GPS and Galileo Precise Point Positioning Performance with Tropospheric Estimation Using Different Products: BRDM, RTS, HAS, and MGEX

Abstract

The performance of Precise Point Positioning (PPP) using different Global Navigation Satellite System (GNSS) product sets, including broadcast ephemerides, International GNSS Service Real-Time Service (IGS-RTS) corrections, Galileo High Accuracy Service (HAS) corrections, and precise products from the Center for Orbit Determination in Europe (CODE) Multi-GNSS Experiment (MGEX), has been evaluated. The availability of solutions, convergence time, position accuracy and Zenith Tropospheric Delay (ZTD) estimation across these products were analyzed using simulated real-time and postprocessing static modes, using data from globally distributed stations with a 1 s observation interval. The results indicate that precise products from the MGEX provide the highest accuracy, achieving centimeter-level precision in post-processed mode. Real-time simulated solutions, such as HAS and IGS-RTS, deliver promising results, with Galileo HAS meeting its target accuracy of 20 cm horizontally and 40 cm vertically and a convergence time under 5 min. However, Global Positioning System (GPS) performance within HAS is limited by a significantly lower correction availability—around 67% on average compared to over 95% for Galileo—which negatively impacts PPP performance. ZTD estimation results show that real-time services (HAS, IGS-RTS) achieved errors within 1–3 cm, sufficient for meteorological applications. This study highlights the growing importance of HAS in real-time positioning applications and suggests further improvements in GPS for enhanced performance.

1. Introduction

Over the past three decades, the concept of precise absolute positioning has evolved significantly since its initial formulation [1,2,3,4,5]. Today, the Precise Point Positioning (PPP) method is widely applied across a broad spectrum of scientific and engineering domains [6], including seismology [7], reference frame determination [8], atmospheric sounding [9,10], natural hazard monitoring [11], and the estimation of drone trajectories [12]. PPP can achieve a millimeter- to centimeter-level accuracy in static, post-processed applications and a decimeter-level accuracy in kinematic and real-time scenarios. However, the primary limitation of PPP remains its relatively long convergence time [13].

In response to this limitation, substantial research efforts in recent years have focused on enhancing the efficiency and reliability of absolute positioning. Notable advancements include the development of PPP with Ambiguity Resolution (PPP-AR) [14,15], PPP-Real-Time Kinematic (PPP-RTK) [16,17], different/combined products that are available [18,19,20], and the use of multi-GNSS and multi-frequency measurements [21,22,23,24]. In parallel, interest has grown in single-frequency solutions and low-cost GNSS receivers, particularly for emerging technologies like smartwatches, drones, and smartphones [25,26].

In the coming years, the adoption of PPP is expected to expand further, particularly in real-time applications. This trend is driven by ongoing technological developments, including the increasing use of unmanned aerial systems, the advancement in smart city infrastructures, and the rising demand for reliable, high-precision positioning in autonomous systems. These use cases require independent, globally available, and highly accurate localization solutions.

Recent advancements in GNSS infrastructure have further accelerated the evolution of precise positioning techniques. Next-generation satellites—such as the GPS Block III, which enables additional observations on the L5 frequency [27]—are gradually being deployed. Concurrently, the number of operational Galileo satellites continues to increase [28]. As the Galileo constellation expands, further improvements in positioning accuracy are anticipated, particularly when leveraging onboard ephemeris products [29,30,31]. Notably, while GPS ephemeris data are updated every two hours, Galileo satellites provide more frequent updates, ranging from every 10 to 60 min.

To facilitate high-accuracy positioning in real time, the International GNSS Service (IGS) initiated the Real-Time Pilot Project in 2007 and officially launched the Real-Time Service (RTS) in 2013 [32,33]. The RTS supports real-time applications by providing access to precise GNSS products, including orbit and clock corrections, as well as code and phase biases [34]. These corrections serve as a viable alternative to ultra-rapid products, thereby enabling global real-time PPP, time synchronization, and natural hazard monitoring.

Currently, IGS RTS offers multi-GNSS combination products—SSRA02IGS1/SSRC02IGS1, which support GPS, GLONASS, and Galileo, and SSRA03IGS1/SSRC03IGS1, which also include BeiDou corrections. These corrections are applied to broadcast data but require an internet connection and compatible software such as the BKG NTRIP Client (BNC) [35]. In addition to the official IGS RTS solutions, several individual Analysis Centers (ACs) provide their own real-time products [36]. A study by Li et al. [37] comparing official combined RTS corrections and individual AC products showed that the highest accuracy was achieved using corrections from CNES and WHU, with CNES offering superior availability.

Despite their utility, the dependence on internet connectivity limits the use of these products in many regions. Recently, new correction services broadcast directly via navigation systems have emerged, offering enhanced accessibility. These include the BeiDou B2b service, Japan’s Centimeter-Level Augmentation Service (CLAS) for QZSS [38], and Europe’s Galileo High Accuracy Service (HAS) [39]. While B2b and CLAS are broadcast via geostationary satellites and thus limited to the Asia–Pacific region, Galileo HAS data are transmitted by a subset of satellites—currently up to 20—from the overall constellation, enabling global coverage with varying levels of availability [40].

