $R_w=461.5 \mathrm{J}·{\mathrm{K}}^{-1}·{\mathrm{K}\mathrm{g}}^{-1}$ are the gas constants for dry air and water vapour, respectively; ${\mathrm{k}}_1=77.60 \mathrm{K}{\mathrm{h}\mathrm{P}\mathrm{a}}^{-1}$ and ${\mathrm{k}}_2^{\prime }=22.1 \mathrm{K}{\mathrm{h}\mathrm{P}\mathrm{a}}^{-1}$ [46]; and $P_{ant}$ (in hPa) is the pressure at the GNSS station height. The first term of the integral in Equation (1) is the zenith hydrostatic delay (ZHD), and the second term is the zenith wet delay (ZWD). $g\left(z\right)$ is the local gravitational acceleration at geometric height z (in km) [47].

$$g\left(z\right)=g_s{\left({\displaystyle \frac{R_s}{R_s+z}}\right)}^2$$

(2)

where $g_s$ is the local acceleration of gravity at mean sea level at latitude $\phi$ and $R_s$ is the effective radius of the earth at latitude $\phi$. These parameters can be determined with Equation (3) [48].

$$\left\{\begin{array}{c}{g}_s\approx 9.80620·\left(1-0.0026442·\mathit{cos}\left(2\phi \right)+5.8·{10}^{-6}·{cos}^2\left(2\phi \right)\right)\\ R_s=6378.137/(1.006803-0.006706·{\mathrm{s}\mathrm{i}\mathrm{n}}^2\left(\phi \right))\end{array}\right.$$

(3)

The PWV (in meters) can be calculated using:

$$\mathrm{PWV}={\displaystyle \frac{1}{{\rho }_w}}{\int }_0^{P_{ant}}{\displaystyle \frac{q}{g\left(z\right)}}dP$$

(4)

where ${\rho }_w=1000 \mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$ is the density of water vapour, P is the pressure (in Pa), and q is the specific humidity.

For GNSS stations located above or below the lowest pressure level of ERA5, an interpolation or extrapolation procedure must be performed to determine the pressure, humidity, and temperature at the GNSS station altitude. More details on the extrapolation or interpolation procedures can be found in our previous studies [49,50]. The procedures for converting the GNSS altitude referring to an ellipsoid to an altitude relative to the mean sea level were also described in our previous study [49].

2.3. Radiosonde

The radiosonde data used in this study were provided by IGRA version 2 and consisted of quality-controlled observations of temperature, humidity, and pressure at stations across all continents. The ZTD and PWV are calculated with Equations (1)–(4) using the atmospheric profiles observed by radiosonde data. The specific humidity $q$ is not included in the radiosonde observations and, thus, needs to be calculated with the total pressure P and the vapour pressure $P_v$ provided by the IGRA using:

$$q={\displaystyle \frac{0.622\cdot P_v}{P-0.378\cdot P_v}}$$

(5)

As suggested by Haase et al. [45], a quality control procedure was carried out to exclude radiosonde observations that had a large pressure gap (greater than 200 hPa) between two adjacent observation levels.

The maximum altitude reached by a weather balloon varies due to weather conditions and other factors, directly affecting the highest pressure level recorded by the radiosonde [51]. As a result, the ZTD derived from radiosonde data only accounts for the atmospheric contribution up to the recorded level (e.g., 50 hPa), inherently underestimating the total ZTD. To correct for this, Equation (6) [45] was utilized to calculate the contribution of the ZHD from atmospheric layers above the radiosonde’s maximum altitude. This value was then integrated with the ZTD obtained from Equation (1) to provide a more accurate estimation.

$$∆ZHD\approx {\displaystyle \frac{k_1{R}_d{P}_1}{g_1}}\left\{1+2{\displaystyle \frac{R_d{T}_1}{(R_s+z_1)g_1}}+2{\left[{\displaystyle \frac{R_d{T}_1}{(R_s+z_1)g_1}}\right]}^2\right\}$$

(6)

where $P_1$, $g_1$, $T_1$, and $z_1$ are the pressure, local gravitational acceleration, temperature, and geometric height at the top of the radiosonde observation profile, respectively. Because the water vapour density above the top of the radiosonde profiles is negligible, no contribution is added to the ZWD.

Similar to the determination of ZTD/PWV with ERA5, interpolation or extrapolation was performed to calculate the atmospheric variables at the GNSS station altitude depending on whether the station was above or below the lowest level of the radiosonde profiles. Figure 2 shows the distribution of GNSS stations (blue point) and their co-located radiosonde sites.

2.4. ZTD and PWV Estimation with PPP

The PPP technique is used in this study for estimating the ZTD with PPP-B2b, CNES, and GBM products. PPP is a fast and efficient means of estimating geodetic parameters such as coordinates and tropospheric delay. The accuracy of the PPP solution is highly dependent on the quality of the satellite orbit and clock because this information is introduced into the PPP processing, and the errors in this information are not eliminated or accounted for. With the improvement in the quality of the satellite orbit and the clock from IGS [52], PPP has become a very promising method in many applications, including the estimation of ZTD from a large network with hundreds or thousands of stations. The accuracy of the ZTD estimated with the PPP solution has been assessed in many studies. Thanks to the establishment of a real-time service in 2011 by IGS, the retrieval of the real-time ZTD or PWV using PPP became possible. Several studies [29,30,31,33,53] have demonstrated that the accuracy of the real-time PWV can reach 2~3 mm using PPP with high-accuracy real-time satellite orbit and clock products. A modified version of the RTKLIB software package [54] was utilized in this study for GNSS data processing. This version supports the PPP-B2b stream and incorporates new GNSS processing features, including the GPT3 model, to enhance the accuracy and efficiency of the data analysis.

