Precise Point Positioning (PPP) leverages multi-signal carrier phase and pseudorange measurements of a single receiver to achieve mm-level accuracy for static, long-sessions –up to daily– processing. In PPP, the joint estimation of the initial carrier phase ambiguities and the coordinates is strictly required; moreover, to fully deploy the PPP potential accuracies, the estimation of tropospheric parameters and the adoption of precise Global Navigation Satellite System (GNSS) products are also required. Therefore, two main problems pose in the real- or quasi-real-time application of PPP:
1. the slow convergence time of the solution, caused by the slow varying configuration of the actual Medium Earth Orbit (MEO) GNSS satellites;
2. the availability of precise GNSS products (satellite ephemerides, clock errors and biases as, for example, the products provided by the International GNSS Service –IGS–).
In the latter case, Galileo, with its High Accuracy Service (HAS), is providing satellite orbits, clock errors and biases enabling PPP globally. Nevertheless, at present, PPP for very short or even kinematic sessions in real-time remains an open challenge.
For understanding how to improve the real-time PPP performance, commercial and governmental activities are evaluating and designing the use of Low Earth Orbit (LEO) satellites also for Positioning, Navigation and Timing (PNT) applications, for example transmitting from LEO signals like the GNSS ones. In this context, LEO constellations, orbiting at heights of 800–1200 km, offer geometric benefits:
1. by introducing additional satellites, resulting in improved user geometry;
2. by ensuring a much faster change in user satellite geometry (compared to MEO GNSS) thanks to their short orbital period (approx. 100 minutes).
Consequently, this should help to decorrelate faster the estimable user parameters and reduce the convergence time of PPP solutions based on the integration of GNSS with LEO.
In this study, the joint processing of GNSS and LEO satellites is performed using the JRC User Navigation Engine (JUNE). JUNE is developed in MATLAB, and performs real-time PPP processing, using the broadcast navigation data and the High Accuracy Service (HAS) corrections. The software has been customized, introducing the processing of LEO satellites as a new additional GNSS.
The aim of this study is to investigate how the integration of LEO-PNT with the actual MEO GNSS can enhance the performance of PPP. Moreover, the investigation can leverage the validated usage of HAS in JUNE.
The GNSS data acquired by existing continuously operating stations in different geographic locations are used. The orbits and measurements of a possible LEO constellation are simulated: from the LEO orbit propagation and the positions of the stations, the LEO pseudorange and carrier phase measurements are reconstructed.
This study compares four processing scenarios:
1. GNSS-only with Broadcast Ephemeris;
2. GNSS+LEO with Broadcast Ephemeris;
3. GNSS-only refined with Galileo HAS corrections;
4. GNSS+LEO refined with Galileo HAS corrections.
The analysis includes different process noise levels.The results show an impact of the LEO satellites in the convergence performance when large process noise of the user state vector is adopted, while it is not so evident with lower process noise.

The continuing growth of Low Earth Orbit (LEO) missions intensifies the need for autonomous, on-board precise orbit determination (POD) capable of ensuring the accuracy, continuity and reliability required by next-generation LEO platforms operating in a highly dynamic environment. This work compares the achievable performance and computational load of two different GNSS-based real-time POD architectures. Both solutions are evaluated using public ESA LEO GNSS datasets from Sentinel-6A (S6A) and Swarm-B (SWB).

The first architecture consists of the sequential combination of GMV’s Gsharp® PPP plus a dynamic least-squares-based filter for the Orbit Determination and Prediction (ODP). Gsharp has been evolved into a 1 Hz real-time, on-board precise orbit and clock determination algorithm based on an Extended Kalman Filter (EKF) processing uncombined, multi-frequency, multi-constellation GNSS measurements, including Galileo’s High Accuracy Service (HAS). The resulting PPP coordinates are accumulated by the ODP filter, which refines the orbit and predicts the satellite trajectory by estimating key dynamical parameters (state vector, solar radiation pressure coefficients, atmospheric drag and nine empirical acceleration parameters), providing a dynamically consistent orbit solution that enhances the initial PPP positions. With S6A data (GPS+Galileo+HAS), the PPP solution achieves <25 cm 3D RMS and <1 ns clock RMS, improved by ODP to <20 cm. For SWB (8 GPS channels only), errors are <60 cm for PPP and <30 cm for ODP. ODP performs the forward-propagation of the estimated orbit achieving 3D RMS of ~16 cm at 10 min, 18 cm at 30 min and 19 cm at 50 min for S6A and corresponding values of ~34 cm, 52 cm, and 60 cm for SWB.