The Galileo HAS will operate at two levels [41]. Level 1 provides global coverage with a target horizontal accuracy below 20 cm and vertical accuracy below 40 cm, with convergence times under 300 s. Level 2, limited to Europe, aims to achieve the same accuracy with a faster convergence time (under 100 s) by incorporating regional atmospheric corrections. HAS’s development comprises three phases: Phase 1 (testing and experimentation, 2020–2022); Phase 2 (Initial Service), launched on 24 January 2023; and Phase 3 (Full Service), which will deliver Level 2 capabilities [40].

As a central element of the European GNSS ecosystem, Galileo HAS offers free access to PPP corrections globally, broadcast via the E6-B signal or through the internet. Although the service is relatively new, its potential is already evident. Open-source tools such as HASlib [42], HAS PPP [43], and Python-based decoding toolboxes have been developed to enable the real-time reception and processing of HAS corrections [44]. Preliminary studies using test signals have demonstrated a promising PPP performance [45,46,47]. Furthermore, integration with tools like RTKLIB [48] highlights the potential of open-source platforms to broaden access to high-precision GNSS positioning. Nevertheless, further research is required to enhance the service’s reliability and broaden its applicability.

One of the key advantages of PPP is its capability to estimate tropospheric delay parameters, particularly the Zenith Tropospheric Delay (ZTD), in both post-processed and real-time modes. These estimates are essential for atmospheric studies, as they can be further converted into Precipitable Water Vapor (PWV) and assimilated into Numerical Weather Prediction (NWP) models to improve short-term weather forecasts. Several studies have highlighted the sensitivity of ZTD estimations to the quality of input products and modeling strategies [49]. For real-time applications, particularly those supporting NWP data assimilation, accuracy thresholds of 0.6 cm (target) and 3 cm (maximum) are typically required [10]. Recent advances in real-time GNSS processing, including PPP based on broadcast ephemerides [46,49] and the integration of multiple GNSS constellations [50,51], have shown the potential to meet these requirements. Additionally, current research continues to investigate how spatial resolution and data assimilation methods affect the accuracy of humidity fields derived from GNSS-based PWV products [52], reinforcing the importance of reliable real-time ZTD estimations in operational meteorology.

Currently, several studies on PPP positioning using HAS corrections have been carried out. However, they differ in terms of the time periods, processing software, and models used, and they often do not compare the obtained results with other products and corrections.

The aim of this study is to analyze PPP performance using different types of products and corrections: broadcast ephemerides, CNES RTS corrections, Galileo HAS corrections, and final precise products from the Center for Orbit Determination in Europe (CODE) within the Multi-GNSS Experiment (MGEX). The analysis is carried out using a uniform PPP processing scheme: all test cases use identical 1 s interval observations from globally distributed stations, the same processing software, and consistent modeling assumptions. This setup enables an objective and direct comparison of PPP performance across the different products.

The key performance indicators evaluated include solution availability, convergence time, positioning accuracy, and ZTD estimation for GPS, Galileo, and combined GPS+Galileo solutions. Importantly, HAS data were collected in real time, enabling a realistic simulation of near-real-time PPP performance. BRDM and CNES RTS corrections were also used in post-processing, representing additional simulated real-time scenarios. The final CODE MGEX products serve as the most precise reference solution and are used as a benchmark for the highest achievable PPP accuracy.

This study also examines the availability of HAS products and PPP solutions, highlighting practical challenges in real-time applications. In addition, 1 s observation intervals were employed with final CODE products—an uncommon approach in post-processing that enables a more detailed analysis of short-term convergence behavior.

Following the introduction, Section 2 describes the data, product sets, and processing methodology. Section 3 presents the results of the conducted analyses. Section 4 provides a discussion, and Section 5 offers a summary of the key findings.

2. Methodology and Data

This analysis utilized data from 12 globally distributed MGEX stations (Figure 1 and

Table 1. Equipment of the used IGS stations.

Station	Receiver	Antenna
ALIC00AUS	SEPT POLARX5	TWIVC6050 NONE
CEBR00ESP	SEPT POLARX5TR	SEPCHOKE_B3E6 NONE
CORD00ARG	SEPT POLARX5	TPSCR.G3 NONE
DAV100ATA	SEPT POLARX5	LEIAR25.R3 LEIT
GANP00SVK	TRIMBLE ALLOY	TRM59800.00 SCIS
HOFN00ISL	LEICA GR50	LEIAR25.R4 LEIT
POHN00FSM	SEPT POLARX5	JAVRINGANT_DM NONE
SASK00CAN	JAVAD TRE_G3TH DELTA	NOV750.R4 NOVS
SOD300FIN	JAVAD TRE_3 DELTA	JAVRINGANT_DM SCIS
URUM00CHN	JAVAD TRE_3	JAVRINGANT_G5T NONE
WIND00NAM	JAVAD TRE_3	JAVRINGANT_G5T NONE
YKRO00CIV	JAVAD TRE_3 DELTA	ASH701945C_M NONE

), which collected multi-GNSS observations at 1 s intervals over a six-day period, from Day of Year (DoY) 223 to DoY 228 in 2024. These days were selected because real-time HAS product data were successfully collected for them. For each day, 8 three-hour sessions were analyzed, resulting in a total of 48 sessions per station across the six-day span. The computations were performed using the raPPPid software (version 3.1), which employs an Extended Kalman Filter (EKF), in combination with the conventional PPP model [53,54].