In PPP processing, the tropospheric delays in the slant direction are usually expressed as [55]:

$$∆L=T_{priori}{·m}_h\left(e\right)+T_{remain}{·m}_w\left(e\right)+{·m}_w\left(e\right)·\mathrm{c}\mathrm{o}\mathrm{t}\left(e\right)\left(G_N\cos \left(\alpha \right)+G_E\sin \left(\alpha \right)\right)$$

(7)

where $T_{priori}$ represents the a priori zenith hydrostatic delay derived from an empirical model and $m_h$ and $m_w$ are the hydrostatic and wet mapping functions, respectively. $e$ and $\alpha$ are the elevation and azimuth, respectively, of the satellites. The remaining tropospheric delay $T_{remain}$, along with two gradient parameters $G_N$ and $G_E$ were estimated during the PPP process.

Thus far, many studies have been conducted with the aim of improving the accuracy of ZTD or PWV using an improved empirical ZHD model [50,56], water vapour-weighted mean temperature calculation methods [49,57,58,59,60,61] advanced ZTD estimation strategies [62,63,64,65,66], and newly developed mapping function and gradient models [61,67,68,69,70,71]. With suggestions from previous studies [64,72,73], a detailed description of the ZTD estimation strategy adopted in this study is presented in

Table 1. ZTD estimation strategy with PPP-B2b.

Items	Strategies
Observables	IFLC of the pseudorange and carrier phase
Frequencies	GPS L1/L2 and BDS-3 B1I/B3I (B1C/B2a)
Elevation cut-off angle	$7°$
ZTD estimation	The a priori value for the hydrostatic delay was calculated using the Saastamoinen model with pressure and temperature from GPT3; the wet delay was estimated as a random walk process noise of $5 \mathrm{mm}/\surd h$
Mapping function	GPT3
Gradient parameters	North and east components of the tropospheric gradient parameters were estimated
Receiver clock	The receiver clock was estimated for GPS and BDS-3 separately
Solution type	Static with float ambiguities
Corrections models	Phase wind-up, relativistic delays, and the effects of the solid Earth pole tide and ocean pole tide were modelled according to IERS Conventions 2010

. Zhang et al. [73] suggested that the adoption of a small cut-off elevation can significantly improve the accuracy of the ZTD; thus, the elevation cut-off angle was set to 7° in this study. The Global Pressure and Temperature 3 (GPT3) mapping function [61] and gradient model proposed by Macmillan [74] were adopted for ZTD estimation. The Saastamoinen model with empirical meteorological parameters from GPT3 was used to calculate the a priori value for the ZHD, and the remaining wet delay was estimated as random walk process noise of 5 mm/$\surd h$ [75].

The estimated ZTD was then converted to PWV using Equation (8) [5]:

$$PWV=(ZTD-{ZHD}_{ERA5})· {\displaystyle \frac{{10}^6}{ \rho R_w\left[\frac{k_3}{T_m}+k_2^{\prime }\right]}}$$

(8)

with ${ZHD}_{ERA5}$ computed using Equation (9) [5],

$${ZHD}_{ERA5}=2.2779·P_{ant}/[1-0.0026·\mathit{cos}\left(2\phi \right)-0.00028h]$$

(9)

and $T_m$ computed using Equation (10) [5],

$$T_m=70.2+0.72·T_{ant}$$

(10)

where $P_{ant}$ and $T_{ant}$ are the pressure and temperature at the GNSS station determined with the ERA5 dataset based on the methods described in previous studies [49,50], and $h$ (in km) is the GNSS height above the ellipsoid.

3. Evaluation of the Results for Clock, Orbit, and DCB

In this study, the PPP-B2b signal was received and decoded based on the published BDS Signal in Space Interface Control Documents for Open Service Signal PPP-B2b Version 1.0 (BDS-SIS-ICD-PPP-B2b-1.0) provided by the China Satellite Navigation Office [76]. The orbit and clock corrections in the PPP-B2b message were used to correct CNAV1 and LNAV for BDS-3 and GPS, respectively. The precise satellite position can be determined with the orbit correction vector in the PPP-B2b orbit correction message and the broadcast ephemeris. The precise clock offset can be calculated using the clock correction parameter in the PPP-B2b message and the broadcast ephemeris. In this study, the orbit, clock, and DCB performances recovered from PPP-B2b messages were evaluated with products from the MGEX pilot project [77]. Before the comparison between PPP-B2b and GBM products, several inconsistencies between these two sets of products needed to be fixed. For more details on PPP-B2b decoding and the methods used to evaluate the orbit, clock, and DCB, see Appendix A, Appendix B and Appendix C.

Because it takes time to obtain the correction information generated and transmitted from the master control station to users via BDS-3 GEO satellites, latency in the correction message received by the user is inevitable. The results show that the latencies of the PPP-B2b clock offsets received by our receiver at station BJ01 range from 5 s to 9 s for both GPS and BDS-3. These offsets are stable and within the nominal validity of the satellite clock corrections, that is, 12 s. As shown in

Table 2. Evaluation of the PPP-B2b orbit and clock.

System	STD of Clock Errors (ns)	RMSE of Orbit Errors (m)
		Radial	Along-Track	Cross-Track
GPS	0.16	0.08	0.36	0.28
BDS-3 MEO	0.13	0.10	0.27	0.28
BDS-3 IGSO	0.18	0.13	0.37	0.40

, for the GPS satellites, the standard deviation (STD) values ranged from 0.14 ns to 0.20 ns, with a mean value of 0.16 ns; for the BDS-3 medium Earth orbit (MEO) satellites, the STD values ranged between 0.11 ns and 0.17 ns, with a mean value of 0.13 ns. The performances of three inclined geosynchronous orbit (IGSO) satellites, that is, PRN C38-40, were worse than those of the BDS-3 MEO satellites, with a mean STD value of 0.18 ns. The results also indicate that there is an obvious day-to-day variation in the STD values for both GPS and BDS-3. For GPS, the daily STD values vary from 0.05 ns to 0.28 ns, with 83.9% and 35.2% of the values being smaller than 0.2 ns and 0.15 ns, respectively. For BDS-3, the daily mean STD values of the clock errors vary from 0.06 ns to 0.29 ns, with 96.3% and 68.9% of the values being smaller than 0.2 ns and 0.15 ns, respectively.

