The recent dramatic development of multi-GNSS (Global Navigation Satellite System) constellations brings great opportunities and potential for more enhanced precise positioning, navigation, timing, and other applications. Significant improvement on positioning accuracy, reliability, as well as convergence time with the multi-GNSS fusion can be observed in comparison with the single-system processing like GPS (Global Positioning System). In this study, we develop a numerical weather model (NWM)-constrained precise point positioning (PPP) processing system to improve the multi-GNSS precise positioning. Tropospheric delay parameters which are derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis are applied to the multi-GNSS PPP, a combination of four systems: GPS, GLONASS, Galileo, and BeiDou. Observations from stations of the IGS (International GNSS Service) Multi-GNSS Experiments (MGEX) network are processed, with both the standard multi-GNSS PPP and the developed NWM-constrained multi-GNSS PPP processing. The high quality and accuracy of the tropospheric delay parameters derived from ECMWF are demonstrated through comparison and validation with the IGS final tropospheric delay products. Compared to the standard PPP solution, the convergence time is shortened by 20.0, 32.0, and 25.0 % for the north, east, and vertical components, respectively, with the NWM-constrained PPP solution. The positioning accuracy also benefits from the NWM-constrained PPP solution, which was improved by 2.5, 12.1, and 18.7 % for the north, east, and vertical components, respectively.

As the first space-based satellite navigation system, Global Positioning System (GPS) consisting of a dedicated satellite constellation has been extensively applied for many geodetic applications in the last decades. In particular, the GPS precise point positioning (PPP, Zumberge et al., 1997) method draws special interest as it enables accurate positioning of millimeter to centimeter accuracy with a single receiver (Blewitt et al., 2006). Due to its significant advantages in terms of operational flexibility, global coverage, cost efficiency, and high accuracy, the PPP approach has been demonstrated to be a powerful tool and it is widely used in various fields such as precise orbit determination (POD) of low-Earth orbiter (LEO), crustal deformation monitoring, precise timing, GPS meteorology, and kinematic positioning of mobile platforms (Zumberge et al., 1997; Kouba and Héroux, 2001; Gao and Shen, 2001; Zhang and Andersen, 2006; Ge et al., 2008). With the continuously improved density of the tracking network infrastructure as well as the enhanced precise satellite orbit and clock correction products with short-latency (e.g., real-time) availability, many innovative applications like geo-hazard monitoring, seismology, nowcasting of severe weather events or regional short-term forecasting based on the PPP technique have also been emerging and undergoing great developments (Larson et al., 2003; Li et al., 2013; Lu et al., 2015). However, the GPS-only PPP shows limitations concerning the convergence time, positioning accuracy, and long re-initialization period due to insufficient satellite visibility and limited spatial geometry, especially under constrained environmental conditions where the signals are blocked or interrupted.

The world of satellite navigation is going through dramatic changes and is stepping onto a stage of multi-constellation GNSS (Global Navigation Satellite System) (Montenbruck et al., 2014). Not only is GPS of full capability and under continuous modernization, but also GLONASS has finished the revitalization and is now fully operational. Besides, two new constellations, Galileo and BeiDou, have recently emerged. The European Galileo currently comprises 12 satellites deployed in orbit and it is working towards a fully operational stage. The Chinese BeiDou officially launched a continuous positioning, navigation, and timing (PNT) service covering the whole Asia Pacific region at the end of 2012. It is continuously developing to a global system in the near future. In addition, the Japanese Quasi-Zenith Satellite System (QZSS) and the Indian Regional Navigation Satellite System (IRNSS) are also growing, with one and five satellites currently (as of 2016) operating in orbit, respectively. So far, more than 80 navigation satellites can be in view and transmit data benefitting from the multi-constellation GNSS, which brings great opportunities for more precise positioning, navigation, timing, remote sensing, and other applications (Ge et al., 2012).

Undoubtedly, the integration of all existing navigation satellite systems
could provide more observations and could thus enable definite improvements
on reliability, positioning accuracy, and convergence time of PPP in
comparison with the stand-alone GPS PPP. Li et al. (2015a) developed a
four-system (GPS

