Global Navigation Satellite Systems (GNSS) have become crucial for providing Positioning, Navigation, and Timing (PNT) services worldwide. Existing GNSS constellations such as GPS, GLONASS, BeiDou, and Galileo operate in Medium Earth Orbit (MEO) at around 20,000 km altitude. Low Earth Orbit Positioning, Navigation, and Timing (LEO-PNT) is an emerging satellite navigation concept to augment current GNSS by placing satellites closer to Earth, at around 600-1200 km altitude. This lower altitude results in a faster change in satellite geometry, which is primarily expected to reduce the convergence time of Precise Point Positioning (PPP). To fully realize this opportunity, accurate knowledge of the LEO-PNT satellite orbital positions and clock offsets at a low latency is required. For existing GNSS constellations, global networks of ground stations are generally used to determine the GNSS satellite positions and clock offsets. This information is then uplinked to the GNSS satellites for dissemination to users. Due to the closer proximity to Earth, LEO-PNT systems would require an extensive ground network to replicate the ground estimation approach of GNSS. However, being situated below MEO, there is an opportunity to leverage GNSS to perform real-time Precise Orbit Determination (POD) on board the LEO-PNT satellites. This thesis aims to quantify the impact on ground user positioning that the LEO-PNT satellites could have when using on-board POD. ... Read more

Over the past decade, there have been significant advancements in both the availability and diversity of satellite navigation systems, on both regional and global scales. The growing significance of GNSS across various fields has led not only to the modernisation of existing systems like the GPS and GLONASS, but also to the creation of new ones such as Galileo. The Navigation Support Office (NSO) operates as a vital component within the European Space Agency, specialising in the precise utilisation of navigation satellite systems. In 2024, NSO underwent a revision of its GNSS processing system, which resulted in a state-of-the-art GNSS processing framework known as CHAMP, Consolidated High Accuracy Multi-GNSS Processing, which is based on constellation-wise data processing and normal equation stacking to efficiently generate GNSS products for all major navigation constellations. This new approach enables internal comparisons between individual constellation solutions and the consolidated multi-GNSS solution, revealing unique characteristics of each constellation and demonstrating the enhanced impact of combining them in critical ways.

This thesis explores and addresses key inconsistencies in the processing of multi-GNSS solutions within the Navigation Support Office, with a particular focus on producing accurate single-constellation solutions that can be reliably combined into a coherent multi-constellation framework. To tackle these inconsistencies, a comprehensive Python-based programme has been developed as an extension of the CHAMP framework, enabling a more efficient and structured approach for analysing large-scale GNSS data. As a result, this new tool provides the basis needed to identify anomalies, track trends, and address inconsistencies across various constellations during the combination process, as a post-processing analysis or within the operational pipeline. The core of this research involves a detailed examination of the parameters estimated in the NSO GNSS precise orbit determination, both in terms of individual and combined multi-GNSS solutions, including Earth orientation parameters, satellite state vectors, ground station positions, clock biases, and empirical accelerations, among others.

The investigation lead to significant inconsistencies in the Length of Day estimates of the individual GPS constellation, affecting the accuracy of the combined multi-GNSS solution. These issues are compounded by the combination of the large weight given to the GPS constellation in the combination due to its low variability, and the GPS non-gravitational a priori models, specially regarding forces like solar radiation pressure, which have been demonstrated to be not as refined as those for other constellations. Additionally, the tuning of empirical accelerations has shown that there is room for improvement to better reflect satellite dynamics.

In conclusion, several key enhancements were identified and proposed to improve the overall performance and reliability of the combined multi-GNSS solution, and subsequently improve the quality of the NSO GNSS products. These mainly comprise the comparison of different non-gravitational a priori models combined with the fine-tuning of empirical accelerations, allowing for a more robust integration of single-constellation solutions into a cohesive multi-constellation framework. Ultimately, recommendations on the way forward are given to create new models based on the results shown on this thesis ... Read more

The Event Horizon Telescope (EHT) is a global array of telescopes that employs Very Long Baseline Interferometry (VLBI) techniques to image the event horizon of black holes. To overcome the limitations of ground-based telescopes, this thesis explores the mission concept involving a two-satellite constellation of space-borne telescopes deployed in Medium Earth Orbit (MEO). The attainment of high-resolution black hole images requires extremely precise baseline determination at the few millimetre level. To address this challenge, each satellite within the constellation is equipped with two hemispherical Global Navigation Satellite System (GNSS) receivers and an optical Intersatellite Link (ISL) for relative navigation. This study aims to assess the feasibility of achieving highly accurate relative positioning within the constellation, particularly considering the large intersatellite distances involved.

