The demand for accurate, real-time positioning is increasing across various domains, including autonomous navigation, public safety, urban mobility, and assistive technologies. While Global Navigation Satellite Systems (GNSS) provide global coverage and reliable Positioning, Navigation, and Timing (PNT) services, their performance in dense urban environments remains a challenge due to signal obstructions, multipath efects, and interference threats such as spoofing and jamming. To enhance positioning performance in such scenarios, this study explores the integration of Low Earth Orbit (LEO)-based PNT constellations with GNSS, focusing on their impact on Precise Point Positioning (PPP) convergence time. A simulated LEO-PNT constellation of 263 satellites, operating at 1200 km altitude with polar or 55° inclined orbits, is introduced to augment GNSS observables. Using real GNSS data and an Extended Kalman Filter (EKF) approach, the hybrid GNSS+LEO system is evaluated in a simulated urban environment with a 40° elevation cutof. The results, based on three test datasets, demonstrate a significant reduction in PPP convergence time, up to 80% improvement in challenging conditions, highlighting the potential of LEO-PNT in enabling faster and more reliable positioning solutions for future urban applications.
Nowadays, positioning and navigation of people and vehicles is a need for society: the computation of precise position, in real time and single epoch, is fundamental for many applications, such as guidance and control, industrial applications, mass market, public security, assistive technologies and recreational purposes. Precise positioning plays a central role in the distribution of the future cities’ services and applications. For instance autonomous driving relies on GNSS (Global Navigation Satellite System), sensors, radar and advanced positioning techniques to enable vehicles to operate without human intervention. In addition, the knowledge of accurate vehicle positioning facilitates trafic optimization, particularly by improving road safety, enhancing the reduction of emissions and contributing to more sustainable urban mobility. Furthermore, location-based services provide personalized information and services based on the user’s location, enabling real-time trafic updates, eficient public transportation, and shared mobility solutions such as bike or car-sharing and ride-hailing services. The optimization of urban mobility improve the overall eficiency of transportation systems. Another example are assistive services for people with disabilities. Innovations such as obstacle detection systems, location-based audio guides, and navigation tools improve accessibility, ensuring safer and more inclusive public spaces. At present, most positioning, navigation, and timing (PNT) services rely on the use of Global Navigation Satellite Systems (GNSS). With GNSS we intend all the constellations of satellites properly designed to provide PNT information to users on the ground, in MEO (Medium, Earth Orbith) and GEO (Geosynchronous Earth Orbit). These systems guarantee global coverage and are designed to operate reliably under all weather conditions, making them indispensable for a wide range of applications across various domains. The four primary systems are the Global Positioning System (GPS) from the United States, Galileo from Europe, the BeiDou Navigation Satellite System (BDS) from China, and the Global
Navigation Satellite System (GLONASS) from Russia. Additionally, several regional satellite navigation
systems have been developed, such as the Indian Regional Navigation Satellite System (IRNSS) in India
and the Quasi-Zenith Satellite System (QZSS) in Japan [
This section outlines the positioning models and the corresponding observation equations for the measurements processed in the positioning software. Specifically, the software processes iono-free GNSS code and phase observables, as well as simulated iono-free LEO-PNT code observables. The system uses an EKF to process these measurements. Additionally, a detailed description of the EKF implementation is provided, outlining its role in improving the accuracy and convergence of the positioning solution.
GNSS satellites, according to the literature, transmit observables modeled at diferent frequencies within
the L-band. Therefore, with a multi-frequency receiver, it is possible to obtain multiple observations
from the same satellite at a given epoch. These observations can be combined to generate several
new observables, among all of them we are going to focus on ionospheric-free observations, which
are a combination of GNSS measurements that eliminates the efects of ionospheric delay, which can
introduce errors in positioning solutions. According to standard literature [
+ ( () + ,, ) + × ( − ) + () Φ,() = ( − ) + () + ( () + ,,Φ)+ × ( − ) + ()Φ, + () (1) (2) where: • = || − || is the distance of the user with respect to the satellite . • is the travel time between the satellite and the . •
is the tropospheric delay between the satellite and the . • is the clock bias of the . • , is the receiver code hardware bias, diferent for each constellation. • is the clock bias of satellite that includes the relative hardware bias. • is the measurement noise.
• Φ, is the phase ambiguity of each mesurement, specific of each satellite.
As previously introduced, the design and implementation of LEO-PNT constellation is still ongoing
and it must consider factors such as cost, coverage, and signal quality in the definition of the final
specifications. Decisions are still being made regarding the types of signals that will be onboard these
satellites and the frequency bands they will operate on [
The LEO-PNT constellation was simulated with 263 satellites at an height of 1200 km. The constellation
of 263 satellites is divided between two orbital configurations: a portion is distributed across polar
orbital planes with an inclination of 89°, ensuring global coverage including high-latitude regions, while
the remaining satellites are placed in planes inclined at 55°, optimized for enhanced coverage over
mid-latitude, densely populated areas. The orbit is assumed to be circular, with eccentricity equal to 0.
The constellation follows a Keplerian orbital model and the relative orbital parameters were sumulated
in order to optimize the coverage, following a constellation model consistent with the existing ESA
literature related to the LEO-PNT project, which considers system architectures tailored for PNT
applications [
() = () () + () () The respective error bias is modeled according to a Random Walk with 2.5 cm standard deviation.
