Evaluating GPS and Galileo Precise Point Positioning (PPP) Under Various Ionospheric Conditions During Solar Cycle 25

Highlights

What are the main findings?

• While twenty months of observations from six stations distributed around the globe demonstrate that PPP solutions can reach stable accuracies below five centimeters, disturbed ionospheric conditions analysed during Solar Cycle 25 can induce meter level errors and lead to long re-convergence times.
• Using Galileo alongside GPS yields more accurate PPP solutions than GPS only under both quiet and disturbed ionospheric conditions. The multi-constellation approach, together with the integration of a Detection–Identification–Adaptation (DIA) procedure into the PPP algorithm, improves positioning performance and robustness during severe ionospheric scintillation.

What is the implication of the main findings?

• Multi-GNSS should be the default, with the processing of GPS + Galileo rather than GPS only to reduce errors and improve solution quality.
• The integration of DIA-based quality control in PPP, especially under ionospheric scintillation, to detect and mitigate/reject outliers, maintains solution integrity and reduces re-convergence times. Robust cycle slip detection and repair should be implemented to improve positioning performance and reduce re-convergence events.

Abstract

As the peak of Solar Cycle 25 approaches, space weather events such as Equatorial Plasma Bubble (EPBs) and geomagnetic storms are expected to become more frequent. While EPBs are a primary source of scintillation, geomagnetic storms can either enhance or suppress this activity depending on storm timing, intensity, and induced electric field effects, thereby causing significant ionospheric disturbances that degrade Global Navigation Satellite System (GNSS) signal reception performance. This study presents a novel, systematic evaluation of GPS + Galileo Precise Point Positioning (PPP) performance under intense ionospheric scintillation during the rising phase of Solar Cycle 25 using datasets from globally distributed stations. More than twenty months of data have been systematically analysed, with a focus on stations located in equatorial regions, which are the most affected by strong scintillation. PPP processing was performed using final products from the European Space Agency (ESA) with Multi-GNSS Experiment (MGEX) products employed as backups when ESA data were unavailable. It is shown that under severe scintillation the accuracy of the final PPP solution is severely reduced, with errors more than doubled with respect to calm days. In this respect, frequent cycle slips and anomalies in the input observations are detected. A comparative analysis of GPS-only and GPS + Galileo PPP solutions confirms that integrating Galileo not only mitigates the impact of scintillation but also improves the reliability and accuracy of positioning in challenging space weather conditions.

1. Introduction

Over recent decades, Global Navigation Satellite System (GNSS) has become the leading technology for geodetic positioning and navigation. Several GNSSs underwent a modernization process and are currently operational, including GPS (USA), Galileo (Europe), GLONASS (Russia), and the Beidou Navigation Satellite System (BDS) (China). This landscape has also been enriched by regional systems such as the Indian Radio Navigation Satellite System (IRNSS) (India) and Quasi-Zenith Satellite System (QZSS) (Japan). The multiplicity of signals provided by these systems significantly enhances positioning accuracy, particularly in dynamic environments and areas with limited coverage [1,2,3].

Despite these advancements, GNSS receiver performance can still be severely degraded by ionospheric disturbances [4,5,6], which become more and more frequent as the peak of the solar cycle approaches. Ionospheric scintillation is a major challenge in GNSS positioning, particularly in equatorial and high-latitude regions. Small-scale irregularities in electron density cause rapid fluctuations in signal amplitude and/or phase, which can lead to loss of signal tracking and disrupt ambiguity resolution in carrier-phase-based techniques [6]. In the equatorial regions, scintillation effects are most intense and frequent after sunset, driven by the Rayleigh–Taylor instability. This instability leads to the formation of Equatorial Plasma Bubbles (EPBs), characterized by extremely low electron densities. These structures align with geomagnetic field lines and drift eastward, with peak occurrence typically around the equinoxes and during periods of high solar activity. While EPBs are a primary source of scintillation, geomagnetic storms can either enhance or suppress this activity depending on storm timing, intensity, and induced electric field effects, thereby causing significant ionospheric disturbances that degrade GNSS signal reception performance [7,8]. In high-latitude regions (auroral and polar cap), scintillation is primarily caused by intense geomagnetic storms, although its effects are generally less severe than those near the magnetic equator. In contrast, mid-latitude regions are usually unaffected by significant scintillation. The occurrence and intensity of scintillation are strongly linked to the solar cycle, with the most severe impacts observed during solar maximum.

The impact of ionospheric disturbances depends not only on the severity of the ionospheric event but also on the positioning approach used. In recent years, significant research effort has been devoted to Precise Point Positioning (PPP) approaches that leverage the availability of precise corrections to achieve decimeter-level position accuracy [9]. PPP typically focuses on standalone positioning by utilizing precise products and ionosphere-free (iono-free) linear combinations of two code and phase observations on each ray path, effectively eliminating first-order ionospheric effects. When phase bias corrections are available, ambiguities can be resolved as a fixed solution, significantly reducing convergence time and making the method more practical for real-time applications. In real-time scenarios, several challenges arise, including the need for continuous communication to ensure that the system can provide orbit and clock corrections with the required accuracy. Currently, real-time PPP accuracy is expected to be within decimeter-level precision, which meets the needs of several end-users.

Several studies investigated the positioning performance of GNSSs using PPP under different scenarios. Veettil et al. [6] proposed a scintillation mitigation strategy that refines the stochastic model by assigning signal-specific weights based on tracking error variances. Although their results showed a 62–75% improvement in 3D accuracy under strong scintillation, their analysis was limited to GPS data. While Galileo was not considered, its potential for enhancing performance was recognized. Song and Zhao [10] assessed Galileo-only PPP performance under quiet ionospheric conditions in Europe, confirming Galileo’s contribution to accurate positioning with different frequency combinations. Afifi and El-Rabbany [11] analysed several PPP models using GPS and Galileo data and Multi-GNSS Experiment (MGEX) products, but did not assess performance under ionospheric disturbances. Hou and Zhou [12] evaluated the PPP performance of three active GNSS constellations (GPS, BDS-3, and Galileo) using static and kinematic solutions across 143 global MGEX stations; however, their analysis did not specifically address conditions of ionospheric activity.

