Tropospheric delay refers to the refraction of the microwave signal when it passes through the neutral atmosphere. The space-borne microwave techniques, including Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Doppler Orbitography, and Radiopositioning Integrated by Satellite (DORIS), or Synthetic Aperture Radar Interferometry (InSAR), are all subjected to tropospheric delays [1
]. GNSS has been proven to be an efficient tool for the retrieval of total tropospheric delays between the observing station and the satellites in view. The observed slant path delays are usually mapped into the zenith direction (zenith total delay, ZTD) at a GNSS station, and it comprises contributions from a hydrostatic and a wet (or more precisely non-hydrostatic) component. The ZTD typically ranges between 2.0 to 2.6 m, and 90% of the ZTD error is caused by the zenith hydrostatic delay (ZHD), which can be corrected with an a priori value from a standard atmosphere model. The zenith-wet delay (ZWD) is then usually estimated from observations as an unknown parameter with an appropriate stochastic model.
The application of high-resolution tropospheric models in Precise Point Positioning (PPP) enhances the coordinates’ accuracy and makes the convergence time of the position solution shorter (Hadas et al. [2
]). Shi et al. [3
] modelled the local troposphere with a set of fitting coefficients and then used it to enhance the PPP. The results indicated that the convergence time of the positioning solutions could be greatly reduced, in particular in the height component. Furthermore, de Oliveira et al. [4
] confirmed the benefits of the troposphere augmentation for PPP convergence and precision improvement. Zhou et al. [5
] demonstrated a better positioning accuracy of multi-GNSS PPP when estimating high-resolution tropospheric gradients. Han et al. [6
] presented the accuracy improvement in the height component when using the external tropospheric delay to enhance the ambiguity-fixed PPP. Besides, investigations have been focused on the combination of a numerical weather model (NWM) and GNSS tropospheric products to enhance PPP. Lu et al. [7
] developed an NWM-constrained PPP processing system to improve multi-GNSS precise positioning and demonstrated the contribution of the NWM model. Lu et al. [8
] also derived horizontal delay gradients from the NWM model to augment the BeiDou System (BDS) PPP, and more than 30% of the precision improvement in the height component was observed. Zheng et al. [9
] developed a real-time tropospheric model in China and used it to shorten the convergence of BDS PPP. Douša et al. [10
] developed a two-stage correction tropospheric model combining data from NWM, precise GNSS ZTDs, and horizontal gradients to support an optimal regional augmentation.
High-precision troposphere observables are prerequisites for any local tropospheric model. Multi-GNSS observations have been intensively used to improve the precision of the tropospheric parameters retrieved from the PPP technique. Lu et al. [11
] evaluated the performance of the real-time ZTD estimated from single and multi-GNSS observations, and the results indicated that the precision and reliability of the troposphere estimates could be improved by using multi-GNSS data. Lu et al. [12
] further demonstrated that the initialization time and the precision of multi-GNSS tropospheric delays could be improved by using the PPP ambiguity-fixing technique, which can meet the requirements of the troposphere estimates for time-critical meteorological applications. Pan and Guo [13
] compared the real-time troposphere solution based on different GNSS combinations and different processing models.
