An Automatic Domain Splitting Initial Orbit Determination Technique for Short-arc Optical Measurements
Creators: name:  A. DE RIZ 
name:   R. CIPOLLONE 
name:   P. DI LIZIA 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: SUSTAINABLE SPACE
LOGISTICS

description: In the last decades, the near-Earth environment has kept growing more and more crowded with a wide variety of resident space objects (RSO), hampering operations, and adding further complexity to future missions design. In this context, RSO catalogue update and maintenance turns out to be fundamental to reach a robust Space Situational Awareness. One of the several crucial activities related to this space operations segment is Initial Orbit Determination (IOD), acting as last resort in case the correlation process fails and a new object has to be included among the catalogued ones. Currently, diverse methods to perform this task compose a richly populated state of the art; nevertheless, there is an increasing drive towards optimization and development of techniques leveraging different aspects of the problem to better suit the amount and kind of data related to sensor observations. In this regard, the present work describes a novel development of the two-body integral-based IOD method, used to extract orbital states from optical tracks, and previously applied to asteroids analysis. Usually, iterative root-finding algorithms are used to obtain the solution and consequently build a first orbit estimate. By exploiting an Automatic Domain Splitting (ADS) technique, based on a squared approximation error splitting rule, and Differential Algebra (DA), the computational burden involved in the procedure can be considerably relieved by assessing a suitable a priori level of approximation. Starting from a couple of optical attributables composed of angles and angular velocity, ranges are retrieved by solving a non-linear system granting that the chosen integrals of motion associated to the problem are kept constant, enforcing the residuals defined across the two available measurements to be null. The DA and ADS blend allows, with low orders of expansion, to progressively discard subdomains and refine only the ones containing solutions while complying to a given error threshold. Multiple solutions are filtered using properly defined compatibility conditions involving orbital parameters to grant that orientation and shape of orbits coming from both obtained ranges are as close as possible, by selecting the solution with the minimum associated parameters difference. As for uncertainty, it is included in the computations as a covariance matrix, expanded to a predefined order thanks to the differential algebra formulation, undergoing non-linear transformations and dynamics propagation throughout the whole pipeline. A polynomial map similar to the one composing the nominal output links uncertainty affecting the sensor at hand to the one associated to the final state, downstream of propagation. This last aspect is fundamental to transfer a reliable uncertainty estimate linked to the measurements to the final orbit. The algorithm has been tested with both simulated and real data from uncorrelated measurements of optical telescopes observing the GEO orbital regime. Both comparison with known IOD outputs and correlation with the originating measurements have been performed to validate the method. A standard version of the two-body integral method has been employed as test bench while, as far as uncertainty propagation is concerned, a Monte Carlo simulation has been used to validate the process. The results have been structured in such a way to detect and easily visualize the orbital bands determined by uncertainty which the uncorrelated target orbit belongs to. The analysis has provided promising results in terms of accuracy and processing time.