The goal of this paper is to provide a systematic and comprehensive performance evaluation of GPS + Galileo PPP under intense ionospheric scintillation. This study investigates the impact of severe ionospheric conditions on GPS and Galileo positioning performance during the rising phase of Solar Cycle 25. Specifically, we evaluate the performance of combined GPS and Galileo PPP solutions under severe ionospheric scintillation by processing globally distributed data—particularly from low-latitude regions known for intense equatorial ionospheric disturbances. We demonstrate the degradation in positioning accuracy and highlight the benefits of multi-constellation integration for robust PPP under challenging conditions.

We begin by presenting the theoretical foundations for GNSS data integration in PPP processing and analysing the performance of static and kinematic PPP under varying ionospheric conditions during Solar Cycle 25. Specifically, we assess data collected under different levels of ionospheric scintillation to evaluate the positioning robustness in challenging environments.

The analysis is based on the processing of open-sky static measurements collected between January 2023 and August 2024, during the rising phase of Solar Cycle 25. Processing was performed using the Real Time PPP (RT_PPP) engine (version 1.0) developed by the São Paulo State University (UNESP) [13,14,15].

The software integrates dual-frequency observations from GPS and Galileo constellations. This integration enhances positioning accuracy compared to GPS-only solutions, while also providing more precise estimates of parameters such as the Zenith Tropospheric Delay (ZTD). The most significant improvements were observed in the kinematic positioning mode, especially for data collected under severe ionospheric scintillation.

The analysis provides insights into the PPP performance achievable using GPS and Galileo dual-frequency measurements under severe ionospheric conditions. Moreover, a long-term performance assessment based on twenty months of continuous data is provided. These results serve as baseline for the performance achievable using the Galileo High Accuracy Service (HAS) and its applications to PPP solutions. While the paper does not specifically focus on HAS, the approach implemented in the RT_PPP software is directly applicable to HAS corrections [15].

The remainder of this paper is organized as follows: Section 2 presents the functional and stochastic models for integrating GPS and Galileo data, along with the experimental setup and data adopted for the characterization of the PPP performance. Section 3 details the experiments and analysis, including the evaluation of daily time series from 2023 and 2024, tropospheric analysis, and PPP performance under strong ionospheric scintillation conditions. Finally, Section 4 and Section 5 provide a discussion and the conclusions originating from the analysis performed.

2. Materials and Methods

This section describes the materials and methods adopted in the paper for the analysis of PPP performance under diverse ionospheric conditions. Section 2.1 describes the mathematical model for GPS and Galileo integration in PPP, whereas Section 2.2 summarizes the experimental setup and the data selection procedure.

2.1. Mathematical Model for GPS and Galileo Integration in PPP

This section briefly summarizes the mathematical model used to integrate GPS and Galileo measurements within the RT_PPP engine, which processes dual-frequency measurements. GPS data were acquired on the L1 (1575.42 MHz) and L2 (1227.60 MHz) carriers, while Galileo observations were collected on the E1 (1575.42 MHz) and E5b (1207.14 MHz) carriers. From these measurements, ionosphere-free linear combinations were formed.

The basic equations for the ionosphere-free linear combination (L3) of pseudorange (PR) and carrier-phase ($\varphi$) measurements, expressed in meters, can be written as [2,16]

$$P{R}_{L_3}^{Sys}={\rho }_{rs}^{Sys}+c\left(d{t}_r^{Sys}-d{t}_s^{Sys}\right)+Tro{p}_r^{Sys}+\delta Or{b}^{Sys}+b_{rs}^{Sys}+\delta m{p}^{Sys}+{\upsilon }_{P{r}_{L_3}^{Sys}}$$

(1)

$$\begin{array}{cc}\hfill {\varphi }_{L_3}^{Sys}& ={\rho }_{rs}^{Sys}+c\left(d{t}_r^{Sys}-d{t}_s^{Sys}\right)+Tro{p}_r^{Sys}+\delta Or{b}^{Sys}+b_{rs}^{Sys}+\delta m{p}^{Sys}\hfill \\ \hfill & +{\lambda }_{L_3}^{Sys}\left(N_{L_3}^{Sys}+{\zeta }_{rs}^{Sys}\right)+{\upsilon }_{{\varphi }_{L_3}^{Sys}}\hfill \end{array}$$

(2)

where

• superscript Sys indicates the GNSS system (“G” for GPS and “E” for Galileo);
• ${\rho }_{rs}^{Sys}$ is the geometric distance between receiver r and satellite s;
• c is the speed of light in a vacuum;
• $d{t}_r^{Sys}$ and $d{t}_s^{Sys}$ are the clock errors for the receiver and satellite, respectively;
• $Tro{p}_r^{Sys}$ is the tropospheric delay;
• $\delta Or{b}^{Sys}$ is the satellite orbital error;
• $b_{rs}^{Sys}$ is the hardware delay for receiver r and satellite s;
• $\delta m{p}^{Sys}$ is the multipath error;
• ${\lambda }_{L_3}^{Sys}$ is the wavelength for the iono-free combination;
• $N_{L_3}^{Sys}$ is the carrier-phase ambiguity term for the iono-free combination;
• ${\zeta }_{rs}^{Sys}$ is the Uncalibrated Phase Delay (UPD), encompassing satellite and receiver hardware delays and initial phase biases [17];
• ${\upsilon }_{P{r}_{L_3}^{Sys}}$ and ${\upsilon }_{{\varphi }_{L_3}^{Sys}}$ are random and unmodeled errors affecting pseudorange and phase, respectively.

