| Abstract: | Safe and sustainable operations in Geocentric Orbit require the acquisition, tracking, and predictive use of a large amount of data pertaining to the existence, characterization, and orbital state of objects in Earth orbit. The acquisition involves initializing the pdf of the objects in a catalog. Tracking involves the recursive update of the multi-target pdf. Conjunction assessment is perhaps the most common use of such a space catalog. This dissertation addresses these three fundamental building blocks of Space Domain Awareness (SDA): initialization, multi target tracking, and conjunction assessment. Towards this, we establish a connection between Reid's Hypothesis Oriented Multi Hypotheses Tracking (HOMHT) and the modern Random Finite Set (RFS)/Finite Set Statistics (FISST) based methods for Multi-Target Tracking. In particular, we examine the different hypotheses, derive the hypotheses update equations under the FISST recursions, and clearly show its relationship to the classical HOMHT hypotheses and hypothesis weight update formula, thereby establishing a connection between the methods. The analytically computed value of the Probability of Collision for long-term engagements between two space objects using traditional schemes, which only consider some time span around the time of closest approach, can sometimes be incorrect by orders of magnitude. Sampling-based methods are presented as a robust alternative to analytical schemes. To decrease the computational burden of simulating a large number of particles, a novel subset simulation-based MCMC scheme is introduced to compute in-orbit space-object collision probability. The collision probability is expressed as a product of larger conditional failure probabilities by introducing intermediate failure events. Well-chosen large (relative to collision probability) values of nested conditional failure probabilities can be estimated by means of simulating only a limited number of samples. The resulting efficiency and accuracy of the suggested scheme are demonstrated against independent benchmarks that use other techniques for calculating the probability of collision. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/198806 |
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