The second architecture presents a unified on-board solution that integrates GNSS measurement processing and dynamic orbit estimation within a single EKF. By estimating the relevant orbit parameters in real time with an advanced orbit determination model, the filter provides a physically consistent navigation solution and eliminates the need for a separate ODP stage. This configuration achieves an RMS clock a synchronization error <0.5 ns for S6A. The position 3D RMS is <10 cm for S6A and <15 cm for SWB in estimation, while forward-propagation results confirm the robustness of the approach, with S6A position RMS of ~10 cm at 10 min, 15 cm at 30 min and 20 cm at 50 min, and corresponding SWB values of ~15 cm, 30 cm and 40 cm.

These results highlight GMV’s ability to offer complementary on-board navigation architectures tailored to different mission and platform constraints. The modular Gsharp+ODP chain provides maximum flexibility, enabling independent deployment of PPP or ODP capabilities when required. Conversely, the unified dynamic Gsharp filter consolidates both functions into a single, high-performance algorithm optimized for minimal CPU and memory consumption, making it especially attractive for resource-constrained LEO spacecraft.

Overall, the study provides a consolidated view of GMV’s advances toward autonomous, high-precision, on-board navigation for LEO platforms, demonstrating that both architectures are technically mature and ready to support future constellation missions, resilient Positioning, Navigation and Timing (PNT) services and spacecraft requiring dependable real-time orbit knowledge.

Tropospheric zenith wet delay (ZWD) is a key parameter influencing high-precision GNSS positioning and providing valuable information on atmospheric water vapor for geodetic and meteorological applications. Spatially continuous ZWD fields are particularly important in regions where GNSS receivers are sparsely distributed or unavailable, motivating the use of network-based interpolation techniques. The increasing availability of dense low-cost GNSS networks offers new opportunities for high-resolution tropospheric monitoring, yet their applicability for ZWD spatial interpolation requires dedicated investigation.
In this study, we investigate the spatial interpolation of ZWD using an exclusively low-cost GNSS network based on an epoch-wise ordinary kriging approach. Zenith wet delays are estimated at network stations using precise point positioning with a 30 s sampling interval, and kriging interpolation is applied to predict ZWD at locations without GNSS receivers. The interpolation performance is evaluated over one year of observations using independent low-cost user stations, with particular attention to temporal variability and changing atmospheric conditions.
The results demonstrate that dense low-cost GNSS networks can provide stable and physically consistent ZWD interpolation when spatial correlations are appropriately modeled. The interpolated ZWD products are suitable not only for characterizing tropospheric conditions at uninstrumented locations, but also for supporting precise point positioning and PPP-RTK initialization, assimilation in meteorological and numerical weather prediction models.

The use of Global Navigation Satellite System (GNSS) carrier phase measurement is essential to obtain high accuracy GNSS positioning solutions. However, it requires us to deal with the carrier phase ambiguity, an unknown constant parameter affecting the carrier phase measurements. Usual algorithms, such as Real-Time Kinematics (RTK) or Precise Point Positioning (PPP), estimate the ambiguities as new variables included in the state vector. Another way is to perform difference of carrier phase measurements from the same satellite at two epochs, the so called Time-Differenced Carrier Phase (TDCP), which gives an observation no longer depending on the ambiguity, but on the positions at the two epochs. Using TDCPs simplifies the estimation problem by reducing the number of estimated states, and provides interesting accuracy gain, thanks to their high accuracy.

Analytical modeling of the errors affecting TDCP is difficult due to the limited knowledge of the time correlation of the various error terms affecting the carrier phase measurement. When performing the time-difference, time-correlated errors will be reduced, while uncorrelated errors will increase. In addition, some time-varying errors may also change with some unknown evolution.

To face these difficulties, this paper presents a characterization of the error affecting TDCP observations based on real data analysis. A residual analysis is performed on data from IGS stations. Special attention has been given to the cycle slip occurrence and ephemeris change, to stay in the hypothesis of a constant ambiguity.

The results provide useful information to better tune positioning algorithms using TDCP. In particular, we observe that the TDCP noise model does not depend on the elevation of the satellites. We also investigated the dependence of the noise model standard deviation on the time interval and found an affine trend.
To demonstrate the validity of the proposed model, an FGO-based solution will be computed using code and TDCP observations. The results will then be compared under different noise models applied to the TDCP observations.