Numerical weather models (NWMs) are able to provide the required information for describing the neutral atmosphere, from which the meteorological parameters can be derived at any location and at any time by applying interpolation, within the area and time window considered by the model (Pany et al., 2001). In the past, the application of NWM in space geodetic analysis mainly focused on the determination of mapping functions (Niell, 1996; Boehm et al., 2006). With respect to the improvements in spatiotemporal resolutions as well as in precision and accuracy of the NWM during recent years, tropospheric delay parameters, such as zenith total delay (ZTD), slant total delays, and tropospheric gradients, derived from the NWM could satisfy the accuracy requirements for most GNSS applications (Andrei and Chen, 2008). Data from the NWM have been used to perform tropospheric delay modeling or correct for the neutral atmospheric effects in GNSS data processing. Hobiger et al. (2008a) made use of ray-traced slant total delays derived from a regional NWM for GPS PPP within the area of eastern Asia. They demonstrated an improvement of station coordinate repeatability by using this strategy in comparison to the standard PPP approach where the tropospheric delays were estimated as unknown parameters. Furthermore, an enhanced algorithm for extracting the ray-traced tropospheric delays of higher accuracy from the NWM in real-time mode was proposed by Hobiger et al. (2008b). The authors presented the potential and the feasibility of applying the NWM-derived tropospheric delay corrections into real-time PPP processing. Besides, Ibrahim and El-Rabbany (2011) evaluated the performance of implementing tropospheric corrections from the NOAA (National Oceanic and Atmospheric Administration) Tropospheric Signal Delay Model (NOAATrop) into GPS PPP. They pointed out an improvement of convergence time by about 1, 10, and 15 % for the latitude, longitude, and height components, respectively, by using the NOAA troposphere model when compared to the results achieved with the previously used Hopfield model.

In this study, we develop a NWM-constrained PPP processing method to improve
the multi-GNSS (a combination of four systems: GPS, GLONASS, Galileo, and
BeiDou) precise positioning. Tropospheric delay parameters, which are derived
from the European Centre for Medium-Range Weather Forecasts (ECMWF,

This article is organized as follows: Sect. 2 illustrates the IGS tracking network for MGEX, the multi-GNSS data collection, and the tropospheric delay parameters retrieved from ECMWF. Two multi-GNSS PPP processing scenarios – the standard and the NWM-constrained PPP – are presented in detail focusing on the modeling of the tropospheric delays. Thereafter, Sect. 3 describes the comparison of tropospheric delay parameters from ECMWF with respect to the IGS final tropospheric delay products. In Sect. 3, the positioning results, in terms of the convergence time and the positioning accuracy, achieved with the NWM-constrained multi-GNSS PPP solution are illustrated in comparison to the ones with the standard PPP solution. The conclusions and discussions are presented in Sect. 4.

In response to the dramatic development of the global satellite navigation
world along with the upcoming systems and signals, the IGS initialized the
MGEX campaign to enable a multi-GNSS service of tracking, collecting, and
analyzing data of all available signals from GPS, GLONASS, BeiDou, Galileo,
QZSS, and any other space-based augmentation system (SBAS) of interest
(Montenbruck et al., 2014). Accordingly, a new worldwide network of
multi-GNSS monitoring stations under the framework of the MGEX project has
been deployed in the past 2 years in parallel with the IGS network, which
only serves for GPS and GLONASS. Currently, the MGEX network consists of
more than 120 stations, which are globally distributed and provide excellent
capability of multi-GNSS constellation tracking and data delivering owing to
the contributions from about 27 agencies, universities, and other
institutions of 16 countries (

The pressure, temperature, and specific humidity fields of the ECMWF
operational analysis are utilized to retrieve the tropospheric delay
parameters. The ECMWF data are available at the German Research Centre for
Geosciences (GFZ) with a horizontal resolution of 1

The geographical distribution of the MGEX stations and their supported navigation satellite constellations. R, E, and C refer to GLONASS, Galileo, and BeiDou, respectively, while GPS can be tracked by each station.

In the PPP processing, precise satellite orbits and clocks are fixed to
previously determined values. The multi-GNSS (here GPS, GLONASS, Galileo,
and BeiDou) PPP processing model can be expressed as follows:

The slant total delay

Concerning the approach for tropospheric delay modeling, two PPP scenarios
are applied in this study: one is the standard PPP processing with
tropospheric delays estimated as unknown parameters, and the other is the
developed NWM-constrained PPP algorithm which utilizes tropospheric delay
parameters derived from ECMWF. For the standard PPP processing, a priori ZHD
is calculated by use of the empirical models (Saastamoinen, 1973) based on
the provided meteorological information (here Global Pressure and
Temperature 2 model, GPT2; Lagler et al., 2013) at a given location. Owing to
the high variability of the water vapor distribution, the ZWD is estimated as
an unknown parameter in the adjustment together with the other parameters,
such as the station coordinates. The horizontal tropospheric gradients,

In order to carry out a rigorous multi-GNSS analysis including the estimation of the inter-system and inter-frequency biases, the observables from the four individual GNSS are processed together in a single weighted least squares estimator. The EPOS-RT software (Ge et al., 2012; Li et al., 2013) is utilized for the GNSS data processing in this study, and the GFZ precise products are used.

