Orbit Determination Under Uncertainty - Differential Algebra Applications for Apophis Precovery

Abstract

Rapid and reliable determination of Near-Earth Object (NEO) orbits is essential for Planetary Defence planning. Precovery, the association of new discoveries with archived observations, can immediately extend an observation arc and reduce impact-risk uncertainty. However NEO observations are typically short arcs, where measurement uncertainty dominates and a large set of possible orbits are defined. Traditionally, orbit uncertainty is captured by a sample-based Monte Carlo approach. This forces computationally intensive, and often slow, uncertainty propagation. Ultimately, this delays precovery and subsequent Planetary Defence planning. This thesis investigates the feasibility of the established Differential Algebra (DA), and Automatic Domain Splitting (ADS), algorithms to accelerate the precovery pipeline. DA utilises high order Taylor expansions to efficiently map the uncertainty domain to the orbit solution. While ADS adaptively partitions the uncertainty domain so a lower order Taylor expansions remain valid within each sub-domain. Combined, these techniques have been thoroughly investigated within spacecraft Orbit Determination (DAIOD+ADS) and propagation. However, these developments are absent within the NEO precovery pipeline. The DA and ADS initial orbit determination (DAIOD+ADS) and propagation algorithms were implemented on (99942) Apophis Ephemeris data to simulate short-arc discovery observations which spanned from one hour to one day. The pipeline’s sky-patch coverage, number of false candidates, and computational performance were benchmarked against classical Monte Carlo approaches. Results show that DA+ADS based Initial Orbit Determination reduce the computational cost of precovery by orders of magnitude. Furthermore, DA+ADS achieves smaller initial sky-patch coverage therefore a reduction of false candidates. However, the accuracy of the solution deteriorates in DA propagation if expansion orders based on wider literature were used. Moreover, the study highlights the failure of the DAIOD+ADS algorithm to outperform traditional approaches for arcs less than 4 hours, this was attributed to the Gauss defined initial solution which the DAIOD+ADS algorithm relies on. Applied to Apophis, the integrated DA+ADS pipeline recovered historical detections up to 3 months prior to the discovery observation. It is faster than traditional methods, reducing the time to obtain a constrained impact corridor. These findings highlight the potential of DA-enabled precovery to deliver earlier impact-risk assessments. It’s suggested an investigation of expansion order, ADS split tolerance and the computational consequence would enable an operations-ready precovery pipeline that would outperform traditional sample based techniques.