Precise orbit determination of low-Earth satellites: a comparison of batch and real-time filtering techniques

Precise Orbit Determination (POD) has become more and more relevant over the past decades due to the ever increasing requirements artificial satellites must satisfy. This is true for both commercial and scientific missions that find applications in a wide variety of fields such as navigation, communication and Earth observation. In most cases, the correct acquisition and interpretation of data would not be possible without extremely accurate knowledge of the satellite's orbit. This is particularly true in the field of space geodesy, where centimeter-level accuracy is required to measure delicate geophysical parameters. In this regard, the objective of this thesis is to analyze and compare the main techniques used in statistical orbit estimation. Unlike Initial Orbit Determination (IOD), we add the realistic assumption that the model used for dynamic propagation is inevitably erroneous, as are the measurements used to track the satellite. These estimation techniques must therefore demonstrate their ability to filter these data in order to derive an optimal estimate of the satellite's state, along with other geometric and dynamic parameters. The comparison is made by distinguishing real-time filtering techniques (Kalman filters) from offline processes that are executed "a posteriori" after the measurements have been collected. In this second case, we are referring to the least squares batch estimators or differential corrections algorithms. Finally, the effects of smoothing techniques are studied as a post-processing solution that allows for the improvement of the estimate previously made with a real-time filter. Furthermore, for the good performance of an orbital estimator, a critical aspect is the correct and complete modeling of the accelerations acting on a satellite in orbit. This is particularly true for offline estimators like the batch, given that since they collect measurements over fairly long time arcs, they are sensitive even to the smallest perturbations. In this regard, within the context of the numerical modeling of forces, a significant part of the work involves analyzing the development and implementation of a routine that allows for the calculation of the perturbation resulting from Earth Radiation Pressure (ERP), considering the contribution of both visible (albedo) and Infrared (IR) components. The entire work is conducted within the context of the Navigation and Space Geodesy group at the University of Padova, led by Professor Stefano Casotto. Here, the use of numerous previously available Fortran libraries, along with independently developed routines and programs, yields results that clearly confirm the validity of the implemented estimation techniques. Generally, sub-decimeter level accuracies are achieved on synthetic data obtained from an estimated orbit of Sentinel-3A, provided by the European Space Agency (ESA). A careful analysis of the results shows that real-time filtering techniques tend to yield better results compared to batch estimation, for which it is necessary to deepen and expand the currently available force model. Furthermore, even though the data are satisfactory, the understanding is that only a test on real measurements can definitively determine the performance of the developed software. Nonetheless, this work has allowed for a deep dive into the issue of precise orbit determination, motivating further efforts aimed at improving the current project.