For the orbit corrections, the latencies were in the range of 21–30 s, which is within the nominal validity of the satellite orbit corrections, that is, 96 s. As shown in Table 2, both GPS and BDS-3 have a higher accuracy in the radial direction than in the along- and cross-track directions. The mean RMSEs for the GPS satellites were 0.08 m, 0.36 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively. For the BDS-3 MEO satellites, the mean RMSEs were 0.10 m, 0.27 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively, which were similar to those of the GPS satellites. For the BDS-3 IGSO satellites, the mean RMSEs in the radial, along-track, and cross-track directions were 0.13 m, 0.37 m, and 0.40 m, respectively, which were worse than those of the BDS-3 MEO and GPS satellites. The results reveal obvious day-to-day variations in the orbit errors for both GPS and BDS-3, especially in the along- and cross-track directions. For GPS, the daily mean RMSEs of the 3D orbit errors vary from 0.22 m to 0.85 m, 57.5% of which are smaller than 0.5 m. For BDS-3, the daily mean RMSEs of the 3D orbit errors vary from 0.19 m to 0.96 m, 71.5% of which are smaller than 0.5 m. The accuracy of ZTD estimation in PPP is heavily dependent on the precision of orbit and clock corrections. Douša [78] reports that tangential orbit errors of 10 cm or radial orbit errors of 1 cm can induce ZTD errors of up to 1.3 cm and 1.0 cm, respectively. However, their study also demonstrated that precise satellite clock corrections can mitigate over 96% of radial orbit errors, aided by the small nadir angle (15°) and ambiguity resolution in PPP. Consequently, even with decimetre-level orbit errors, centimetre-level accuracy for ZTD, and millimetre-level accuracy for PWV, assuming a scale factor of 0.15 between the ZTD and PWV [5], can be achieved, as most orbit errors can be compensated by precise satellite clock corrections and the estimated ambiguity parameter in the PPP approach.

The DCBs that refer to the B3I signal at frequencies of $f_{B1I}$, $f_{B1C}$, and $f_{B2a}$ for BDS-3 were compared to those from DLR and CAS provided by the MGEX pilot project, and the mean values of the differences for the study period are shown in

Table 3. STD values of the differences between different DCB products (unit: ns).

	${\mathbf{D}\mathbf{C}\mathbf{B}}_{\mathbf{D}\mathbf{L}\mathbf{R}}$$\mathbf{-}{\mathbf{D}\mathbf{C}\mathbf{B}}_{\mathbf{P}\mathbf{P}\mathbf{P}-\mathbf{B}2\mathbf{b}}$			${\mathbf{D}\mathbf{C}\mathbf{B}}_{\mathbf{C}\mathbf{A}\mathbf{S}}$$\mathbf{-}{\mathbf{D}\mathbf{C}\mathbf{B}}_{\mathbf{P}\mathbf{P}\mathbf{P}-\mathbf{B}2\mathbf{b}}$			${\mathbf{D}\mathbf{C}\mathbf{B}}_{\mathbf{D}\mathbf{L}\mathbf{R}}$$\mathbf{-}{\mathbf{D}\mathbf{C}\mathbf{B}}_{\mathbf{C}\mathbf{A}\mathbf{S}}$
Frequency	B1I	B1C(P)	B2a(P)	B1I	B1C(P)	B2a(P)	B1I	B1C(P)	B2a(P)
STD	0.36	0.37	0.22	0.35	0.37	0.27	0.15	0.14	0.13

. The systematic bias between each DCB product caused by the zero-assumption adopted in the DCB estimation must be removed before the comparison is conducted. This systematic bias between different DCB products is absorbed by the receiver clock parameter and, thus, does not affect the final positioning or ZTD results. Table 3 shows the STD values of the differences between the different DCB products. We found that the STDs of the differences between the DCBs of DLR and CAS are 0.15 ns, 0.14 ns, and 0.13 ns for frequencies of $f_{B1I}$, $f_{B1C}$, and $f_{B2a}$, respectively. For the frequencies $f_{B1C}$, $f_{B2a}$, and $f_{B1I}$, the STD values of the differences between the DCB from PPP-B2b and the DCB from DLR or CAS were all within 0.4 ns. Although the error in the DCB would lead to a longer convergence time, it could be mostly absorbed by the receiver clock and ambiguity parameter for PPP and, thus, had no effect on the accuracy of the troposphere and coordinate estimates.

The signal-in-space ranging error (SISRE) is a key performance indicator for comparisons of different navigation systems [79]. The instantaneous SISRE, considering that the clock and orbit can be calculated using Equation (11), and the orbit-only SISRE can be calculated using Equation (12):

$${SISRE}_{clk+orb}=\sqrt{{(w_R·∆r_R-∆C)}^2+w_{A,C}^2·\left({∆r_A}^2+{∆r_C}^2\right)}$$

(11)

$${SISRE}_{orb}=\sqrt{{(w_R·∆r_R)}^2+w_{A,C}^2·\left({∆r_A}^2+{∆r_C}^2\right)}$$

(12)

where $w_R$ and $w_{A,C}^2$ are GNSS-dependent SISRE weight factors for the statistical contribution of radial (R), along-track (A), and cross-track (C) errors to the line-of-sight ranging error; $∆r_R$, $∆r_A$, and $∆r_c$ are the residuals of the satellite orbit in the R, A, and C directions, respectively; and $∆C$ is the clock error. The weight factors $w_R$ and $w_{A,C}^2$ used for different satellite constellations were suggested by Montenbruck, Steigenberger, and Hauschild [79].

With the instantaneous SISREs at different epochs for a specific satellite during the period from DOY 069 to 311 in 2022, the RMSE values of ${SISRE}_{clk+orb}$ and ${SISRE}_{orb}$ for each satellite type were calculated and are presented in

Table 4. Statistical results for the SISREs (unit: m).