The methodology employed in this simulation study encompasses several steps. Initially, the satellite orbits are estimated independently for each satellite using GNSS observations. Following this, the orbit of one of the satellites is held fixed as a reference, while the orbit of the other satellite is re-estimated by incorporating the ISL observations. To enhance the accuracy of the orbit estimation, integer GNSS ambiguity resolution is implemented in the precise orbit determination process. The simulated data incorporates an extensive set of realistic error sources, including thermal noise, instrumental delays, clock biases, errors in the GNSS ephemerides and clocks, uncertainties in the geopotential and solar radiation pressure models, and white noise in the ISL observations.

The results highlight the importance of integer ambiguity resolution in meeting the stringent relative navigation requirements of the mission. The analysis also reveals that the ISL observations primarily improve the baseline estimation along the direction of the link itself. However, in the direction of the black hole, the impact of ISL observations is minimal, indicating that the ISL does not significantly contribute to meeting the specific relative navigation requirements. Furthermore, the study identifies that large intersatellite distances lead to degraded relative orbit accuracy due to fewer shared errors between the two satellites. As a consequence, the objective of achieving a 3.5 mm (3-sigma) one-dimensional relative position accuracy along the black hole direction is not met, with the obtained results showing a 3-sigma of 8.29 mm. To tackle this, it is recommended to focus on mitigating the most prominent error sources, namely uncertainties in the dynamical model and errors in the GNSS orbits and clocks. Other alternatives, such as a network processing scheme, could also be investigated in the future to overcome this challenge. ... Read more

Traditional Global Navigation Satellite Systems (GNSS) are subject to intentional or unintentional disturbances in the northern regions of Norway, leading to loss of critical infrastructure. The novel VHF Data Exchange System (VDES) has been suggested as an alternative positioning, navigation and timing (PNT) system for a possible GNSS contingency service, based on signal simulations and statistical estimates. However, an empirical investigation into the feasibility of such a GNSS contingency service remains to be done, and has only recently become possible after the launch of the NorSat-TD satellite with purpose-designed VDES ranging capabilities. This paper presents an analysis of the characteristics of empirical VDE-SAT range measurements and a system-level performance analysis of a GNSS-contingency system based on the signal performance of empirical ranging data gathered from NorSat-TD. Using the equated error level of the signal, the positioning performance of simulated autonomous systems of VDE-SAT PNT-sources is analysed, followed by an assessment of the combination of the empirical VDE-SAT range measurements and traditional GNSS measurements in a critical GNSS contingency scenario. In total, 236 VDE-SAT pseudorange observations obtained from eleven satellite passes recorded in July 2023 were used. Residual analysis shows that these observations have a large and constant mean error of about 416 km, with a standard deviation of 260.8 m. The previously neglected atmospheric propagation effects on a VDE-SAT range measurement is shown to be significant, and the largest effect is likely to be the time-delay due to the ionosphere. The system performance analysis shows that VDE-SAT as a PNT-source could be used as a possible future general navigation backup system, with a positioning accuracy within 1000 m. Finally, an important conclusion is that a contemporary GNSS-contingency system is possible with the measured signal performance, where NorSat-TD acting as a PNT-source can, under the correct geometric conditions, allow a positioning accuracy within 1000 m in combination with partial GNSS coverage at the user. ... Read more

The first close-up image of a black hole has been taken recently by means of a network of high-resolution telescopes situated all around the globe, also known as Event Horizon Telescope (EHT). In that regard, this Master Thesis reviews the feasibility of establishing accurate inter-satellite baselines in a two-satellite constellation of satellites placed in co-planar Medium Earth Orbits (MEO) equipped with telescopes to, amongst other applications, allow performing Very Long Baseline Interferometry (VLBI) on celestial bodies such as the supermassive black hole in the centre of our galaxy.

Regarding the workflow of this study, first a thorough analysis of the visibility conditions from the GPS and Galileo constellations has been performed for the pair of MEO-placed satellites. The results have shown that the receiver antennas need to adapt a nadir orientation to maximize the number of visibility contacts from mentioned GNSS constellations. Second, an assessment on the impact of different error sources in the absolute orbit accuracy has been conducted for the pair of satellites. The sensitivity analysis comprises errors that derive from realistic uncertainties in the geopotential model, GNSS orbits and clocks, satellites’ solar radiation pressure model, centre of mass and antenna reference point. The results have shown that the error sources that most affect the accuracy of the absolute orbit solution are disturbance aligned with the velocity component in both centre of mass of the satellites and reference point of the receiver antennas.