For what concern the implemented solution algorithm, GNSS and LEO measurements are jointly processed with an EKF. The system state is structured as follow: ⎡ ⎤
, = ⎢⎢⎣ ⎦⎥⎥ Θ,Φ (5) (6) (7) is the position of the receiver in ITRF. , is the vector containing the clock ofsets of the receiver with respect to code measurements, comprehending the UE clock ofset and the receiver code hardware bias, diferent for each constellation: , = , + , . The number of , is equal to the number of available constellations (MEO and LEO). is the zenithal wet tropospheric delay. Θ,Φ is a vector containing the unknown relative to phase measurements: Θ,Φ = × (,Φ() + , ) + ()Φ, . It is important to emphasize that this approach was adopted because the software is designed for navigation rather than geodetic processing. By structuring the system in this way, the number of unknowns is minimized, thereby maximizing system redundancy. For the EKF implementation we refer to standard literature [24], the implemented dynamic model is: ̂︀ = − 1 + where represents the design matrix of the dynamic model, which is = under the assumption of a nearly static system. ̂︀ denotes the predicted state at epoch based on the dynamic model, while represents the model error. A covariance matrix, , is assigned to the model error to account for its uncertainty: the standard deviation of the coordinates , , is 0; the code clock ofset , is 5; the residual wet Tropospheric delay is 0.01 and Θ,Φ is 10.
The following section summarizes the results obtained from processing 12 hours of data acquired over three diferent days in 2024: Test 1 (DOY: 278), Test 2 (DOY: 289), Test 3 (DOY: 308). GNSS data were collected at a 1 Hz sampling rate from the permanent station in Milan, which is part of the SPIN GNSS network. SPIN (Sistema di Posizionamento Integrato Nazionale) is a high-precision GNSS network that provides continuous positioning services for geodetic, scientific, and engineering applications. The network consists of 39 reference stations distributed in the north of Italy. Only measurements from GPS, Galileo and BeiDou constellations have been processed.
For what concerns the LEO data, they’ve been simulated according to the methods described in Section 2.3. In order to have a better understanding of the satellite availability, in particular of the simulated LEO constellation, the number of the satellites in LOS is computed for 24 hours of data. Figure 1 shows the number of available GNSS satellites in open-sky condition (cutof 0) and urban environment (cutof 40); Figure 2 report the number of LoS satellites for LEO constellation in the same scenarios. It is evident that, in both cases the number of satellites decreases significantly after applying the cutof. However, this condition afects more significantly LEO constellation: in many epochs we have no satellites in LoS, while for GNSS the minimum number of LoS satellites never gets lower 4.
Two diferent processing configurations are tested: GNSS-only and hybrid GNSS+LEO. Since this work aims to assess the improvements in PPP convergence time in challenging environments such as urban canyons, a satellite elevation cutof of 40 degrees is applied to satellite’s measurements. The UE location is then estimated using the EKF and compared with the true position of the network base station (BS) as provided by SPIN. The errors in the East, North, and Up components are computed, along with the overall 2D error, for both tested configuration. To evaluate the improvement in convergence time, we identify the last epoch in the time series where the 2D error exceeds the 30 cm threshold. From that point onward, the error remains below this threshold, consistently meeting our accuracy requirement. Table 1 reports the convergence time (in minutes) for both GNSS-only and GNSS+LEO configurations for all the tested days. The results show a significant improvement in convergence time, reaching up to an 80% reduction on the day with the worst performance GNSS-only (DOY = 308). Figures 3, 4, 5 show the 2D error trend over time, focusing on the first hour for better visualization of the convergence process, as the solution remains stable once convergence is achieved. It is clearly visible that with the introduction of LEO, the increased number of satellites in LOS helps both to reduce the convergence time and to stabilize the solution more quickly over time. Tables 2 and 3 report the statistical analysis of the time series of the East, North, and Up errors once convergence is reached. It is evident that the solution is stable and optimal in both GNSS-only and GNSS+LEO configurations, with average errors at the centimeter level for both the components. However, the introduction of LEO helps reduce the standard deviation, bringing it to the millimeter level for the horizontal components. In conclusion, the introduction of LEO can significantly improve the convergence time of the PPP solution, making it more eficient and reliable. The analysis demonstrates that the increased number of satellites in line-of-sight (LOS) provided by LEO enhances both the speed of convergence and the overall stability of the solution. In addition, even if with the application of a 40-degree cutof the number of LEO satellites is very reduced and can reach zero for some epochs, LEO satellites still contribute significantly to reduce the convergence times. This is also due to their faster geometry and the fact that, traveling at nearly twice the speed of GNSS satellites, periods of signal outage are limited. Additionally, the statistical evaluation of positioning errors highlights a reduction in standard deviation, particularly for the horizontal components, reaching the millimeter level. These findings suggest that integrating LEO into GNSS can be a valuable enhancement for precise positioning applications, especially in challenging environments where rapid convergence and high accuracy are crucial. The next steps of this work include conducting a measurement campaign using a GNSS receiver in an urban environment to collect real data in both static and kinematic conditions. This will enable testing of real scenarios with the developed software using field-collected measurements. These steps will provide further validation of the proposed approach and assess its performance in more challenging and dynamic conditions.
In this work, we developed a dedicated software for simulating LEO observations and processing GNSS+LEO measurements. The results demonstrate significant improvements in the convergence of the PPP solution, highlighting the advantages of integrating LEO satellites. The increased number of satellites in line-of-sight and their rapid motion contribute to a faster and more stable solution in harsh environments, simulated by applying 40-degree cutof on satellites’ elevation. Moreover, the statistical analysis confirms a reduction in positioning errors, particularly in the horizontal components. Future work will focus on testing the proposed approach in kinematic conditions and extending the simulation framework to include LEO phase observations. Additionally, a measurement campaign in an urban environment will be conducted to validate the methodology with real field data, further assessing the performance in dynamic and challenging scenarios.
International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2024), Baltimore, MD, USA, 2024, pp. 2308–2322. [24] M. I. Ribeiro, Kalman and Extended Kalman Filters: Concept, Derivation and Properties, Technical Report, Institute for Systems and Robotics, 2004.