System	Satellite Type	${\mathit{S}\mathit{I}\mathit{S}\mathit{R}\mathit{E}}_{\mathit{o}\mathit{r}\mathit{b}}$ [RMSE]	${\mathit{S}\mathit{I}\mathit{S}\mathit{R}\mathit{E}}_{\mathit{c}\mathit{l}\mathit{k}+\mathit{o}\mathit{r}\mathit{b}}$ [RMSE]	${\mathit{S}\mathit{I}\mathit{S}\mathit{R}\mathit{E}}_{\mathit{c}\mathit{l}\mathit{k}+\mathit{o}\mathit{r}\mathit{b}}$ [STD]
GPS	IIR	0.11	1.94	0.07
	IIR-M	0.10	0.94	0.06
	IIF	0.11	0.96	0.06
	III	0.12	0.63	0.04
	Mean	0.11	1.12	0.06
BDS-3	MEO	0.12	0.58	0.03
	IGSO	0.14	0.87	0.04
	Mean	0.13	0.72	0.03

. The RMSE of ${SISRE}_{clk+orb}$ varies from 0.60 m to 3.05 m, with a mean value of 1.12 m for GPS, and from 0.36 m to 1.25 m, with a mean value of 0.72 m for BDS-3. It should be noted that GPS satellites with large ${SISRE}_{clk+orb}$ values mostly belong to the block IIR series. To further investigate the contributions of the orbit and clock errors to ${SISRE}_{clk+orb}$, the orbit-only SISRE, that is, ${SISRE}_{orb}$, was calculated. The mean RMSE values of ${SISRE}_{orb}$ are 0.11 m and 0.13 m for GPS and BDS-3, respectively. These values were much smaller than those of ${SISRE}_{clk+orb}$, indicating that clock systematic errors have a much larger contribution to ${SISRE}_{clk+orb}$ than satellite orbit errors. Therefore, ${SISRE}_{clk+orb}$ is confirmed to be dominated mainly by clock errors. For tropospheric parameter estimation, we were more concerned about the accuracy of the ZTD estimation than about the convergence time. Therefore, the STD of ${SISRE}_{clk+orb}$ was investigated in this study. As shown in Table 4, the STD of ${SISRE}_{clk+orb}$ for BDS-3 (0.03 m) was smaller than that for GPS (0.06 m), which may have benefited from the use of intersatellite laser measurements for the generation of the BDS-3 satellites in the PPP-B2b product.

Figure 3a,b present the variations in the daily ${SISRE}_{clk+orb}$ [STD] for GPS and BDS-3, respectively, which show obvious fluctuations during the period of DOY 193-216. For GPS, 54.5% and 90.7% of the days have ${SISRE}_{clk+orb}$ [STD] values smaller than 0.05 m and 0.1 m, respectively. BDS-3 has a much better performance than GPS, with approximately 93.8% of the days having ${SISRE}_{clk+orb}$ [STD] values less than 0.05 m.

4. PPP-B2b ZTD Estimation and Evaluation of the Results

4.1. Evaluation of Real-Time PPP-B2b ZTD at Station BJ01

Using the PPP-B2b corrections and GNSS observations received in real time at station BJ01, the real-time ZTD was computed and compared to the post-processed ZTD, which was calculated using a combination of GPS and BDS-3 constellations with accurate orbit and clock products from GBM from DOY 117 to the end of DOY 130, 2022. As shown in Figure 4a, the ZTDs derived using the PPP-B2b method with different systems agreed very well with those derived from GBM products. The results in Figure 4b depict that while the differences between PPP-B2b ZTD and GBM ZTD generally fall within the range of $\pm$3 cm, there is noticeable daily variation in these differences. This variation could be attributed to the daily fluctuations in the accuracy of the PPP-B2b orbit/clock products.

As listed in

Table 5. Comparison between the real-time ZTDs derived with PPP-B2b corrections and post-processed ZTDs derived with the GBM final orbit/clock products.

Strategy	Error Range [Min, Max]	Percentage in the Range [−30 mm, 30 mm] (%)	Bias (mm)	RMSE (mm)
GPS-only	[−57.7, 67.5]	91.1	−0.3	17.8
BDS-only	[−41.9, 32.2]	98.5	−6.4	13.9
BDS + GPS	[−44.6, 40.3]	98.2	−2.5	13.4

, using the post-processed ZTDs derived with the GBM final orbit/clock products as a reference, the ZTD errors stemming from the PPP-B2b corrections were calculated across different satellite systems. Table 5 shows that the ZTDs derived from GPS observations have the smallest bias but the largest RMSE compared to those of the other solutions. The ZTDs derived from the BDS-3 observations have an RMSE of 13.9 mm, which is slightly larger than that of the ZTDs derived from the combination of BDS-3 and GPS observations but smaller than that of the GPS-only solution. As shown in Table 5 and Figure 5, 91% of the errors for the GPS-only solution were in the range of −30 mm to 30 mm, while the percentage for the other solutions reached approximately 98%. For the coordinate accuracy, the RMSEs were 0.9 cm, 0.6 cm, and 4.8 cm in the north, east, and vertical directions, respectively, for the BDS-3/GPS combination solution, which is slightly better than the GPS-only or BDS3-only solution. As suggested by Vey et al. [80], a scaling factor of 4.4 between ZTD and station height is observed for a 10° elevation cutoff angle, meaning that a 4.4 cm error in station height corresponds to a 1 cm error in ZTD. Thus, theoretically, a 4.8 cm error in station height would result in approximately a 1 cm error in the ZTD estimate, which would result in about a 2 mm error in the derived PWV, assuming a scaling factor of 0.15 between ZTD and PWV [5].

4.2. Comparison between ZTD Derived with PPP-B2b/CNES and the Post-Processed Results

As shown in Figure 2, 32 stations were selected for this study to further investigate the performance of the ZTD derived from the PPP-B2b orbit/clock products at different locations. Since the receivers at these stations are not capable of decoding PPP-B2b corrections, the ZTDs at these stations were calculated using the stored PPP-B2b orbit/clock products in SP3 format at station BJ01. As shown in

Table 6. Information on the GNSS stations and co-located radiosonde stations.