The undifferenced ionosphere-free linear combinations for GPS and Galileo code and carrier-phase observations (in units of length) are expressed as

$$\begin{gathered} {\mathrm{P}\mathrm{R}}_{\mathrm{I}\mathrm{F},\mathrm{G}}={\mathsf{\rho }}_{\mathrm{r}}^{\mathrm{G}}+\mathrm{c}\left({\mathsf{\delta }}_{\mathrm{r},\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k},\mathrm{G}}-{\mathsf{\delta }}_{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}^{\mathrm{G}}\right)+{\mathrm{T}}_{\mathrm{r}}^{\mathrm{G}}+{\mathsf{\epsilon }}_{\mathrm{I}\mathrm{F}} \\ {\mathsf{\Phi }}_{\mathrm{I}\mathrm{F},\mathrm{G}}={\mathsf{\rho }}_{\mathrm{r}}^{\mathrm{G}}+\mathrm{c}\left({\mathsf{\delta }}_{\mathrm{r},\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k},\mathrm{G}}-{\mathsf{\delta }}_{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}^{\mathrm{G}}\right)+{\mathrm{T}}_{\mathrm{r}}^{\mathrm{G}}+{\mathsf{\lambda }}_{\mathrm{I}\mathrm{F}}^{\mathrm{G}}{\mathrm{N}}_{\mathrm{I}\mathrm{F}}^{\mathrm{G}}+{\mathsf{ϵ}}_{\mathrm{I}\mathrm{F}} \\ {\mathrm{P}\mathrm{R}}_{\mathrm{I}\mathrm{F},\mathrm{E}}={\mathsf{\rho }}_{\mathrm{r}}^{\mathrm{E}}+\mathrm{c}\left({\mathsf{\delta }}_{\mathrm{r},\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k},\mathrm{E}}-{\mathsf{\delta }}_{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}^{\mathrm{E}}\right)+{\mathrm{T}}_{\mathrm{r}}^{\mathrm{E}}+{\mathsf{\epsilon }}_{\mathrm{I}\mathrm{F}} \\ {\mathsf{\Phi }}_{\mathrm{I}\mathrm{F},\mathrm{E}}={\mathsf{\rho }}_{\mathrm{r}}^{\mathrm{E}}+\mathrm{c}\left({\mathsf{\delta }}_{\mathrm{r},\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k},\mathrm{E}}-{\mathsf{\delta }}_{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}^{\mathrm{E}}\right)+{\mathrm{T}}_{\mathrm{r}}^{\mathrm{E}}+{\mathsf{\lambda }}_{\mathrm{I}\mathrm{F}}^{\mathrm{E}}{\mathrm{N}}_{\mathrm{I}\mathrm{F}}^{\mathrm{E}}+{\mathsf{ϵ}}_{\mathrm{I}\mathrm{F}} \end{gathered}$$

(1)

where

• G, E denote the GPS and Galileo systems, respectively;
• ${\mathrm{P}\mathrm{R}}_{\mathrm{I}\mathrm{F}}$ and ${\mathsf{\Phi }}_{\mathrm{I}\mathrm{F}}$ are ionosphere-free linear combination for code and carrier-phase observations, respectively [m];
• ${\mathsf{\rho }}_{\mathrm{r}}^{\mathrm{S}}$ is the true geometric range between the satellite in the emission time and the receiver in the reception time [m];
• c is the speed of light [m/s];
• ${\mathsf{\delta }}_{\mathrm{r},\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k},\mathrm{G}}$, ${\mathsf{\delta }}_{\mathrm{r},\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k},\mathrm{E}}$ represent the receiver clock offsets in the GPS and Galileo system time, respectively [s]
• ${\mathsf{\delta }}_{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}^{\mathrm{G}}$, ${\mathsf{\delta }}_{\mathrm{c}\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{k}}^{\mathrm{E}}$ denote the satellite clock offsets for GPS and Galileo satellites, respectively [s];
• ${\mathrm{T}}_{\mathrm{r}}^{\mathrm{S}}$ is the slant tropospheric delay [m];
• ${\mathsf{\lambda }}_{\mathrm{I}\mathrm{F}}$ is the wavelength for the ionosphere-free linear combination [m];
• ${\mathrm{N}}_{\mathrm{I}\mathrm{F}}$ is the real value of the ambiguity ionosphere-free linear combination [cycles];
• ${\mathsf{\epsilon }}_{\mathrm{I}\mathrm{F}}$, ${\mathsf{ϵ}}_{\mathrm{I}\mathrm{F}}$ are other errors, for example noise and multipath [m].

This model also requires the inclusion of errors such as receiver and satellite phase center corrections, relativistic correction for code and carrier-phase observations of the ionosphere-free linear combinations and carrier-phase wind-up for phase observations, and the use of site displacement effects, which are defined in the IERS conventions [55].