The unknown parameters estimated by the PPP engine include the receiver’s coordinates $(X_{rec},Y_{rec},Z_{rec})$, the receiver clock error ($d{t}_r$), the Zenith Wet Tropospheric Delay ($Z_{WD}^{Sys}$), and phase ambiguities ($N_{L_i})$ for each satellite at a specific band $L_i$. Satellite orbits are typically treated as fixed during the adjustment, implying that any inaccuracies in the orbit data will propagate into the estimated parameters.

The total tropospheric delay, $Tro{p}_r^{Sys}$ is modeled as the sum of the Zenith Hydrostatic Delay (ZHD), $Z_{HD}^{Sys}$, and the Zenith Wet Delay (ZWD), $Z_{WD}^{Sys}$, components, projected into the satellite–receiver line-of-sight using appropriate mapping functions, as shown in (3).

$$Tro{p}_r^{Sys}={\mathrm{mf}}_H\left({\mathrm{el}}^{\mathrm{Sys}}\right)·Z_{HD}^{\mathrm{Sys}}+{\mathrm{mf}}_w\left({\mathrm{el}}^{\mathrm{Sys}}\right)·Z_{WD}^{\mathrm{Sys}}$$

(3)

The mapping functions ${\mathrm{mf}}_H$ and ${\mathrm{mf}}_w$ account for the satellite elevation angle ${\mathrm{el}}^{\mathrm{Sys}}$, allowing the projection of the zenith delays into the slant path delays. In the PPP solution, the Zenith Hydrostatic Delay, $Z_{HD}^{Sys}$, can be derived either from empirical models (e.g., Hopfield or Saastamoinen) [18,19] or from numerical weather models, such as those provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) [20]. The Zenith Wet Delay is estimated as part of the adjustment process, potentially absorbing any residual hydrostatic delay not captured by the a priori model.

The linearized mathematical model relating residual observations and unknowns in the PPP approach can be expressed as $\mathrm{E}\left\{\delta \mathbf{y}\right\}=\mathrm{E}\left\{H\mathbf{X}\right\}+\mathrm{E}\left\{\upsilon \right\}$, where $\mathrm{E}\left\{.\right\}$ denotes the mathematical expectation. It can be explicitly rewritten as

$$\underset{\delta \mathbf{y}}{\underbrace{\left[\begin{array}{c}\delta P{R}_{L_3}^G\\ \delta {\varphi }_{L_3}^G\\ \delta P{R}_{L_3}^E\\ \delta {\varphi }_{L_3}^E\end{array}\right]}}=\underset{H}{\underbrace{\left[\begin{array}{cccccccc}{a}^G& b^G& c^G& 1& 0& m{f}_w\left(e{l}^G\right)& 0& 0\\ a^G& b^G& c^G& 1& 0& m{f}_w\left(e{l}^G\right)& {\lambda }_{L_3}^G& 0\\ a^E& b^E& c^E& 1& 1& m{f}_w\left(e{l}^E\right)& 0& 0\\ a^E& b^E& c^E& 1& 1& m{f}_w\left(e{l}^E\right)& 0& {\lambda }_{L_3}^E\end{array}\right]}}\underset{\mathbf{X}}{\underbrace{\left[\begin{array}{c}\Delta X_{rec}\\ \Delta Y_{rec}\\ \Delta Z_{rec}\\ cd{t}_{rec}^G\\ cIS{B}_{E,G}\\ Z_{WD}\\ N_{L_3}^G\\ N_{L_3}^E\end{array}\right]}},$$

(4)

where H denotes the Jacobian matrix and the term $\delta \mathbf{y}$ is the vector of differences between observed and computed measurement values. The contribution of the terms estimated using models, such as the Zenith Hydrostatic Delay, is included in $\delta \mathbf{y}$. The vector $\mathbf{X}$ contains the unknown parameters. The expectation of residual errors, $\mathrm{E}\left\{\upsilon \right\}$, is zero, assuming the lack of biases. The additional variables involved in (4) are as follows:

• $a^{Sys}$, $b^{Sys}$, and $c^{Sys}$ are the partial derivatives of the basic Equations (1) and (2) with respect to the receiver coordinates, where $Sys=G$ for GPS and $Sys=E$ for Galileo;
• $\Delta X_{rec}$, $\Delta Y_{rec}$, and $\Delta Z_{rec}$ are the corrections to the receiver’s approximate coordinates $(X_{rec}^0,Y_{rec}^{0}e{Z}_{rec}^0)$;
• $N_{L_3}^G$ and $N_{L_3}^E$ are the iono-free phase ambiguities for GPS and Galileo, respectively.

The GPS receiver clock error is represented by $cd{t}_{rec}^G$, and the inter-system time offset between GPS and Galileo, known as the Inter-System Bias (ISB), is denoted by $IS{B}_{E,G}$. Therefore, the Galileo receiver clock error is computed as follows:

$$d{t}_r^E=d{t}_{rec}^G+IS{B}_{E,G}.$$

(5)

In PPP data processing, correlations among measurements are typically ignored, and thus the Variance–Covariance Matrix (VCM) of the observations ($\mathbf{y}$) is represented in diagonal form. Consequently, when applying the iono-free combination, the VCM ($Q_y$) for both code and phase measurements can be expressed as:

$$Q_y=\left[\begin{array}{ccc}{\sigma }_{P{R}_{L_3}^s}^2& \dots & 0\\ ⋮& \ddots & ⋮\\ 0& \dots & {\sigma }_{{\varphi }_{L_3}^s}^2\end{array}\right]$$

(6)

For each satellite s, ${\sigma }_{P{R}_{L_3^s}}^2$ and ${\sigma }_{{\varphi }_{L_3^s}}^2$ ($s=1,2,\dots ,n$) represent the variances of the iono-free combinations for pseudorange and phase observations, respectively. These variances are propagated from the original precision of the L1, L2, and L5 observations, along with the coefficients used to eliminate the first-order ionospheric effect.