GNSS					Co-Located Radiosonde
Station Name	Latitude (°)	Longitude (°)	Height (m)	Observation System	Station Name	Horizontal Distance (km)	Height Difference (m)
ULAB	47.9	107.1	1575.6	G + C	MGM00044292	14.98	−117.4
URUM	43.8	87.6	858.9	G + C	CHM00051463	3.09	2.4
CHAN	43.8	125.4	271.5	GPS only	CHM00054161	21.89	20.1
BIK0	42.9	74.5	744.9	GPS only	N/A	N/A	N/A
TASH	41.3	69.3	439.7	G + C	N/A	N/A	N/A
BJ01	40.1	116.3	85.5	G + C	N/A	N/A	N/A
BJFS	39.6	115.9	87.4	GPS only	CHM00054511	49.19	64.6
USUD	36.1	138.4	1508.6	G + C	N/A	N/A	N/A
GAMG	35.6	127.9	925.9	G + C	N/A	N/A	N/A
JFNG	30.5	114.5	71.3	G + C	N/A	N/A	N/A
LHAZ	29.7	91.1	3646.3	GPS only	CHM00055591	3.00	1.0
LCK4	26.9	81.0	64.2	G + C	INM00042369	19.43	7.2
SHLG	25.7	91.9	1007.2	G + C	N/A	N/A	N/A
TWTF	25.0	121.2	201.5	G + C (C19-37)	N/A	N/A	N/A
NCKU	23.0	120.2	98.2	G + C (C19-30)	N/A	N/A	N/A
HKFN	22.5	114.1	41.2	G + C (C19-30)	N/A	N/A	N/A
HKQT	22.3	114.2	5.2	G + C (C19-30)	HKM00045004	6.10	−17.2
PTGG	14.5	121.0	84.9	G + C	N/A	N/A	N/A
CUSV	13.7	100.5	76.1	G + C	N/A	N/A	N/A
GUAM	13.6	144.9	201.9	G + C	GQM00091212	14.86	70.3
IISC	13.0	77.6	843.7	G + C	N/A	N/A	N/A
SGOC	6.9	79.9	−78.5	G + C	N/A	N/A	N/A
SEYG	−4.7	55.5	−37.6	G + C	SEM00063985	1.62	−1.0
CIBG	−6.5	106.8	169.1	G + C	N/A	N/A	N/A
DGAR	−7.3	72.4	−64.9	G + C	N/A	N/A	N/A
COCO	−12.2	96.8	−35.3	G + C	CKM00096996	0.10	−0.2
KAT1	−14.4	132.2	184.3	G + C	N/A	N/A	N/A
PTVL	−17.7	168.3	86.4	G + C	N/A	N/A	N/A
VACS	−20.3	57.5	421.2	G + C	N/A	N/A	N/A
MCHL	−26.4	148.1	534.6	G + C	N/A	N/A	N/A
YARR	−29.0	115.3	241.4	G + C	ASM00094403	68.58	229.45
MOBS	−37.8	145.0	40.6	G + C	N/A	N/A	N/A

, the heights of the stations vary from −78.5 m (SGOC, Sri Lanka) to 3646.3 m (LHAZ, Tibetan Plateau). Among these stations, there are four stations with only GPS observations, four stations with GPS observations and some of the BDS-3 satellites, and 24 stations with both GPS and BDS-3 observations.

To simulate the real-time experiment, the GNSS observations and PPP-B2b and CNES orbit/clock products were read and processed epoch by epoch, and the ZTDs were estimated using the strategy listed in Table 1. Using the ZTDs computed with the GBM final products (a combination of GPS and BDS-3) and the ZTD provided by IGS as a reference, the ZTDs computed with the PPP-B2b products were then evaluated over these 32 stations from DOY 069 in 2022 to DOY 054 in 2023.

The results show that the CNES solution outperforms the PPP-B2b solution for all stations, regardless of whether the results are compared with those of the GBM or IGS solution. Using the GBM solution as a reference, the RMSEs of the CNES results range from 5.6 mm to 11.3 mm, with a mean value of 8.0 mm. For the PPP-B2b solution, the RMSEs range from 11.1 mm to 35.3 mm, with a mean value of 21.7 mm. In addition, the ZTDs calculated with the CNES products agree better with the GBM solutions than with the IGS solution in terms of the RMSE at all stations. This could be because both the CNES and GBM solutions were calculated using a combination of GPS and BDS-3 observations, while the IGS solutions were calculated using only GPS observations [81]. The statistical results presented in

Table 7. Comparison between the ZTD derived with PPP-B2b/CNES corrections and the GBM/IGS final orbit/clock products (unit: mm).

Solutions	Latitude Range	IGS Results as Reference		GBM Results as Reference
		RMSE	Bias	RMSE	Bias
CNES	30~48° N	10.0	−1.3	8.0	−0.4
	0~30° N	11.2	0.1	8.0	−0.4
	0~38° S	10.3	−0.9	7.9	0.3
	Mean	10.4	−0.8	8.0	−0.1
PPP-B2b	30~48° N	16.2	1.5	15.7	2.7
	0~30° N	25.7	2.5	23.9	2.6
	0~38° S	24.8	−1.0	25.0	1.1
	Mean	22.2	0.7	21.7	2.1

indicate the noticeable dependence of the RMSE of the PPP-B2b ZTD on latitude. Using the GBM ZTD data as a reference, the average RMSE of the PPP-B2b ZTD within the latitudinal band from 30° N to 48° N is 15.7 mm, whereas it is 23.9 mm within the latitudinal band from 0° to 30° N and 25.0 mm between 0° and 38° S. In contrast, the accuracy of the CNES-derived ZTDs does not exhibit a pronounced dependence on latitude. The mean biases of the GNES-derived ZTDs are −0.8 mm and −0.1 mm for the IGS and GBM solutions, respectively, and 0.7 mm and 2.1 mm for the PPP-B2b solution compared to the IGS and GBM solutions, respectively.