For the two multi-GNSS PPP scenarios, the receiver position increment

In this section, the quality of tropospheric zenith delay parameters derived from ECMWF analysis is evaluated by comparing with the zenith path delay products offered by IGS (Byram et al., 2011). Specifically, the ECMWF ZTDs for 34 globally distributed stations from the IGS MGEX network during September 2015 are validated by the official IGS ZTD products which are provided with a temporal resolution of 5 min. As the ECMWF ZTDs are sampled every 6 h, we do not interpolate in time but restrict the comparison to the ECMWF data epochs.

As typical examples, the ZTD series derived from ECMWF and IGS at stations KIRU (Kiruna, Sweden) and NNOR (New Norcia, Australia) are shown in Fig. 2. The ECMWF ZTDs are represented by black triangles, while the IGS ZTDs are displayed by red squares. One can notice that the ECMWF ZTDs show good agreement with the IGS ZTDs in general. Most of the peaks in the ZTD series, which are mainly caused by rapid changes of the water vapor content above a station, are captured by ECMWF and IGS solutions.

The time series of ECMWF and IGS ZTDs at stations KIRU

The corresponding linear correlations between the ECMWF and the IGS ZTDs at
stations KIRU and NNOR are illustrated in Fig. 3. It can be seen that ZTDs
from the two solutions are highly correlated, with the correlation
coefficients being about 0.93 and 0.97, respectively. Figure 4 presents the
distribution of ZTD differences between ECMWF and IGS for the two stations
during the same period. One can notice that the ZTD differences mainly range
from

Scattergram of ECMWF and IGS ZTDs at stations KIRU

Distribution of ZTD differences between ECMWF and IGS at stations
KIRU

Figure 5 illustrates the map of station-specific mean biases and rms values
of ZTD differences between ECMWF and IGS for all stations. One can notice
that the mean biases are within

The map of the station-specific mean biases (top) and rms values (bottom) of ZTD differences between ECMWF and IGS for DOY 244–272, 2015.

To investigate the performance of applying tropospheric delay parameters derived from ECMWF into multi-GNSS PPP, two PPP scenarios including the standard PPP and the NWM-constrained PPP are carried out for comparison and validation, following the data processing algorithms presented in Sect. 2.3. Observational data from stations of the IGS MGEX network (see Fig. 1) in September 2015 are considered in this study. The post-processing weekly solution is used as the reference position. The convergence time is defined as the time required for the horizontal components to be better than 10 cm, and the one needed for the vertical component to be better than 20 cm.

As an example, Fig. 7 illustrates the estimated north, east, and vertical coordinates
obtained from the two multi-GNSS PPP processing methods at station WIND
(Windhoek, Namibia; 22.57

The rms values of ZTD differences between ECMWF and IGS as a function of geographical latitudes. A fitted second-order polynomial is also shown in black.

The multi-GNSS PPP (GREC) solution (left) and the stand-alone
GPS PPP (G) solution (right) at station WIND (Windhoek, Namibia;
22.57

As for the east component, a convergence time of about 40 min for the standard vs. 25 min for the NWM-constrained PPP solution is noticed. Accordingly, the solution convergence is improved by about 37.5 % with the NWM-constrained PPP. For the vertical component, a convergence time of about 20 and 15 min is required for the standard PPP solution and the NWM-constrained PPP solution, respectively, indicating an improvement of about 25.0 % when applying the NWM-constrained PPP. Besides, the positioning series exhibit many more jumps and fluctuations with the standard PPP solution, in particular before the solution convergence, which was significantly improved when the NWM-constrained PPP is performed.

The summary over the solution improvements of the NWM-constrained PPP with respect to the standard PPP for both multi-GNSS and GPS solutions.

The rms values for the north, east, and vertical components with multi-GNSS PPP solution, shown at different session lengths (5, 8, 10, 15, 17, 20, 25, 30, 40, 50, and 60 min) for all 21 four-system stations of the MGEX network from 1 to 30 September 2015. The standard PPP solution is shown in orange, the NWM-constrained PPP solution in green.

As shown in the right figures, for the standard GPS PPP, an accuracy of better than 10 cm is obtained after about 50 and 60 min for the north and east components, respectively. In comparison, it takes about 20 and 40 min for the NWM-constrained GPS PPP solution to become converged for the north and east components, shortening the solution convergence time by about 60.0 and 33.3 %. In the NWM-constrained GPS PPP solution, a convergence time of about 10 min is required for the vertical component, in comparison to 50 min in the case of the standard GPS PPP solution, revealing an improvement of up to 80.0 %. Moreover, it can be found that the NWM-constrained PPP reveals significant contribution to improving the positioning series of all three components, showing more stable and less fluctuated results. Furthermore, it is noteworthy that the positioning performance, not only the convergence time but also the positioning series of the GPS-only solution (right figures), becomes remarkably improved with the multi-GNSS processing (left figures). In addition, the corresponding summary over the solution improvements of the NWM-constrained PPP with respect to the standard PPP for both multi-GNSS and GPS solutions is listed in Table 1.