Higher-Order Ionospheric (HOI) effects are not explicitly corrected in the PPP processing implemented here; instead, they are acknowledged as a potential source of residual error [21,22,23,24,25].

GNSS observations can be weighted based on a function of the satellite elevation angle, such as by applying the inverse of the sine function. Alternative weighting strategies can also be employed to mitigate the impact of ionospheric scintillation or multipath effects [5,6,26]. For real-time data processing, we compute the variance of the observations as follows: a user-defined ($fix\_{\sigma }_{Obs}^2$) constant is added to the uncertainties associated with orbit (${\sigma }_{Orb}^2$) and clock corrections (${\sigma }_{clk}^2$), weighted by the inverse sine function of the satellite elevation angle ($e{l}^{Sys}$):

$${\sigma }_{Obs}^2=(fix\_{\sigma }_{Obs}^2+{\sigma }_{Orb}^2+{\sigma }_{clk}^2){\displaystyle \frac{1}{sin\left(e{l}^{Sys}\right)}}.$$

(7)

PPP data processing can be carried out using a recursive accumulative solution for static and kinematic scenarios. A discrete recursive Kalman filter is applied, incorporating correlation models to account for noise in the parameter time series, such as random walk noise for the wet troposphere component and white noise for receiver clock errors. Detailed information on stochastic processes and Kalman filter theory is extensively covered in the literature [27,28,29]. Depending on the models implemented in the Kalman filter, static or kinematic processing is obtained. In this respect, it is important to note that kinematic positioning refers to the model implemented in the RT_PPP positioning engine. However, this model was applied to the processing of measurements from static stations, which allowed an effective evaluation of positioning accuracy.

The RT_PPP software integrates dual-frequency observations from the GPS and Galileo constellations: the geodetic reference frames of both systems are currently aligned with the International GNSS Service (IGS) International Terrestrial Reference Frame 2020 (ITRF2020), ensuring consistency and compatibility within the geodetic framework. The processing system has been prepared to handle Galileo-HAS corrections, ensuring that the correction components—radial, in-track, and cross-track—are accurately centred at the satellite’s iono-free antenna phase centre for both Galileo (E1, E5b) and GPS (L1 C/A, L2C) signals. When using alternative observables, Differential Code Biases (DCB) corrections must be applied to maintain compatibility [9].

For the analysis conducted in this work, twenty months of continuous observations were processed using IGS final products. With these post-processed corrections, the RT_PPP software achieves centimeter-level accuracies. The characterization of performance achievable using real-time products is beyond the scope of this paper, and the interested reader is referred to [14,15] for more details on the subject.

Quality control follows the Detection, Identification, and Adaptation (DIA) paradigm. Detection evaluates the overall model using the Local Overall Model (LOM) statistic, which follows a central F-distribution with $mk$ observations and infinite degrees of freedom, expressed as $F_{{\alpha }_k}(mk,\infty ,0)$, where ${\alpha }_k$ represents the significance level. In this step, the null hypothesis

$$H_0:\mathrm{E}\left\{{\mathit{v}}_k\right\}=0$$

(8)

is tested, where ${\mathit{v}}_k$ is the vector of predicted residuals at epoch k. Under $H_0$, the expectation of the residuals is assumed to be zero. The alternative hypotheses are written in the following general form:

$$H_i:\mathrm{E}\left\{{\mathit{v}}_k\right\}={\mathit{C}}_i{b}_i$$

(9)

where $b_i$ is the scalar outlier and ${\mathit{C}}_i$ takes the form of a canonical unit vector ${\mathit{c}}_i\in {\mathbb{R}}^{mk}$, having a one as its i-th entry and zeros elsewhere. The LOM statistic is given by

$$T_{LOM}^k={\displaystyle \frac{1}{mk}}{\mathit{v}}_k^T{Q}_{vk}^{-1}{\mathit{v}}_k$$

(10)

where $Q_{v_k}$ is the covariance matrix associated with the vector ${\mathit{v}}_k$ and T denotes transposition. If the LOM test fails, the process moves to the identification stage, where the objective is to determine which observation(s) are contaminated by model errors. In this case, $H_0$ is rejected, and a search is carried out among the set of alternative hypotheses, $H_i$ with $i=1,\dots ,mk$. The identification step is commonly performed using Baarda’s data snooping test [30,31,32], where the statistic $w_i$ is constructed as

$$w_i={\displaystyle \frac{{\mathit{C}}_i^T{Q}_{vk}^{-1}{\mathit{v}}_k}{\sqrt{{\mathit{C}}_i^T{Q}_{vk}^{-1}{\mathit{C}}_i}}}.$$

(11)

Two possible outcomes can be distinguished: (i) one of the hypotheses, say $H_i$, is confidently identified as the source of error; (ii) none can be reliably identified, resulting in a lack of decision. It is important to note the difference between the recursive (Kalman filter) implementation used here and the classical batch DIA approach. In the recursive case, ${\mathit{v}}_k$ and $Q_{vk}$ are epoch-wise predicted residuals and their covariance, respectively. In the batch DIA formulation, the misclosure vector $\mathit{t}$ and its co-factor matrix $Q_{tt}$ represent the residuals and covariance matrix over the entire adjustment. Despite this difference, the statistical principle of detecting and identifying model errors remains analogous in both frameworks.

Finally, in the adaptation stage, the Kalman filter is updated to account for the detected model error, thereby ensuring the robustness of the estimation process [33,34]. The positioning engine also incorporates essential corrections for high-precision PPP, including absolute Phase Center Variation (PCV), phase wind-up, Ocean Tide Loading (OTL), Earth Body Tides (EBTs), and cycle slip detection. The system supports orbit and clock corrections in either SP3 format or State Space Representation (SSR) for real-time applications.