However, operational troposphere solutions are still mainly based on Global Positioning System (GPS) and GLObal NAvigation Satellite System (GLONASS) ionosphere-free linear combinations of dual-frequency observations. The main reason is that the performance of the new GNSS constellations, including BDS and Galileo, for troposphere estimation deserve assessment and improvement. Xu et al. [14
] assessed the ZTD performance estimated from the BDS-2 regional constellation. Li et al. [15
] assessed the precision of precipitable water vapor calculated from BDS-only observations and demonstrated the potential of BDS observations for high precision meteorological applications in Asia–Pacific regions. Due to the limited number of Galileo satellites, the performance of Galileo-only troposphere solution has not yet been evaluated. Until 14/12/2019, the Galileo constellation has reached 24 satellites, which enables the Galileo-only global positioning. Hadas et al. [16
] have compared the positioning accuracy using dual-frequency Galileo observations and different processing techniques. An important innovation of the Galileo system is the availability of signals using five frequencies centered at E1 (1575.42 MHz), E5a (1176.45 MHz), E5b (1207.14 MHz), E5 (1191.795 MHz), and E6 (1278.75 MHz) for commercial and civilian use [17
], and they are already available from all active satellites. Moreover, the introduction of an Alternate Binary Offset Carrier (AltBOC) signal is expected to deliver smaller pseudorange noise thanks to its large bandwidth. The availability of multi-frequency signals has been proven to bring a great opportunity for PPP ambiguity resolution. Liu et al. [18
] demonstrated that the Galileo triple-frequency PPP, with ambiguity resolution, was helpful in reducing the convergence time and to improve the positioning accuracy. Li et al. [19
] also showed that the average Time To the First Fix (TTFF) of triple-frequency PPP can be reduced by more than 10%, compared to the dual-frequency solutions. Moreover, the results indicate that the fractional parts of extra-wide-lane ambiguities for all Galileo satellites are all zero, which may be associated with the characteristic of the AltBOC signal. Li et al. [20
] analyzed the multi-frequency PPP ambiguity resolution method based on the Galileo five-frequency observations. While the use of more frequencies contributes in a minor way to the TTFF, decimeter-level positioning accuracy can be achieved within 0.5 min by utilizing triple-/quad-/five-frequency PPP wide-lane ambiguity resolution. In comparison, the benefits of the multi-frequency observations for troposphere estimations still deserve further investigation.
In this contribution, we investigate the performance of the standalone Galileo troposphere estimates and the impact of multi-frequency observations. The paper is organized as follows: After this introduction, the PPP-based ionosphere-free and raw-observation troposphere estimation methods are introduced. Next, the precision of the Galileo-only ZTD and gradient solutions are compared to the GPS solution. Then, we characterize the noise of Galileo code observations residuals from multiple frequencies, and analyze the impact of multi-frequency observations on the accuracy of estimated ZTD. Finally, the conclusions are derived.
3. Status of Standalone Galileo Troposphere Solution
The Galileo system Initial Services was announced on 15 December 2016, and it is expected to be completed for full operational capability (FOC) in 2020. However, the Galileo system achieved an important milestone when the constellation reached, altogether, 26 satellites after the successful launch of Ariane-5 on 25 July 2018. Four new Galileo satellites (E13, E15, E33, and E36) became healthy on 11 February 2019, when the Galileo constellation reached 22 active satellites, two satellites on highly eccentric orbits in testing mode (E14 and E18), one satellite that was unavailable (E20), and one satellite that was excluded from the constellation (E22). The constellation change in the first quarter of 2019 is clearly depicted in Figure 1
. The color represents a daily percentage of navigation messages, indicating a healthy status of the Signal-In-Space for each satellite when considering: 1) The Signal Health Status flag (SHS), 2) the Data Validity Status flag (DVS), 3) Signal-In-Space Accuracy (SISA) value, and 4) the navigation data validity period [28
]. Note that the satellite health status can be used as an indicator for the quality of the satellite broadcast ephemeris, which is important for real-time users. However, MGEX final products are using the satellite signals even when they are unhealthy, since robust quality control strategies can be used to identify the actual status of the satellites by post-processing.
The Position Dilution Of Precision (PDOP) is calculated on a regular grid of 10 x 10 degrees, considering healthy Galileo satellites and the 5-degree elevation mask cut-off. Figure 2
shows the change in the monthly mean availability of PDOP < 6 for the Galileo system on a global scale between January and March. Four new satellites dramatically improved the availability of PDOP less than 6, reaching almost 100% globally in March, 2019.