The results in Figure 6 and Figure 7 also indicate that the accuracy of the ZTDs derived with PPP-B2b is strongly dependent on the location of the stations. For nine stations (i.e., ULAB, URUM, BIK0, CHAN, TASH, BJ01, BJFS, GAMG, and JFNG) between 30° N and 48° N, the RMSEs of the ZTD range from 11.1 mm to 22.8 mm, with a mean value of 15.7 mm. Among these nine stations, three (CHAN, BIK0, and BJFS) have only GPS observations, and their ZTD results are worse than those of the other stations when a combination of GPS and BDS-3 observations is used. The RMSE of the ZTD results obtained with PPP-B2b at the LHAZ station on the Tibetan Plateau reaches 27.4 mm, which might be due to the lack of BDS-3 observations at this station. For the other stations between 30° N and 38° S, the RMSE ranges from 17.8 mm to 35.3 mm, with a mean value of 24.4 mm, which is obviously larger than that at the stations located between 30° N and 48° N. The results also reveal that the PPP-B2b service for the MOBS station was rarely applicable during most epochs, resulting in no resolution obtained for over 70% of the epochs. This limitation arises from the fact that the PPP-B2b correction information is derived from tracking stations deployed within the territory of China, and its service is primarily designed for China and its surrounding areas. Consequently, the performance of PPP-B2b in regions distant from China, such as southern Australia, could degrade significantly, while in more remote areas like Antarctica, it may even become unavailable, due to a decrease in available satellites and worsening satellite geometry.

4.3. Comparison of the GNSS-Derived ZTD/PWV with That Derived from ERA5

In this study, GNSS-derived ZTD/PWV values are compared with those obtained with ERA5 from DOY 069, 2022 to DOY 059, 2023 at 32 stations.

Table 8. Comparison between ZTD/PWV derived from GNSS and ERA5 (unit: mm).

Solutions	Latitude Range	ZTD		PWV
		RMSE	Bias	RMSE	Bias
IGS	30~48° N	18.3	−3.0	2.9	−0.5
	0~30° N	22.4	0.8	3.6	0.1
	0~38° S	16.4	−0.6	2.7	−0.1
	Mean	19.0	−0.9	3.1	−0.1
GBM	30~48° N	15.7	−3.5	2.5	−0.6
	0~30° N	21.2	−0.9	3.4	−0.3
	0~38° S	16.8	−1.0	2.7	−0.3
	Mean	18.4	−1.7	3.0	−0.4
CNES	30~48° N	17.8	−4.1	2.8	−0.7
	0~30° N	22.3	−1.4	3.6	−0.4
	0~38° S	17.3	−0.7	2.8	−0.2
	Mean	19.6	−2.0	3.2	−0.4
PPP-B2b	30~48° N	20.9	−0.7	3.2	−0.2
	0~30° N	31.2	1.3	5.0	0.1
	0~38° S	29.9	0.9	4.8	0.0
	Mean	27.8	0.7	4.4	0.0

shows the comparison results between the GNSS-derived ZTD/PWV (IGS, GBM, CNES, and PPP-B2b) and the ERA5-derived ZTD/PWV. The comparison results reveal that the ZTDs derived from GBM products exhibit the best agreement with the ERA5-derived ZTDs, with a mean RMSE of approximately 18.4 mm across 32 stations. The RMSEs of the IGS and CNES results are 19.0 mm and 19.6 mm, respectively. The PPP-B2b results exhibit the least agreement with the ERA5-derived ZTDs, with a mean RMSE of 27.8 mm. As shown in Table 8 and Figure 8, the RMSE variations for all GNSS solutions exhibit a latitudinal pattern, with higher RMSE values observed between 0° and 30° N than within the latitudinal bands of 30° N to 48° N and 0° to 38° S. In general, the RMSEs of the ZTDs for the IGS, GBM, and CNES solutions are approximately 22 mm between 0° and 30° N, exceeding that between 30° N and 38° S, where the mean value is approximately 17 mm. These spatial variations might be attributed to the fact that the atmospheric parameters in ERA5 are not of the same quality in all regions of the globe. Similarly, GNSS measurements and processing errors can change spatially. For the PPP-B2b ZTDs, the RMSE is 20.9 mm within the latitudinal band from 30° N to 48° N, which is slightly greater than that of the other three GNSS solutions. However, the RMSE of the PPP-B2b ZTDs reaches approximately 30 mm between 30° N and 38° S, which is significantly worse than that of the other solutions. The large errors in the PPP-B2b ZTD results are mainly dominated by the errors in the PPP-B2b orbit/clock products. The mean biases for the IGS, GBM, CNES, and PPP-B2b solutions are −0.9 mm, −1.7 mm, −2.0 mm, and 0.7 mm, respectively.

Figure 9 illustrates the spatial variation in the RMSEs and biases in the GNSS-derived PWV using the ERA5-derived PWV as a reference. As shown in Table 8, the mean RMSE values for the IGS-, GBM-, and CNES-derived PWVs are 3.1 mm, 3.0 mm, and 3.2 mm, respectively. Similar to the spatial variation in the RMSEs of ZTD, the RMSEs of PWV also exhibit a latitude-dependent pattern, with higher values observed between 0° and 30° N than within the latitudinal bands from 30° N to 48° N and 0° to 38° S. The PPP-B2b solutions demonstrate the poorest agreement with the ERA5-derived PWV, with a mean RMSE of 4.4 mm. Generally, the PPP-B2b solution within the latitudinal band from 30° N to 48° N has a smaller RMSE (3.2 mm) than that of the stations within the latitudinal bands from 0° N to 30° N (5.0 mm) and from 0° to 38° S (4.8 mm). The biases of the GNSS-derived PWVs compared to the ERA5-derived PWVs at these 32 stations are mostly within ±1 mm for the IGS, GBM, and CNES solutions and ±2 mm for the PPP-B2b solution.

To further investigate the temporal characteristics of the differences between the GNSS-derived PWV and the ERA-derived PWV, the monthly RMSE of the GNSS-derived PWV was calculated. The results in Figure 10 show that the differences between the GNSS-derived PWV and the ERA-derived PWV strongly depend on the duration at which the PWV has a large seasonal variation. Taking station CHAN as an example (Figure 10c), the RMSE of the IGS-derived PWV increases from 2.44 mm to 5.58 mm when the PWV varies from approximately 1 mm (March 2022) to 60 mm (July 2022). For the COCO station (Figure 10k) located in the equatorial region where the PWV is approximately 40–60 mm throughout the year, the RMSE value remains at approximately 2 mm during the study period and shows no obvious seasonal variation.