The next section outlines the experimental procedures employed in our investigation.

2.2. Experimental Setup and Data Selection Procedures

To conduct the experiments, we selected seven stations situated in distinct global regions, representing geomagnetic low, medium, and high latitudes (see Figure 1). The dataset encompasses twenty months of continuous data, spanning from January 2023 to August 2024. This period coincides with the recent peak of solar activity during Solar Cycle 25.

The stations ALGO, NYA1, YKRO, CUT0, and SYOG are part of the IGS network, which provides high-quality GNSS data for global geodetic and geophysical research. In contrast, the stations PPTE and PRU2 are associated with the Brazilian National Institutes of Science and Technology (INCT) GNSS-NavAer project, which focuses on studying atmospheric effects—particularly ionospheric scintillation—to enhance GNSS-based positioning, navigation, and aeronautical applications in the region.

Using dedicated Python scripts, it was possible to automatically download and process observations stored in Receiver INdependent EXchange (RINEX) format from these stations. While RINEX data allow for the analysis of positioning results, they are not suitable for easily detecting ionospheric scintillation events. For this reason, additional data from the PRU2 station were used. This station, which is directly managed by the UNESP-Brazil, is located (Lat.: ∼−22°; Lon.: ∼−51°) near the crest of the Equatorial Ionization Anomaly (EIA) and equipped with a Septentrio PolaRxS receiver that provides scintillation indices. This allowed us to identify quiet and disturbed ionospheric conditions. The Equatorial Ionization Anomaly is characterized by two bands of enhanced electron density around 10°–20° geomagnetic latitude, resulting from the fountain effect, where plasma rises at the equator and descends along geomagnetic field lines, creating pronounced latitudinal TEC gradients. PPTE was considered for the long-term analysis presented in this work and is located near to PRU2. For this reason, data from PRU2 are used only for the identification and analysis of strong ionospheric events, and their long-term analysis is not provided in order to avoid the repetition of results similar to those of PPTE.

For data processing, we used precise orbit and clock products, along with DCB corrections. Primarily, orbital products from the European Space Agency (ESA) (https://gssc.esa.int, accessed on 30 January 2025) were applied; however, when ESA data were unavailable, our PPP processing engine automatically retrieved alternative products from the MGEX database (https://igs.org/mgex, accessed on 30 January 2025).

Regarding the troposphere parameter, the ZHD and ZWD were computed using the Saastamoinen model, with GPT2w [20] providing the a priori meteorological parameters. The ZWD residual was modeled as a random walk process and estimated with a noise level of 5 mm/$\sqrt{\mathrm{hour}}$. The Global Mapping Function (GMF) was applied as the mapping function.

Table 1. Configuration parameters for PPP processing.

Configuration	Option
GNSS in use	GPS or GPS + Galileo
Code and phase observables	GPS: L1 and L2C; Galileo: E1, E5b
Processing mode	Static or kinematic
Precise orbits and clocks	Mainly from ESA; alternatively from MGEX
Ionosphere correction	Ionospheric-free combination for first-order correction; higher-order corrections not applied
Troposphere	- ZHD and ZWD from Saastamoinen + gpt2_1w as a priori value; - Residual ZWD modeled as random walk process; - Global Mapping Function (GMF) applied
Fixed obs. precision	0.8 m and 1.0 m for code and 0.008 m and 0.01 m for phase, corresponding to frequencies L1, L2 (GPS) and E1, E5b (Galileo), respectively (see (7))
Elevation mask	10°
Ambiguity resolution	Float solution
Relativistic effects, phase wind-up, ocean and loading tides	Corrected model
Receiver clock	Estimated based on white-noise model
Satellite DCBs	Data applied from CODE

presents the configuration parameters used in this study. The use of dedicated Python (version 3.11) scripts for data retrieval enabled the processing of the entire data period from January 2023 to August 2024.

The coordinates estimated using RT_PPP were compared to the daily coordinates provided by the National Geodetic Laboratory (NGL), which are derived using the GipsyX (version 1.0/IGS14/Repro3.0) software [35]. For this comparison, we converted the NGL solution from ITRF14 to ITRF20 using the parameters provided by IERS/ITRF. The Root Mean Square Error (RMSE) was used as the primary metric for evaluating accuracy. Additionally, we assessed other estimated parameters, including tropospheric delay and residuals, among others. The following sections present the results and analyses.

3. Results

For the experiments, we performed static and kinematic PPP on the data collected in 2023 and 2024 and analysed the results. The analyses include the positioning time series, variations of the estimated tropospheric delays, and correlation between positioning error and ionospheric scintillation. PPP performance has been analysed considering different time intervals. While an important contribution of this work is the long-term characterization of PPP outputs considering twenty months of data, results representative of the behavior of the RT_PPP software are at first provided in Section 3.1 considering a single day of observations. At this scale, it is possible to characterize the quality of the individual position solutions, including convergence time and accuracy as reflected by the related error time series. Aggregated results are then provided in Section 3.2, whereas Section 3.3 focuses on the impact of strong scintillation.

3.1. Analysis of Selected Daily Time Series

We selected a representative day, 26 May 2024 (DOY 147), for the PPTE station in Brazil (see Figure 1) and processed the data using the static PPP model. Figure 2 illustrates the number of satellites involved in the processing, along with the LOM test (see Section 2.1), in the top row. The bottom row displays the estimated ZTD and compares the results from processing with GPS only versus GPS + Galileo. Additionally, it shows the final coordinate precision (24 h of data) in the Geodetic Local System (GLS) for the East, North, and Up components.