In this way, the station coordinates, clock correction of the receiver for each system, wet component of the tropospheric delay, and real ambiguity values were estimated. A list of the used products, models, and methods are shown in

Table 2. Solutions names and input data sources.

Solution Name	Products
BRDM	broadcast products BRD400DLR; GPS LNAV and Galileo INAV
HAS	broadcast products BCEP00BKG0 with HAS corrections SSRA00EUH0; GPS LNAV and Galileo INAV; collected in real-time with BNC software (https://igs.bkg.bund.de/ntrip/bnc (accessed on 14 June 2025))
CNES	broadcast products with IGS RTS CNES corrections converted to daily CNES archive products as SP3, CLK, and BIA (http://www.ppp-wizard.net/products/REAL_TIME/ (accessed on 14 June 2025)
CODE	precise CODE MGEX FINAL products: SP3 with 5 min interval, CLK with 30 s interval

and

Table 3. Methods and models used. I think the table should be on one page.

Items	Models/Methods
Positioning mode	static mode
PPP model	conventional PPP model using undifferenced dual-frequency code and phase ionosphere-free linear combination
Sessions	eight three-hour sessions per day (48 sessions for each station from six days)
Signals	BRDM, CNES, and CODE solutions: L1/L2 for GPS and E1/E5a for Galileo HAS solution: L1/L2 for GPS and E1/E5b for Galileo
Stochastic modeling	${\sin }^{2}ele$
Constellation	GPS (G), Galileo (E), GPS+Galileo (GE)
Standard deviation of raw observations	code = 0.300 m, phase = 0.002 m
Cut-off elevation angle	10°
Interval estimation	1-s
Periods	six days: from 223 DoY to 228 DoY of 2024
Reference frame	IGS20
Reference coordinates	daily IGS SINEX files
PCO and PCV for satellite antenna	igs20.atx for CNES and CODE solutions; for BRDM and HAS the products were referred to APC
PCO and PCV for receiver antenna	igs20.atx
Ionospheric delay	ionosphere-free linear combination
Tropospheric delay	a priori value: GPT3 (VMF3 for CODE solution) estimated: wet component mapping function: GPT3 (VMF3 for CODE solution) gradients: estimated
Solid tides, ocean loading, Shapiro effects, phase wind-up	IERS convention 2010
Ambiguities	float
Receiver clock correction	estimated separately for each system

.

Four different solutions were computed for GPS, Galileo, and GPS+Galileo constellations:

• ‘BRDM’ solution: computed using only broadcast products, with the BRD400DLR broadcast ephemerides downloaded;
• ‘HAS’ solution: computed using broadcast ephemerides combined with HAS corrections. The products were collected in real-time using BNC software;
• ‘CNES’ solution: computed using CNES archive products. The broadcast ephemerides and real-time CNES corrections were converted to SP3 and CLK files;
• ‘CODE’ solution: computed using the final CODE MGEX products. These products were downloaded as SP3 and CLK with 5 min and 30 s intervals, respectively.

The analysis was conducted using a 10° elevation angle cut-off, with the ${\sin }^{2}ele$, function applied for stochastic modeling. The reference coordinates were based on the daily IGS20 SINEX reference frame. The estimated tropospheric delay was compared with the official IGS value.

To estimate the ZTD for the BRDM, HAS, and CNES solutions, the GPT3 model was applied, while the VMF3 model was used for the CODE solution [56]. Additionally, for the CODE solution, the CODE MGEX satellite biases were included as observable-specific signal bias (OSB) files [14]. For the HAS and CNES solutions, bias corrections were obtained from the respective correction streams. In the case of the CNES solution, phase bias corrections were also applied, while for the HAS solution, only code bias corrections were used. For the BRDM solution, the Time Group Delay (TGD) data, as transmitted in the navigation messages, were utilized [57].

3. Results

The analysis focused on four key evaluation criteria: solution availability, convergence time, accuracy, and the precision of ZTD estimation. The following subsections present the results for each of these aspects.

3.1. Solution Availability

Solution availability was defined as the ratio of epochs in which position solutions were successfully derived to the total number of epochs for which position solutions were obtained using the CODE products. The analysis included only epochs where both GNSS observations and the corresponding orbit and clock products (or corrections) were available, which allowed the computation of positions and enabled an objective comparison of the performance of different solutions.

Table 4. Availability of obtained solutions and used satellites. Averaged across all analyzed stations.

Solution	GNSS	Number of Used Satellites	Availability [%]
BRDM	G	8.9	100.0
	E	6.8	99.8
	GE	15.6	100.0
HAS	G	5.0	74.0
	E	6.9	99.9
	GE	10.6	99.1
CNES	G	9.0	100.0
	E	6.5	99.7
	GE	15.5	100.0
CODE	G	9.3	-
	E	8.1	-
	GE	17.4	-

presents the results of this analysis, including the average number of satellites used for each solution.

For both the BRDM and CNES solutions, a 100% availability was achieved for the GPS and combined GPS+Galileo constellations, with an average of approximately 9 GPS satellites and approximately 15.5 satellites, respectively, for the combined systems. For Galileo-only solutions, the availability was slightly lower—99.8% for BRDM and 99.7% for CNES—with a slightly reduced number of satellites: 6.8 and 6.5 on average, respectively. This is due to the fact that fewer Galileo satellites were available in BRDM and CNES products; for CNES products, about 20–21 Galileo satellites were available.