In Fig. 8, the statistical results of the multi-GNSS PPP solutions are presented with different session lengths (5, 8, 10, 15, 17, 20, 25, 30, 40, 50, and 60 min). The rms values of the positioning results for the north, east, and vertical components are calculated for all 21 four-system stations from the MGEX network over a sample period from 1 to 30 September 2015. The standard PPP solution is shown in orange, the NWM-constrained PPP solution in green. Obviously, the positioning accuracy of each component improves along with the increase of the session length for both PPP scenarios. In general, the positioning accuracy of the north component is better than that of the east and the vertical components, while the vertical component performs the worst, which may be attributed to the configuration of the satellite constellation.

For the north component, the rms values obtained from the NWM-constrained PPP solution are smaller than the ones from the standard PPP solution at the same session length, especially before the convergence. The positioning accuracy for the north component achieved with the NWM-constrained PPP is improved by about 2.5 % compared to the one with the standard PPP. Besides, a convergence time of about 20 and 25 min is observed for the NWM-constrained PPP solution and the standard PPP solution, respectively: an improvement of about 20.0 %. In terms of the east component, higher accuracy can be found again for the NWM-constrained PPP solution, with the rms values reduced by about 12.1 %. Meanwhile, the NWM-constrained PPP solution takes about 17 min to become converged in comparison to 25 min for the standard PPP solution, a significant reduction of about 32.0 % in the convergence time.

As for the vertical component, it can be noticed that the positioning accuracy achieved from the NWM-constrained PPP solution is obviously higher than that from the standard PPP solution, an improvement of about 18.7 %. More than 20 min are required for the standard PPP solution to obtain convergence, while the NWM-constrained PPP solution becomes converged in less than 15 min, indicating an improvement of more than 25.0 %.

We developed a NWM-constrained PPP processing system where tropospheric delay parameters derived from the ECMWF analysis were applied to multi-GNSS precise positioning. Observations of stations from the IGS MGEX network were processed, with both standard PPP and the developed NWM-constrained PPP algorithm. The accuracy of the tropospheric delays derived from ECMWF was assessed through comparisons with the IGS final tropospheric delay products at all IGS MGEX stations. The positioning performance, including convergence time and positioning accuracy, achieved with the NWM-constrained PPP were investigated. The benefits of applying tropospheric delay parameters from the NWM to improve multi-GNSS PPP were demonstrated by comparing with the standard PPP solution.

Our results show that the mean biases between the ECMWF and IGS ZTDs are
within

For the north component, it takes about 20 min for the NWM-constrained multi-GNSS PPP to achieve convergence, in comparison to 25 min for the standard PPP solution, showing a reduction of about 20.0 % in the convergence time. An accuracy of better than 10 cm is achieved for the east component after a convergence time of about 25 and 17 min from the standard and the NWM-constrained PPP solutions, respectively. The convergence time is shortened by 32.0 % with the NWM-constrained PPP. For the vertical component, a convergence time of about 20 and 15 min is required for the standard PPP solution and the NWM-constrained PPP solution, respectively, indicating an improvement of about 25.0 % when applying the NWM-constrained PPP. Meanwhile, the positioning accuracy obtained from the NWM-constrained multi-GNSS PPP solution is also improved in comparison with the standard PPP solution after the same session length, in particular before the convergence. An improvement of positioning accuracy resulting from the NWM-constrained PPP solution of about 2.5, 12.1, and 18.7 % for the north, east, and vertical components, respectively, can be found.

Besides, the positioning performance of the NWM-constrained GPS PPP solution achieves remarkable improvement compared to that of the standard GPS PPP solution, with the convergence time shortened by 60.0, 33.3, and 80.0 % for the north, east, and vertical components, respectively, as well as more stable and less fluctuated positioning results for each coordinate component. Based on these results, it can be concluded that the performance of precise positioning benefits greatly from the multi-GNSS fusion in comparison to the stand-alone GPS solution, which can be further improved when the tropospheric delay parameters derived from NWM are implemented to the multi-GNSS PPP processing.

In future studies, we will investigate the performance of applying tropospheric delay parameters derived from the NWM into precise positioning with other single satellite navigation systems, such as the Russian GLObal NAvigation Satellite System (GLONASS) and the Chinese BeiDou Navigation Satellite System (BDS). Another research focus is the evaluation of the accuracy and performance of different numerical weather models, in order to find the most appropriate one to improve precise GNSS positioning.

The GNSS observations were obtained from the
IGS MGEX project, available at

Many thanks go to the International GNSS Service (IGS) for providing multi-GNSS data and the IGS final tropospheric products. The ECMWF data are provided to GFZ via the German Weather Service (DWD). Cuixian Lu is supported by the China Scholarship Council, which is gratefully acknowledged. The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association. Edited by: O. Bock Reviewed by: two anonymous referees