The charts in Figure 2 show a significantly higher number of available satellites for positioning and lower LOM values when using the integrated GPS + Galileo constellation. The ZTD values exhibit slight variations, with a Root Mean Square (RMS) difference of 1.18 cm between the GPS-only and GPS + Galileo solutions. We then compared the RT_PPP-estimated coordinates with the ground truth (from the NGL). Figure 3 presents the time series of 2D and 3D errors, demonstrating improved convergence in PPP processing in the dual-constellation case.

From Figure 3, we observe that when using only GPS, the 2D and 3D time series oscillate during the convergence period, reaching peak deviations of approximately 11 cm and 17 cm, respectively, around 3:00 UTC. Additionally, day 147 of 2024 is characterized as a geomagnetically calm day, with the Kp index remaining below 3, indicating no significant disturbances in the Earth’s magnetic field. GNSS data were not affected by strong scintillation effects, as the maximum S4 index remained near 0.3 throughout the day. Therefore, the oscillations in the 2D and 3D GPS time series were primarily caused by the addition and removal of satellites around a specific hour of the day (see Figure 2), which affected the PPP convergence process.

RT_PPP employs a strategy that resets the ambiguity parameter when a satellite exits and re-enters the processing. When this occurs during the convergence period, particularly with a limited number of GPS satellites, it can impact the estimated coordinates. However, incorporating the Galileo constellation significantly improves the convergence period. After several hours of processing, both the GPS-only and GPS + Galileo solutions achieve similar final convergence, yielding daily 3D positioning errors of approximately 1 cm.

The data from the PPTE station on DOY 147 in 2024 was also utilized to assess the expected accuracy of kinematic PPP. Figure 4 shows the errors in the East, North, and Up components for the kinematic case, while

Table 2. RMSE of kinematic PPP for GPS and GPS + GAL at PPTE station on DOY 147 (values in meters).

Constellation	E (m)	N (m)	Up (m)	2D (m)	3D (m)
GPS	0.124	0.054	0.115	0.135	0.178
GPS + GAL	0.071	0.034	0.068	0.078	0.104

presents the corresponding RMSE values, considering the entire period (24 h).

Figure 5 shows the estimated residuals for pseudorange (code) and phase measurements from the kinematic PPP solution for both the GPS and Galileo systems. These residuals were obtained from the integrated GPS + Galileo PPP processing and plotted by individual satellites. The top row displays the pseudorange residuals, while the bottom row shows the phase residuals. Notably, both the code and phase residuals for Galileo are smaller than those for GPS, an observation further validated by the RMSE values of the residuals provided in

Table 3. RMSE of residuals at PPTE station on DOY 147-2024 (units in meters).

Constellation	Pseudorange (m)	Phase (m)
GPS	2.078	0.013
Galileo	1.152	0.012

.

The results presented in this section demonstrate that the RT_PPP software (version 1.0) achieves centimeter-level accuracy in daily static PPP. The integration of the GPS + Galileo constellation enhances both convergence and accuracy in PPP compared to GPS alone, for both static and kinematic cases. The next section presents the analysis of data from 2023 and 2024.

3.2. Overall Analysis of Static PPP with GPS and Galileo for the Years 2023-2024

Data from six globally distributed stations (see Figure 1) were daily processed using static PPP solutions from January 2023 to August 2024. Figure 6 presents the time series of 2D positioning errors for each station, comparing PPP results using GPS only (blue dots) and the integrated GPS + Galileo (red dots) constellation. Additionally, Figure 7 shows the corresponding vertical errors.

The 2D and height errors shown in Figure 6 and Figure 7 are notably larger for low-latitude stations, such as CUT0, PPTE, and YKRO, with maximum 2D errors reaching approximately 6 cm and height errors up to 5.5 cm (absolute mode) at the PPTE station. These higher errors may be attributed to unmodeled higher-order ionospheric effects and atmospheric loading, which are not currently accounted for by our PPP processing engine. In contrast, high-latitude stations, such as SYOG, ALGO, and NYA1, exhibit lower positioning errors, with 2D errors peaking at around 2 cm and height errors reaching up to 4 cm in absolute mode. The data gaps visible for the ALGO and CUT0 stations are due to issues with the retrieval of the related RINEX files and are not due to ionospheric effects. Nonetheless, more than 14 months of data are available in both cases.

Table 4. RMSE of the static PPP considering the entire period from January 2023 to August 2024 (values in centimeter).

	GPS (cm)					GPS + Galileo (cm)
Station	E	N	Up	2D	3D	E	N	Up	2D	3D
SYOG	0.53	0.74	0.80	0.91	1.21	0.55	0.71	0.81	0.90	1.21
CUT0	1.51	0.37	2.55	1.56	2.99	1.37	0.40	2.40	1.43	2.79
PPTE	1.19	0.47	2.36	1.28	2.68	1.19	0.51	2.25	1.30	2.60
YKRO	2.52	0.57	2.02	2.59	3.28	2.34	0.52	1.98	2.39	3.11
ALGO	0.72	0.38	1.36	0.82	1.59	0.53	0.41	1.32	0.67	1.48
NYA1	0.31	0.33	1.40	0.45	1.47	0.29	0.31	1.28	0.42	1.35

presents the RMSE values for all stations over the period analysed. Overall, RMSE values improve when using the combined GPS + Galileo constellation in daily static PPP compared to GPS alone. The largest horizontal improvement is observed at station ALGO, where the 2D RMSE decreases from 0.82 cm with GPS only to 0.67 cm with the integrated constellation, an improvement of approximately 18%. For the 3D case, the greatest improvement is at station NYA1, where the 3D RMSE reduces from 1.47 cm with GPS only to 1.35 cm with the integrated constellation, representing an improvement of about 8%.

An another output of the RT_PPP engine is the ZTD, which is estimated at each epoch within the implemented Kalman filter. This parameter is treated as random walk noise (see Table 1 for more details). The daily mean ZTD values were then computed for both GPS-only and GPS + Galileo PPP processing. Figure 8 presents the time series of these daily mean ZTD values.