Furthermore, to achieve the high standards of relative navigation, optical ISL observations with micro-meter precision level were employed. This precision level was determined by the limits of the employed software tool, as the state-of-the-art precision of these measurements is at the nano-metre level. Due to the 1D nature of the ISL observation, it has been found that they cannot be processed alone and require the GNSS code and phase observations to be processed along with them. In these processes, the system architecture of the inter-satellite ranging system has been assumed to be two-way to rule out the errors that derive from the non-synchronization of the satellites’ clocks. The relative POD results have shown that the shorter the distance between the satellites, the higher the precision of the relative orbit solution in radial and along-track components, ultimately being limited by the precision of the ISL observations. The fact that the satellites are placed in co-planar orbits makes the cross-track component not be visible and probably yield conditioning problems to the LSQ matrix. Therefore, the impact of angular separations ranging from 1 to 10 degrees on the relative POD accuracy is also investigated. The most promising results come from the case in which the relative distance between the MEO-placed satellites is low (1,000km) and an angular separation in the orbital planes of 10 degrees has been induced. In that case, the relative orbit solution is improved in all components (radial, along-track and cross-track) and placed in the few millimetre level.
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In recent years, with the increasing number of man made objects in space the need for accurate satellite orbit prediction has increased tremendously. Prediction of satellite trajectories is important to plan collision avoidance manoeuvres between space assets and debris, to autonomously maintain formation flying missions and to plan manoeuvres for ground-track maintenance of Earth-observation missions. For satellites in very low LEO, aerodynamic drag is the largest and the most difficult force to model because of the changing nature of atmospheric density. This report describes the efforts made towards improving the orbit prediction of SAOCOM-CS with a focus on drag force modelling. This is accomplished by orbit determination using GPS state vector measurements and precise deterministic force models, during periods of high and low solar activity. Drag scale factors are estimated with different resolutions. Different methods are used to choose the estimated drag scale factors for orbit prediction. GRACE-A and PROBA-V satellites are used as test cases. For a prediction arc length of one day, the best prediction strategy results in maximum position errors (3D) of 243.5 m and 24.1 m for GRACE-A \& PROBA-V, respectively during high solar activity. Based on the prediction results of GRACE-A \& PROBA-V, a rule of thumb analysis is used to derive the maximum position error in the orbit prediction of SAOCOM-CS, which lies between 40 and 75 m. Changes in the mean estimated drag scale factors of the satellites are observed between high and low solar activity which might indicate deficiencies in the NRLMSISE-00 density model. The report also provides the effect of the space weather forecast errors on the best prediction strategy. Introducing a 10 \% error in the solar activity index resulted in mean maximum along-track prediction errors of 393 m and 16 m for GRACE-A \& PROBA-V, respectively during high solar activity. Similarly, including random errors in the geomagnetic activity index resulted in mean maximum along-track prediction errors of 443 m and 15 m for GRACE-A \& PROBA-V, respectively during high solar activity. Finally, the optimization of the estimation and prediction methods for the computational efficiency of PROBA-V is presented. A six hour estimation arc length with the force model comprising Earth gravity field of degree and order 30 of the model ITU\_GRACE 16 with luni-solar perturbations and devoid of atmospheric drag, solar radiation pressure and tidal forces is the most computationally efficient combination for a prediction arc length of one day. ... Read more

The Low Earth Orbit (LEO) region has been attractive to many space agencies and organisations because of its ease of access and the ideal opportunity for remote sensing. Due to the low altitudes, a satellite's orbital state is highly affected by the atmospheric drag force acting on the satellite's body. The largest variation in this drag force is caused by the changes in thermospheric density due to the complex interactions of the Sun with the Earth's thermosphere. In order to properly forecast the orbital state of a LEO satellite, the thermospheric densities need to be predicted as accurately as possible. The thermospheric density values can be estimated by using for example empirical atmospheric density models, such as the DTM2013 (Drag Temperature Model). During this thesis study it has been investigated whether the highly researched field of machine learning models could be used to develop a predictor for the along-track density values for the Swarm satellite constellation. This constellation has an abundant amount of trajectory-based time series of thermospheric density values from Precise Orbit Determination (POD) data. This research has focused on the development of Multi-layer Perceptron (MLP) models which are a type of Feed-Forward Neural Network. These MLP models have been trained and tested on past acceleration and solar activity data sets provided by the Swarm satellite mission and space weather observatories, respectively. The performance of these MLP models was then compared to two baseline models, namely a Calibrated Persistence Model (CPM) and the density values modelled by DTM2013. The results in this research led to the conclusion that a three-layer MLP model performed best when it was trained on data of the same spacecraft like the one it was supposed to perform along-track density forecasts for. The forecasting accuracy increased the most when the model was trained on long periods of training data characterised by high solar and low geomagnetic activity. When trained on these data sets, the MLP model has shown to outperform the baseline models when making predictions up until two days into the future during periods of high solar activity. The DTM2013 seems the best option to forecast density values during low solar activity. As an alternative to the DTM2013, the CPM seems a suitable model when one needs to quickly implement a forecasting model with decent performance irrespective from the presence of geomagnetic storms. ... Read more