The impact of such a constellation improvement on the tropospheric parameters is demonstrated via the comparison of the multi-GNSS solution with the standalone PPP solutions using only satellites from individual systems, namely GPS, GLONASS, and Galileo. We processed observations from 215 days (from October 27, 2018 to May 30, 2019) to demonstrate the evolution of the Galileo standalone troposphere solution. The final orbit and clock products provided by the Center for Orbit Determination in Europe (CODE) within Multi-GNSS Experiment (MGEX) project were used for PPP troposphere estimates when using the IF linear combinations with float ambiguities. The troposphere product exploiting combined GPS/GLONASS/Galileo observations was used as a reference. The selection of multi-GNSS combined troposphere solutions, rather than the external tropospheric products, as the reference was to demonstrate the consistency of GPS/Galileo/GLONASS standalone tropospheric with respect to the combined solutions. The standard deviation (STD) of the differences between the reference solution and Galileo-only troposphere solution presented in Figure 3
illustrates the visible change of STD for station ZIM2 and GOP6. A clear improvement can be observed after the four new Galileo satellites became available. The average STDs before February 11 was 4.3 and 5.0 mm for stations ZIM2 and GOP6, respectively. Significant decreases were observed after 11 February 2019, reaching 2.7 and 2.7 mm, respectively. Figure 4
presents the evaluation of GPS, GLONASS, and Galileo standalone ZTD solutions, as compared to the multi-GNSS solution. The dark and light colors represent the results before and after 2019–02–11, respectively. Overall, GPS-only ZTD had the best precision compared to the GLONASS-only and Galileo-only solution in the two stations before 2019–02–11. After that, the Galileo-only ZTD solution achieved comparable precision, like the GPS-only solution for the two stations. However, the GLONASS ZTD solution was always worse than that of GPS and Galileo. Precision improvement can be observed for three different ZTD solutions after 2019–02–11, which can attribute to the improvement of the reference multi-GNSS ZTD solutions after the availability of new Galileo satellites.
The recent evolution of the Galileo constellation has made Galileo capable of the standalone positioning and troposphere estimation. We analyzed the performance of Galileo observations for ZTDs and tropospheric horizontal gradient estimation. In addition, the benefits of multi-frequency observations are evaluated on the basis of the raw PPP model.
When four FOC satellites (E13, E15, E33, and E36) became healthy after 11 February 2019, the PDOP significantly improved, and therefore, the Galileo-only observations could be used for positioning on a global scale. The precision of the Galileo-only ZTD solution is first evaluated in comparison to the multi-GNSS solution based on two European stations. The average standard deviation of the Galileo-only ZTD solution decreased by 37% after its globally operational convergence.
As the raw model is more flexible for tropospheric parameter estimation, based on multi-frequency observations, the accuracy of raw and IF dual-frequency processing is first compared with solutions from real-time EPN RT demonstration. The results indicate that the raw dual-frequency model can achieve a comparable accuracy with the traditional IF model, with the mean biases and standard deviation of the ZTD difference below 2 and 6 mm, respectively. Additionally, the performance of the GPS-only and Galileo-only ZTD solutions are evaluated in comparison to the IGS final troposphere products, based on the globally distributed MGEX stations. The average mean biases over all stations are −0.3 and 0.0 mm for GPS and Galileo, respectively. The average STD is 5.8 and 6.2 mm for GPS and Galileo, respectively. The results demonstrate that the Galileo-only ZTD solution can achieve similar precision, compared to that of the GPS. However, the comparison of the GPS and Galileo gradient solutions indicate that Galileo still provides less accurate gradient components compared to GPS, which are expected to be improved with the refinement of the Galileo correction model. Besides, although the receiver PCO calibration is not completed for Galileo observations, using corresponding GPS PCO corrections does not degrade the PPP troposphere solutions.
After demonstrating the potential of the raw model and Galileo-only observations for ZTD estimations, the benefits of the Galileo multi-frequency observations on tropospheric parameters estimated with the raw PPP model are evaluated. The precision of the multi-frequency Galileo troposphere ZTDs is evaluated. The dual-frequency raw observations improve the precision of ZTD compared to the IF model by 6%. Besides, the addition of more frequency signals can further improve the ZTD accuracy by 4%. The results demonstrate a bright prospect for the improvement of GNSS ZTD with the additional use of Galileo multi-frequency observations.