We also computed the first, second, and third quartiles (Q1, Q2, and Q3) for each day. Figure 9 presents a histogram of the daily differences in ZTD mean and quartile values between GPS-only and GPS + Galileo PPP solutions. The maximum observed difference in the quartile ranges is approximately 1 cm.

Figure 10 shows the histogram of daily estimated ZTD precision. The PPP with GPS + Galileo data yields a narrower range of ZTD precision values, as confirmed by the values presented in

Table 5. Statistics of the estimated daily ZTD precision.

	GPS (cm)					GPS + Galileo (cm)
Station	Mean	StDev	Min	Max	Range	Mean	StDev	Min	Max	Range
SYOG	0.78	0.46	0.24	5.42	5.18	0.75	0.34	0.26	2.18	1.92
CUT0	1.49	0.87	0.48	10.47	9.99	1.42	0.76	0.42	5.51	5.09
PPTE	1.90	1.10	0.51	12.70	12.19	1.79	0.97	0.50	7.68	7.18
YKR0	1.59	0.69	0.50	7.43	6.93	1.56	0.58	0.62	4.31	3.69
ALGO	1.47	1.01	0.32	7.06	6.74	1.40	0.93	0.23	5.53	5.30
NYA1	0.86	0.68	0.18	6.50	6.33	0.82	0.57	0.15	4.43	4.28

.

Table 5 demonstrates the improvements in daily estimated ZTD precision when using the combined GPS + Galileo constellation compared to GPS only. The combined solution yields lower values for the mean, standard deviation, and range, that is, the difference between the minimum and maximum values in the ZTD precision time series.

The following section evaluates the performance of kinematic PPP using GPS and Galileo data collected under varying ionospheric scintillation conditions.

3.3. Performance of PPP with GPS and Galileo Under Ionospheric Scintillation Conditions

To analyse the impact of GPS and Galileo integration on data under varying ionospheric conditions, we selected data from the PRU2 (Lat: $-22.122$°; Lon: $-51.407$°) station on days 66–67 (6–7 March 2024), which experienced strong ionospheric scintillation, and calm days 90–91 (30–31 March 2024) for comparison. The station belongs to the INCT GNSS NavAer project [36,37,38,39].

Ionosphere scintillation predominantly occurs in low-latitude, high-latitude, and polar geomagnetic regions. In low-latitude regions, scintillation is associated with the equatorial anomaly together with ionospheric plasma bubbles that form in this region after sunset. Small irregularities within these bubbles become sources of intense scintillation. The magnitude and frequency of scintillation are correlated with the solar cycle. Ionospheric scintillation occurrences can be monitored through amplitude (S4) and phase standard deviation (${\sigma }_{\varphi }$) indices, which are currently obtainable from specialized GNSS monitoring receivers [5,6,37]. The PRU2 station, located in Brazil, is equipped with a Septentrio PolarRxS PRO receiver capable of monitoring ionospheric scintillation through ionosphere indices. The ionosphere scintillation is classified as in

Table 6. Scintillation classification.

Classification	S4	${\mathit{\sigma }}_{\mathit{\varphi }}$ at each 60 s. (Phi60)
Strong	>1.0	>0.8
Moderate	0.5–1.0	0.4–0.8
Weak	<0.5	<0.4

[38]:

Figure 11 presents the Total Electron Content (TEC), S4, and ${\sigma }_{\varphi }$ (PhI60-L1) [39] values observed on the selected days. The values shown in the figure were obtained considering satellites with elevation angles greater than 20° to mitigate the multipath effect.

The GNSS data were processed starting at 12:00 UTC on the selected day and ending at 12:00 UTC of the following day. In this case, positioning convergence had already occurred before the beginning of the ionospheric scintillation period, which is around 21:00 UTC for stations in equatorial regions.

Figure 12 and Figure 13 present the results for days 66–67 and 90–91 of 2024, respectively. The top rows show the precision of the planimetric coordinates, derived from the adjustment of observations. The bottom rows display the positioning errors, defined as the differences between the estimated coordinates and the ground truth. On days 66–67, a significant increase in positioning error due to scintillation is evident, particularly between 00:00 and 03:00 UTC on DOY 67.

Table 7. RMSE for kinematic PPP for days 66–67 (strong scintillation) and 90–91 (calm days) of 2024 (units in centimeters).

DOY	Constellation	E (cm)	N (cm)	U (cm)	2D (cm)	3D (cm)
66–67	GPS	0.25	0.11	0.57	0.27	0.63
	GPS+GAL	0.16	0.14	0.53	0.21	0.57
90–91	GPS	0.11	0.08	0.08	0.14	0.16
	GPS+GAL	0.09	0.04	0.05	0.10	0.11

presents the RMSE values for the kinematic PPP processing on days 66–67 and 90–91 of 2024. The combined GPS + Galileo constellation generally shows improvements across all cases, except for the North component on scintillation-affected days 66–67, where the RMSE is $0.11$ m using GPS alone compared to $0.14$ m with GPS + Galileo. Nevertheless, the 2D and 3D errors are reduced when using the integrated GPS + Galileo solution.

One of the most significant impacts of ionospheric scintillation on the receiver position estimation is the frequent occurrence of cycle slips. When a cycle slip occurs, the ambiguity parameter in the Kalman filter is typically re-initialized, affecting the positioning accuracy. Our cycle slip detector is based on the Turbo Edit algorithm [40], which employs the Melbourne–Wübbena combination to analyse the wide-lane bias ($b{\overline{w}}_i$) using a recursive mean filter. The wide-lane bias ($b{w}_i,i=1,2,\dots ,n$) is computed for each epoch, and any value deviating beyond a 4-sigma threshold from the mean is flagged as a potential cycle slip. Figure 14 illustrates the deviations of $b{w}_i$ from the mean at epochs identified as cycle slips, highlighting a significant number of cycle slips during periods of strong ionospheric scintillation events on DOY 66–67 of 2024.