Different results were observed for the HAS products. For Galileo, solution availability reached 99.9% with about 6.9 satellites used, while for GPS it was significantly lower—only 74%, with an average of 5 satellites used. The HAS service is not yet fully operational and is primarily focused on the Galileo system, which may explain the lower availability and accuracy of the GPS-based solutions [44]. This is further illustrated in Figure 2, which shows the average availability of HAS orbit and clock corrections per satellite for both the Galileo and GPS constellations, averaged over the entire observation period. The dashed line marks the 90% availability threshold, highlighting that Galileo consistently exceeds this level with average availabilities of 95.49% for orbit corrections and 95.95% for clock corrections. In contrast, GPS average availabilities are much lower, at 67.11% for orbit and 67.64% for clock corrections. Notably, 10 GPS satellites show an availability below 50%, with 4 of them even below 20%—G07 (IIR-M), G13 (IIR), G15 (IIR-M), and G30 (IIF)—which negatively impacts the overall GPS performance in HAS products. While these satellites come from different blocks—IIR, IIR-M, and IIF—there is no clear dependency between satellite block type and correction availability. This indicates that other factors, such as satellite-specific conditions, operational status, or current HAS configuration, may be more influential in determining the performance of individual satellites.

Combining GPS and Galileo for HAS products slightly reduced the overall solution availability to 99.1%, with an average of 10.6 satellites used. This is likely due to the lower accuracy of the HAS products for GPS satellites, negatively affecting the overall quality of position solutions.

The highest number of satellites used was recorded for the CODE solution: 9.3 GPS satellites, 8.1 Galileo satellites, and 17.4 satellites for the combined GPS+Galileo constellation.

3.2. Convergence Time

This subsection analyzes the convergence times relative to the required accuracy levels. Additionally, the number of observational sessions meeting the specified thresholds was determined. Convergence time was defined as the moment when the errors reached the specified threshold and remained within it for at least the next 30 min. The thresholds were defined as 10 cm for both 2D and 3D for the CNES and CODE solutions. For the BRDM and HAS solutions, the thresholds were set at 20 cm horizontally (2D) and 40 cm vertically (U), which is the main objective of the HAS service; additionally, a 40 cm threshold was applied for spatial (3D). Identical accuracy thresholds were used for both BRDM and HAS to ensure a fair comparison, as the main goal is to highlight the impact of HAS corrections relative to broadcast-only data.

Figure 3 presents the results, and detailed data are provided in Appendix A.

Table 5. Percentage of sessions in which the convergence time met the defined accuracy thresholds for all solutions and constellations.

Solution	GNSS	U	2D	3D
BRDM	G	80.7	27.4	35.9
	E	92.0	64.6	70.8
	GE	93.2	62.8	74.0
HAS	G	45.1	22.2	26.0
	E	75.0	70.7	73.3
	GE	75.0	71.0	74.0
CNES	G	99.1	99.5	97.6
	E	96.2	96.7	91.7
	GE	99.6	99.6	99.0
CODE	G	100.0	99.5	99.5
	E	99.8	99.6	98.8
	GE	100.0	99.8	99.6

summarizes the percentage of sessions meeting the required accuracy levels.

Solutions based on CNES and CODE products demonstrated a consistently outstanding convergence performance, with success rates approaching or exceeding 99% in the most favorable configurations. For the CODE solution, convergence times were remarkably short, averaging approximately 1.2 min in 2D and 1.5 min in 3D when using GPS-only signals, with a slightly better performance observed for Galileo signals in 2D. The combined GPS+Galileo (GE) configuration yielded the best results, achieving convergence in less than 1 min in 2D and approximately 1 min in 3D, with success rates reaching up to 99.6%.

The CNES solution, simulating real-time operational conditions, also demonstrated a high percentage of sessions that successfully met the defined convergence criteria, indicating a reliable convergence performance, although convergence times were slightly longer compared to CODE. For GPS-only observations, convergence thresholds were achieved in 99.5% of sessions for 2D and 97.6% for 3D positioning. However, when using Galileo-only signals, the percentage of sessions that successfully reached convergence dropped to 96.7% for 2D and 91.7% for 3D, with average convergence times increasing to 2.09 min in 2D and 2.87 min in 3D. Nevertheless, when combining GPS and Galileo signals, the CNES solution achieved convergence within approximately 1.1 min in 2D and 1.5 min in 3D, with the percentage of sessions successfully reaching convergence closely matching that of the CODE solution—up to 99.6% for 2D and 99.0% for 3D.