In addition to seasonal variations, previous studies have shown that there are strong diurnal variations in PWV time series. In this study, the hourly diurnal anomaly in PWV was calculated by subtracting the daily mean PWV from the corresponding observed hourly PWV. Figure 11 shows the mean diurnal PWV anomaly in March 2022 at six stations, which reveals that the amplitude of the diurnal PWV variation at these stations is approximately 1–2 mm.

4.4. Comparison of the GNSS-Derived ZTD/PWV with That Derived from Radiosonde Data

To further investigate the accuracy of the GNSS-derived ZTD/PWV, the ZTD/PWV data were compared with those derived from co-located radiosonde observations. As shown in

Table 9. Comparison between the ZTD/PWV derived from GNSS and radiosonde (unit: mm).

Solutions	Latitude Range	ZTD		PWV
		RMS	Bias	RMS	Bias
IGS	30~48° N	12.7	2.3	2.1	−0.1
	0~30° N	15.3	−1.4	2.5	−0.5
	0~38° S	11.6	−0.9	2.2	−0.8
	Mean	13.1	0.2	2.3	−0.4
GBM	30~48° N	10.2	−1.7	1.9	−0.8
	0~30° N	12.2	−3.4	2.2	−1.0
	0~38° S	13.1	−5.2	2.4	−1.4
	Mean	11.7	−3.2	2.1	−1.0
CNES	30~48° N	13.5	−1.9	2.4	−0.9
	0~30° N	12.9	−3.9	2.4	−1.1
	0~38° S	13.9	−6.4	2.6	−1.7
	Mean	13.4	−3.8	2.4	−1.2
PPP-B2b	30~48° N	17.0	−0.4	2.8	−0.9
	0~30° N	25.1	4.6	4.1	−1.3
	0~38° S	26.1	5.0	4.4	−0.1
	Mean	22.4	2.9	3.7	−0.8

, the RMSEs of the GNSS-derived ZTDs are 13.1 mm, 11.7 mm, 13.4 mm, and 22.4 mm for the IGS, GBM, CNES, and PPP-B2b solutions, respectively, which are much smaller than the RMSEs calculated using ERA5 as a reference for these 11 stations. The mean biases are 0.2 mm, −3.2 mm, −3.8 mm, and 2.9 mm for the IGS, GBM, CNES, and PPP-B2b solutions, respectively. As depicted in Figure 12, the RMSEs for the IGS, GBM, and CNES solutions are generally less than 15 mm at most stations. However, for the PPP-B2b solution, the RMSE of the ZTD exhibits significant variation with latitude. Only three stations, namely, ULAB (47.9° N, 107.1° E), URUM (43.8° N, 87.6° E), and CHAN (43.8° N, 125.4° E), had RMSEs smaller than 20 mm. The largest value was observed at station SEYG (4.7° S, 55.5° E), with a value of 31.6 mm.

Regarding the RMSE of the PWV shown in Table 9, the GBM solutions have the best agreement with the radiosonde-derived PWV, with an RMSE of 2.1 mm, followed by the IGS and CNES solutions, with RMSEs of 2.3 mm and 2.4 mm, respectively. The worst agreement was found between the PPP-B2b solution and the radiosonde results, with an RMSE of 3.7 mm. As shown in Figure 13, for the IGS, GBM, and CNES solutions, the RMSE is smaller than 3 mm at most stations, while the RMSE for the PPP-B2b solution shows an obvious latitude-dependent pattern and is smaller than 3 mm only at stations ULAB, URUM, and CHAN. Like the ZTD comparison results, the GNSS-derived PWVs agree better with the radiosonde-derived PWV than with the ERA5-derived PWV. The biases of the GNSS-derived PWV are mostly within ±2 mm for the four solutions.

Figure 14 shows the variations in the radiosonde-derived PWV (red dots) and the monthly RMSEs of the GNSS-derived PWV. The results also show that the RMSE of the GNSS-derived PWV usually increases with the PWV values when the PWV has a large seasonal variation, which is very evident at stations CHAN, BJFS, and LHAZ.

5. Discussion

Traditionally, real-time estimation of ZTD or PWV requires stable internet access to obtain orbit and clock corrections. The PPP-B2b service, transmitted via BDS-3 satellites, introduces a significant advancement by enabling real-time atmospheric sensing without internet dependence. This capability is particularly beneficial for remote and low-income regions, where access to real-time atmospheric data can mitigate the disastrous impacts of severe weather events.

Our study demonstrates that while the PPP-B2b service achieves acceptable ZTD accuracy in certain regions, such as northern China, with an RMS of approximately 15 mm, comparable to results from previous studies, its performance is notably latitude-dependent. Accuracy decreases to around 25 mm between 30° N and 38° S, and the service becomes nearly unavailable beyond 38° S due to insufficient satellite visibility and poor geometric conditions. This reduction in accuracy significantly limits the global applicability of PPP-B2b, especially for users in the southern hemisphere who require reliable atmospheric data for applications such as real-time weather monitoring, disaster preparedness, and climate research. In regions where accurate weather data are critical for agricultural planning or emergency response, these limitations could lead to less informed decision-making. Previous studies were mostly conducted over very short periods (such as one week). In contrast, our findings, based on a one-year period, reveal that the RMSE of PPP-B2b-derived PWV generally increases with higher PWV values, particularly in regions with significant seasonal variation, when compared with radiosonde-derived PWV.

