Importance of adding perturbations in the optimized boundary value initial orbit determination using shooting method

Mann, H. K.; Vananti, A.; Schildknecht, T. (2021). Importance of adding perturbations in the optimized boundary value initial orbit determination using shooting method. In: 8th European Conference on Space Debris. Darmstadt, Deutschland. 20. April 2021 - 23. April 2021.

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Space debris is becoming a major threat for functionalspacecraft. Since, out of thousands of tracked objects inthe Earth’s orbits, only a small percentage correspondsto the operational satellites. It is clear that this problemneeds to be addressed immediately. The first step towardssolving it requires the monitoring of the space environ-ment and cataloguing the debris. This work focuses onthe high-altitude orbits (near GEO regime) which is doneusing optical surveys. The latter result in angles-only ob-servations of objects on very short arcs when compared tothe periods of these orbits. These observations are sparseand cover a very small part of the orbit, hence the initialorbit determination becomes challenging. Two observa-tion series are associated together to find out if they be-long to the same object and an initial orbit is computed.One way to do it is by using the Optimized BoundaryValue Initial Orbit Determination (OBVIOD). This al-gorithm does not include perturbations. To include thelatter we use a so-called shooting method. The shoot-ing scheme is a boundary-value approach, which workslike an initial-value method. It takes a hypothesis at theinitial boundary and propagates it to the second bound-ary, where the computed value and the original bound-ary value are compared. The hypothesis, which givesthe desired output at the second boundary, is accepted asthe solution. In the proposed algorithm, the propagationfrom the initial boundary to the final one involves pertur-bations such as solar radiation pressure, Earth’s geopo-tential terms, solar and lunar gravitational forces. Aroot finding method based on bisection is used inside theshooting method. An admissible region originating fromthe semi-major axis is used in order to reduce the numberof scenarios to be computed. In the original version ofthe OBVIOD, the initial orbit determination takes placeby solving the Lambert’s problem. This version doesnot work well for the high area-to-mass (AMR) objects,especially over multiple revolutions. In this paper, OB-VIOD’s performance is compared with the new shootingOBVIOD for different AMR values and varied numberof revolutions between the boundaries. This comparisonhelps to identify the cases where it becomes important tomake use of the proposed algorithm.

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