In contrast, products based on BRDM and HAS corrections exhibited significantly longer convergence times and a lower percentage of sessions successfully reaching convergence. It should be noted that different convergence thresholds were applied for BRDM and HAS compared to CODE and CNES solutions. For the BRDM solution using GPS-only observations, the average convergence time was approximately 3.17 min for the vertical component (U), 3.35 min in 2D, and 3.13 min in 3D, with a relatively high variability between sessions (standard deviations of ±2.04 min for 2D, ±1.91 min for 3D, and ±2.04 min for U). The percentage of sessions achieving the required thresholds was noticeably lower, amounting to only 80.7% for U, 27.4% for 2D, and 35.9% for 3D positioning. Using Galileo-only signals resulted in slightly worse average times—3.51 min for U, 3.92 min in 2D, and 3.66 min in 3D—but the variability was considerably smaller (±0.69 min for 2D, ±0.78 min for 3D, and ±0.69 min for U), and the percentage of sessions successfully reaching convergence improved to 92.0% for U, 64.6% for 2D, and 70.8% for 3D. A moderate improvement was observed when combining GPS and Galileo signals, with average convergence times of 2.86 min for U, 3.10 min in 2D, and 2.91 min in 3D, although the percentage of sessions successfully converged remained relatively modest.

The HAS solution, benefiting from additional correction data, generally outperformed BRDM, although the differences were not uniform across all configurations. When using GPS-only observations, the convergence performance was noticeably worse, with average times of 2.59 min for U, 3.10 min in 2D, and 2.89 min in 3D, accompanied by a large variability between sessions of ±2.07 min for U, ±2.07 min for 2D, and ±2.00 min for 3D. In this case, the percentage of sessions achieving the required convergence thresholds was very low, amounting to only 45.1% for the vertical component (U), 22.2% for 2D positioning, and 26.05% for 3D. A clear improvement was observed when using Galileo-only signals, where the convergence times decreased to 1.47 min for U, 2.94 min for 2D, and 2.25 min for 3D, with a relatively low variability (±0.80 and ±0.83 min for 2D and 3D and ±0.80 min for U), and success rates exceeded 70%. The best performance for the HAS solution was again obtained when combining GPS and Galileo signals, achieving average convergence times of 1.39 min for U, 2.91 min in 2D, and 2.16 min in 3D, with a relatively small variability (±0.76 and ±0.75 min for 2D and 3D and ±0.76 min for U) and with over 70% of sessions meeting the required accuracy thresholds.

These results indicate that although HAS corrections significantly enhance the positioning performance compared to relying on broadcast data alone (BRDM), the convergence is still slower and less stable than what can be achieved with post-processing (CODE) or with real-time precise products (CNES).

Detailed convergence results for each coordinate component are available in Appendix A.

3.3. Accuracy

The positioning accuracy was evaluated by comparing the coordinates obtained in this study with the daily reference coordinates provided in the IGS20 SINEX files. To mitigate the influence of the initial convergence period, the first 10 min of data were excluded from the analysis. Mean errors and standard deviations are summarized in

Table 6. Mean coordinate difference to reference coordinates of all stations for all stations for all analyzed solutions. Values in cm.

Solution	GNSS	N	E	U	2D	3D
BRDM	G	−1.9	1.4	−6.1	64.8	93.2
	E	−3.4	3.56	−0.7	50.3	71.3
	GE	1.0	−1.5	−0.9	49.6	69.4
HAS	G	0.4	−7.9	−2.5	86.2	128.5
	E	0.2	0.1	1.5	18.9	28.8
	GE	−0.2	0.1	0.4	19.9	29.5
CNES	G	−0.5	−1.2	0.0	5.7	8.0
	E	−1.0	−1.4	−0.2	7.2	11.2
	GE	−0.6	−1.0	0.0	4.0	5.7
CODE	G	0.3	−0.7	−0.2	3.8	5.4
	E	0.1	0.0	−0.4	3.2	4.9
	GE	0.2	−0.2	−0.2	2.2	3.3

and

Table 7. Standard deviation of coordinate differences to reference coordinates of all stations for all analyzed solutions. Values in cm.

Solution	GNSS	N	E	U	2D	3D
BRDM	G	11.4	25.0	31.8	17.6	21.7
	E	6.8	19.6	14.9	13.1	16.8
	GE	15.7	26.6	24.1	28.5	35.8
HAS	G	21.8	41.8	47.0	38.9	47.4
	E	3.2	6.1	9.1	6.1	10.2
	GE	3.4	7.4	8.6	6.7	10.0
CNES	G	1.7	3.1	2.2	3.0	4.2
	E	1.2	2.6	3.2	2.8	4.7
	GE	1.5	2.2	2.1	2.0	2.8
CODE	G	1.5	2.1	1.4	2.9	4.1
	E	0.6	1.1	1.3	1.9	3.0
	GE	1.2	1.1	0.8	1.8	2.5

.

The results obtained for the BRDM, HAS, CNES, and CODE products show significant differences in positioning accuracy, particularly depending on the GNSS signals used. For the BRDM solution, the results indicate a relatively low positioning accuracy, particularly for GPS signals. The mean errors in the N, E, and U components were −1.92 cm, 1.43 cm, and −6.14 cm, respectively, resulting in 2D and 3D accuracies of 64.83 cm and 93.18 cm. Despite relatively small mean errors, the significant standard deviations (±11.38 cm in N, ±24.98 cm in E, and ±31.78 cm in U) indicate considerable variability. For Galileo signals, although the mean errors in N, E, and U slightly increased, the 2D and 3D accuracies improved significantly, reaching 50.33 cm and 71.34 cm, respectively, which was notably better than for GPS. The use of combined GPS and Galileo (GE) signals slightly improved the results, with mean errors of 0.99 cm (N), −1.50 cm (E), and −0.87 cm (U), resulting in 2D and 3D accuracies of 49.57 cm and 69.40 cm, with the standard deviations remained high (±15.66 cm in N, ±26.63 cm in E, ±24.07 cm in U).