In contrast, ZTD/PWV accuracy derived from CNES data consistently outperforms PPP-B2b across all stations when compared to post-processed data from ERA-5 and radiosonde observations. According to the World Meteorological Organization (WMO), the threshold and breakthrough accuracy requirements for IWV in nowcasting and real-time monitoring are 5 mm and 2 mm, respectively. While IWV accuracy derived from CNES approaches the “breakthrough” level with a mean RMS of 2.4 mm, the PPP-B2b service currently meets only the “threshold” in China and its surrounding areas. This underscores the need for further refinement of the PPP-B2b service to achieve “breakthrough” accuracy, which is crucial for its operational use in high-accuracy IWV products. Achieving “breakthrough” accuracy is essential because it represents a level of precision that significantly enhances the reliability and utility of atmospheric data in critical applications. While “threshold” accuracy ensures that the data are adequate for basic monitoring purposes, “breakthrough” accuracy enables more precise predictions and timely responses, particularly in nowcasting and very short-range forecasting, where the accuracy and timeliness of data are paramount. Attaining this level of accuracy would make PPP-B2b a more viable tool for operational use, enabling it to compete with or even surpass more established systems in regions where internet access is limited but precise atmospheric data are crucial.

Despite these limitations, satellite-based PPP services like PPP-B2b and Galileo’s High Accuracy Service offer valuable alternatives for real-time positioning and related applications by providing high-accuracy satellite orbit and clock corrections without requiring internet access. To support further research and application development, we have established a server to broadcast these corrections in real-time at stream.champ.org.cn via port 2101. Researchers interested in accessing these corrections can request access by contacting the authors.

6. Conclusions

In this study, the accuracy of the BDS-3 and GPS orbit and clock corrections of PPP-B2b was assessed using GBM products from the GFZ as a reference. The DCB for BDS-3 from the PPP-B2b service was assessed using DLR and CAS data. For the period between DOY 069 and DOY 311 in 2022, the comparison between the PPP-B2b clock and GBM clock yielded STD values of 0.16 ns, 0.13 ns, and 0.18 ns for GPS, BDS-3 MEO satellites, and three BDS-3 IGSO satellites, respectively. Regarding the orbit quality, the mean RMSEs for the GPS satellites were 0.08 m, 0.36 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively. For the BDS-3 MEO satellites, the mean RMSEs were 0.10 m, 0.27 m, and 0.28 m in the radial, along-track, and cross-track directions, respectively, which were similar to those of the GPS satellites. For the BDS-3 IGSO satellites, the mean RMSEs in the radial, along-track, and cross-track directions were 0.13 m, 0.37 m, and 0.40 m, respectively, which were slightly worse than those of the BDS-3 MEO and GPS satellites. The differences between the DCB from PPP-B2b and the DCB from DLR or CAS were within $\pm 2$ ns, and the differences between the DCBs from DLR and CAS were within $\pm 1$ ns. In terms of the SISREs, BDS-3 performed better than the GPS satellites.

The ZTD derived with PPP-B2b and CNES was initially assessed at 32 stations within the region defined by latitude ranging from 38° S to 48° N and longitude from 55° E to 170° E. This evaluation spanned from Day of Year (DOY) 069 in 2022 to DOY 054 in 2023 and involved comparing the derived ZTD with post-processed ZTD obtained using the GBM clock/orbit and ZTD provided by the IGS. The results highlight a strong dependency of the ZTD accuracy derived with PPP-B2b on the latitude of the stations, whether compared to IGS or GBM ZTD results. When utilizing GBM-derived ZTD as a reference, the mean RMSE of PPP-B2b ZTD is 15.7 mm for nine stations situated between 30° N and 48° N. These stations span across diverse locations including northern China (URUM, CHAN, BJ01, and BJFS), Mongolia (ULAB), Uzbekistan (TASH), Japan (USUD), the Republic of Korea (GAMG), and Kyrgyzstan (BIK0). Conversely, for stations positioned between 0° and 30° N, and 0° and 38° S, the mean RMSE increases to 23.9 mm and 25.0 mm, respectively, significantly higher than that observed between 30° N and 48° N. This latitude-dependent pattern of PPP-B2b ZTD remains consistent when compared to the IGS-, ERA5-, and radiosonde-derived ZTD. Additionally, the results indicate that the PPP-B2b service for the MOBS station was rarely applicable at most epochs, with no resolution obtained for more than 70% of the epochs. This limitation arises because the PPP-B2b correction information is derived from tracking stations deployed in China and is intended solely for China and its surrounding areas. Consequently, the performance of PPP-B2b in regions distant from China may degrade due to a reduction in available satellites and a deterioration in satellite geometry. CNES performed much better than PPP-B2b in ZTD estimation, with a mean RMSE of 8.0 mm for 32 stations using GBM-derived ZTD as a reference. The GNSS-derived ZTD/PWV were also compared with those derived from ERA5 and radiosonde. The comparison results reveal that the RMSEs of the GBM-, IGS-, and CNES-derived ZTD and PWV are approximately 20 mm and 3 mm, respectively. For the PPP-B2b solutions, the RMSEs of ZTD and PWV are 27.8 mm and 4.4 mm, respectively, which are worse than those of the IGS, GBM, and CNES solutions. Using the radiosonde-derived ZTD/PWV as a reference, the RMSEs of ZTD and PWV derived with PPP-B2b are 22.4 mm and 3.7 mm, respectively, which are also worse than those of the IGS, GBM, and CNES solutions. The performance of PPP-B2b PWVs also exhibits a strong dependence on location compared to post-processed, ERA-derived, or radiosonde-derived PWVs. In addition, the comparison results also indicate that there are obvious seasonally dependent differences in the GNSS-derived PWV when compared to the PWV computed from ERA5.

The PPP-B2b service represents a significant advancement in GNSS-based atmospheric sensing by enabling real-time orbit and clock corrections without the need for internet access. This capability is particularly beneficial for remote and low-income regions where reliable internet connectivity may be limited, thereby democratizing access to high-accuracy weather and climate data. However, despite these advantages, the current performance of the PPP-B2b service exhibits considerable spatial variability, with diminished accuracy and reliability in regions distant from China. This limitation highlights the need for further enhancements to bring PPP-B2b to the level of robustness and precision found in internet-based real-time services like CNES, which currently outperform PPP-B2b in ZTD and PWV accuracy. Nonetheless, the innovative approach of PPP-B2b provides a strong foundation for expanding real-time GNSS applications, particularly in underserved regions.