In addition to cycle slips, a notable increase in outlier identification is observed when using the DIA procedure (see Section 2). Figure 15 presents the maximum statistical values $(max{w}_i)$ exceeding the tolerance threshold, computed during the identification stage for both code $(max{w}_{i_{PR}})$ and phase $(max{w}_{i_{PH}})$ measurements on DOY 66–67 and DOY 90–91 of 2024. During identification, the observation corresponding to the largest detected $w_i$ value (see (11)) is flagged as erroneous. In the adaptation stage, this observation is excluded, and the epoch is re-processed without it in the recursive procedure.

It should be noted that the phase measurements have been affected by scintillation more than pseudorange observations. This is due to the vulnerability of the phase measurements to scintillation effects. In contrast, on the calm days of DOY 90–91, 2024, only a single satellite observation is flagged as an outlier.

The impact of strong ionospheric scintillation is also evident in the residuals from the PPP processing. Figure 16 and Figure 17 show the computed residuals for DOY 66–67 and DOY 90–91 of 2024, respectively. In both figures, the top row presents the code/pseudorange residuals, while the bottom row shows the phase residuals, all in meters. The residuals were derived from GPS + Galileo processing, but are plotted separately by constellation: the left panels correspond to GPS satellites, and the right panels to Galileo satellites.

Figure 16 clearly shows the impact of strong ionospheric scintillation on positioning accuracy, particularly in the phase residuals (bottom row) for both GPS and Galileo data on DOY 66–67 of 2024. In contrast, Figure 17 presents a typical time series of code and phase residuals for the same satellite systems on DOY 90–91 of 2024.

The effect of ionospheric scintillation on the estimation of the ZTD was also analysed. Figure 17 compares ZTD estimates obtained during DOY 66–67 (strong scintillation) with those of DOY 90–91 (weak scintillation) of 2024.

The results shown in the left part of Figure 18 indicates that the ZTD is not significantly affected by the impact of ionospheric scintillation. PPP positioning errors for DOY 66–67 of 2024 are analysed in Figure 16, and a significant performance degradation can be observed after midnight when scintillation occurred. Similar effects or discontinuities are not visible in the left part of Figure 18, and this indicates the marginal impact of scintillation on the estimation of this parameter.

When comparing the results for the two cases in Figure 18, it is important to note that the PRU2 station is located in a tropical climate region, with an annual mean air temperature of approximately 24 °C and an average annual relative humidity (RH) of 65.1%, with the highest value occurring in February (73.2%) and the lowest in August (53.6%). A slight decrease in the estimated ZTD values is observed from days 66–67 through days 90–91: this is consistent with the reduced relative humidity. This reduction directly influences the estimation of the wet component of the troposphere, which is known to exhibit greater variability than the hydrostatic component. Moreover, when using GPS + Galileo data, the ZTD estimates show faster convergence compared to using GPS alone.

4. Discussion

This paper presented a comprehensive analysis of the performance achievable by a PPP software integrating multi-constellation measurements. Specific focus was devoted to the impact of the ionospheric conditions observed during the peak of Solar Cycle 25. Data from six globally distributed stations, covering geomagnetic regions of low, medium, and high latitudes, were processed. For static positioning, time series with daily solutions were generated for the years 2023 through mid-2024, and the estimated coordinates were compared to the NGL solution, which uses the Gipsy software. Under calm ionospheric conditions, the RT_PPP software demonstrated accuracy within a few centimeters. Moreover, the integration of GPS and Galileo constellations led to improvements in positioning accuracy and enhanced ZTD estimates.

Ionospheric conditions were constantly monitored, and data collected under scintillation were used to study its impact on PPP solutions. In particular, measurements from PRU2 station in Brazil, near the magnetic equator, were used from the analysis. Two specific days were analysed: one calm day (days 90–91 of 2024) and one with occurrence of strong ionospheric scintillation (days 66–67 of 2024). Results obtained for these two days were thoroughly compared. The analysis shows that the PPP solution accuracy can be significantly affected by ionospheric scintillation, with cycle slips and anomalies in multiple measurements. These effects can, in turn, compromise the convergence time of the PPP algorithm, either when data collection begins during a period affected by scintillation or during subsequent re-convergence phases triggered by signal degradation. Mitigation measures can be implemented using approaches such as the DIA method, modifying the original stochastic model, or excluding observables affected by scintillation. However, these strategies present significant challenges and remain an active area of scientific research worldwide. The paper also confirmed the importance of multi-constellation solutions where the increased measurement availability compensates, at least partially, for the negative effects induced by ionospheric scintillation.

5. Conclusions

The paper contributes to the field of positioning and navigation by evaluating the performance of PPP through the integration of GPS and Galileo data, collected under diverse ionospheric conditions during Solar Cycle 25. In this study, we performed a comprehensive evaluation of positioning accuracy across different ionospheric conditions and also demonstrated the benefits of multi-constellation solutions under severe ionospheric scintillation using the in-house software, RT_PPP.

The analysis conducted considering almost twenty months of data from six different stations provides a baseline in terms of achievable performance for future studies on PPP algorithms. This is particularly relevant for services such as the Galileo HAS, which provides PPP corrections for both GPS and Galileo. The RT_PPP software is HAS-ready, and the study considered GPS and Galileo to have conditions comparable to those enabled by HAS. In this respect, the performance shown in the paper should be considered as a lower bound for HAS performance.

While the analysis of observations from six stations covers quite diverse ionospheric conditions, additional testing is needed to explain the characteristics of ionospheric discrepancies at different latitudes. This analysis is left for future work.