For the HAS solution, the results show an intense variability for GPS. The mean errors for GPS were 0.40 cm in N, −7.87 cm in E, and −2.52 cm in U, corresponding to 2D and 3D accuracies of 86.15 cm and 128.50 cm, which are even worse than those for BRDM. GPS results were characterized by particularly large standard deviations (±21.81 cm in N, ±41.82 cm in E, and ±46.98 cm in U). A substantial improvement was observed with Galileo signals, where the mean errors decreased to 0.15 cm (N), 0.06 cm (E), and 1.47 cm (U), achieving 2D and 3D accuracies of 18.91 cm and 28.81 cm. For the GE combination, the mean errors were −0.23 cm in N, 0.09 cm in E, and 0.42 cm in U, with accuracies of 19.93 cm (2D) and 29.50 cm (3D). These results meet the requirements of the HAS service, except for GPS-only. This variability is consistent with the significantly lower availability of HAS corrections for GPS satellites, averaging around 67%, compared to over 95% for Galileo (Section 3.1). The HAS service primarily focuses on Galileo, and several GPS satellites have an availability below 50%, which negatively impacts the GPS positioning accuracy.

The CNES solution, based on real-time precise corrections, achieved a markedly better performance. For GPS, the mean errors were −0.48 cm (N), −1.25 cm (E), and −0.02 cm (U), resulting in 2D and 3D accuracies of 5.66 cm and 7.98 cm. For Galileo, there were mean errors of −0.95 cm (N), −1.39 cm (E), and −0.17 cm (U), leading to accuracies of 7.21 cm (2D) and 11.17 cm (3D), which were not as good as for GPS. The GE combination provided the best performance, with mean errors of −0.64 cm (N), −1.05 cm (E), and −0.04 cm (U) and accuracies of 3.95 cm (2D) and 5.73 cm (3D). Standard deviations were exceptionally low (e.g., ±1.74 cm in N, ±3.11 cm in E, and ±2.21 cm in U for GPS), confirming the high precision and stability of the CNES solution.

The CODE solution, based on precise products, demonstrated the best performance. For GPS, the mean errors were 0.26 cm (N), −0.72 cm (E), and −0.15 cm (U), corresponding to 2D and 3D accuracies of 3.80 cm and 5.39 cm. For Galileo, the mean errors were minimal (0.06 cm in N, 0.00 cm in E, and −0.36 cm in U), with 2D and 3D accuracies of 3.24 cm and 4.88 cm. The GE combination further improved the results, with mean errors of 0.16 cm (N), −0.23 cm (E), and −0.24 cm (U), and 2D and 3D accuracies of 2.21 cm and 3.26 cm, respectively. Standard deviations remained very low across all components, confirming the superior precision and consistency of the CODE solution.

It should be noted that the 2D and 3D values represent the mean absolute differences from the reference coordinates. Therefore, these values may appear large, which is consistent with the large standard deviations.

In summary, worse results were obtained for GPS in both BRDM and HAS solutions. The inclusion of Galileo significantly improved the achieved accuracy. The best results for each of the products were obtained by combining GPS and Galileo signals, which provided the best convergence times and the highest measurement accuracy.

3.4. ZTD (Zenith Tropospheric Delay)

The ZTD analysis was performed by comparing the estimated zenith delays with the reference values provided by the IGS. The results are illustrated in Figure 4. The figure also highlights the 6 mm (target) and 3 cm (maximum acceptable) thresholds commonly required for real-time applications [10].

The BRDM solution, based solely on broadcast ephemerides, demonstrated a somewhat lower performance, particularly for GPS signals. The mean ZTD errors reached 3.2 mm for GPS, 2.7 mm for Galileo, and 1.5 mm for the combined GPS+Galileo solution. Although these mean values are within the 6 mm target, the associated standard deviations were relatively high: ±30.6 mm for GPS, ±21.9 mm for Galileo, and ±27.6 mm for GPS+Galileo. Notably, the standard deviation for GPS slightly exceeded the 30 mm threshold, while for Galileo and GPS+Galileo it remained within acceptable limits. This indicates that while the average ZTD estimation was satisfactory, the variability of the results, particularly for GPS, could impact reliability in real-time applications.

In the case of the HAS solution, a larger variability was observed, especially for GPS signals. The mean ZTD errors were 5.0 mm for GPS, −0.2 mm for Galileo, and 7.5 mm for the combined GPS+Galileo solution. The corresponding standard deviations were ±43.1 mm for GPS, ±15.4 mm for Galileo, and ±19.3 mm for GPS+Galileo. These results indicate that the use of Galileo signals, either alone or in combination with GPS, provides a noticeably better stability and precision compared to using GPS signals alone when applying HAS corrections.

The CNES solution, based on real-time precise corrections, demonstrated outstanding performance in ZTD estimation. The mean ZTD errors were 0.7 mm for GPS, 1.3 mm for Galileo, and 0.7 mm for GPS+Galileo. The associated standard deviations were also exceptionally low: ±4.6 mm for GPS, ±8.0 mm for Galileo, and ±4.4 mm for GPS+Galileo.

Similarly, the CODE solution, based on post-processed precise products, yielded very high-quality results. The mean ZTD errors were 1.7 mm for GPS, 2.4 mm for Galileo, and 2.0 mm for GPS+Galileo. The standard deviations were also the lowest among all the solutions analyzed: ±3.9 mm for GPS, ±4.6 mm for Galileo, and ±3.2 mm for GPS+Galileo.

Overall, while BRDM and HAS demonstrated acceptable mean errors, their standard deviations—particularly for GPS signals—slightly exceeded the thresholds, which could pose challenges for high-reliability real-time applications. However, despite these slight exceedances, both solutions remain highly useful and can still be considered reliable for many applications. In contrast, the CNES and CODE solutions clearly outperformed the others, achieving both target mean errors and maintaining a low variability, ensuring robust and accurate ZTD estimations suitable for operational NWP systems. Additionally, as the Galileo HAS service continues to evolve, improvements in its performance are expected, which could further enhance its reliability and precision in the near future.

4. Discussion

In the conducted research, various GNSS solutions were compared under simulated real-time conditions using 1 s interval observations for static positioning. The analysis revealed significant differences in performance, particularly regarding solution availability, convergence time, accuracy, and ZTD estimation. Notable differences were observed between solutions based on broadcast ephemerides (BRDM), real-time precise corrections (CNES RTS), post-processed precise products (CODE MGEX), and the HAS service.

Convergence time was one of the key factors differentiating GNSS solutions based on PPP positioning. For the BRDM and HAS services, more lenient accuracy thresholds were applied (20 cm horizontally (2D) and 40 cm vertically (U) and spatially (3D)), whereas stricter thresholds (10 cm both horizontally and spatially) were used for CNES and CODE. BRDM and HAS exhibited longer and more variable convergence times compared to CNES and CODE, especially when using GPS-only data. However, integrating signals from Galileo (or combined GPS+Galileo) improved performance, although convergence times remained longer. These differences stem from the limitations associated with broadcast ephemerides in BRDM solutions and the focus of the HAS service on the Galileo system.

In contrast, for HAS solutions, the use of Galileo signals significantly improved availability and accuracy, whereas relying solely on GPS limited these parameters. The reduced availability of HAS orbit and clock corrections for GPS satellites indicates the need for the further development of this service. Similarly, Zhao et al. (2024) [44] demonstrated that HAS products for GPS are of a lower accuracy and that the positioning results for GPS were worse compared to those for Galileo. In the case of CNES, slightly worse results were obtained for Galileo signals compared to GPS. However, the combined use of both signals (GPS+Galileo) provided better results, both in terms of positioning accuracy and ZTD estimation. This clearly demonstrates that employing both systems together substantially enhances the overall solution performance.

The ZTD analysis showed that BRDM solutions had a poorer ZTD estimation quality, especially for GPS, where large standard deviations were observed. In comparison, integrating GPS with Galileo improved the results by reducing ZTD variability. A similar dependency was reported by Yang et al. (2024) [49], confirming that the addition of Galileo signals enhances the stability and precision of ZTD retrieval. Moreover, this study also demonstrated that the use of broadcast ephemeris products allows for a ZTD estimation with sufficient accuracy, especially when using the Galileo signal. HAS further showed improvements when using Galileo signals, with standard deviations of ZTD being significantly lower than for GPS. However, the CNES and CODE solutions, which utilize precise corrections and products, proved to be the most accurate and stable in ZTD estimation, making them suitable for high-reliability applications such as weather forecasting.

5. Summary

The research shows that GNSS solutions based on broadcast ephemerides (BRDM) and correction services like HAS exhibit a lower performance in terms of convergence time, accuracy, and ZTD estimation, especially when using GPS-only data. The HAS service demonstrated significant improvement when integrated with Galileo, enhancing solution availability and accuracy. In real-time applications, Galileo consistently provides better results than GPS alone, partly because of more frequent updates of broadcast ephemerides. Nevertheless, solutions such as CNES and CODE, offering real-time precise corrections and post-processed precise products, continue to deliver a higher performance for high-precision applications.

The shortened convergence times observed in this study (1–2 min for CODE and CNES, below 5 min for HAS) were achieved using 1 s interval observations, demonstrating the potential for rapid solution stabilization, which is essential for real-time GNSS applications. While HAS meets its accuracy and convergence time requirements, further development of the service, particularly regarding GPS support, could further enhance its performance.

The presented results are based on real-time/near real-time simulation conditions under ideal circumstances and compared with the best possible results obtained using postprocessed precise CODE MGEX products. It should also be emphasized that the conditions assumed in the study were ideal, and deviations from them could occur in real-world real-time applications, for example, interruptions in receiving corrections or signal outages.