<p dir="ltr">On-orbit breakup events threaten the sustainability of space operations -- many of which humans rely on for everyday subsistence on Earth -- and hinder our ability to expand human presence deeper into space. The continuous influx of objects into orbit without sufficient mechanisms for debris removal contributes to an imbalance of sources and sinks within the volume of interest of space, intensifying orbital hazards in valuable orbits. Near-Earth fragmentation analysis methods have been developed over the course of decades, yet over 23% of all breakups over the past 10 years have, to date, unknown causes. For many additional cases, breakup causes are only partially understood. Furthermore, observation data used to decipher the causes of any fragmentation event inherently contain uncertainty, stemming from, for example, orbit determination and measurement errors. This research aims to address the role of uncertainty in near-Earth fragmentation analysis through a hybrid application of the unscented transformation technique to the forensic investigation of three unclassified Atlas V Centaur upper stage breakup events in 2018 and 2019. </p><p dir="ltr">While advancements in near-Earth space situational awareness protocol are still ongoing, the aerospace community has now set its sights farther afield, in an entirely different and more complex regime: cislunar space. With heightened international interest in support of a long-lasting presence in the vicinity of the Moon, cislunar space debris has already begun to follow. How a single fragmentation plays out is highly sensitive to slight changes in initial condition in the chaotic cislunar domain. This drives the need for appropriate debris characterization tools and a detailed dynamical understanding of the region. In response to the challenges presented, this investigation evaluates the nature of cislunar debris evolution under various initial conditions through exploitation of fundamental dynamical behaviour and structures in the neighbourhood of prominent cislunar orbits. The work finds that there is large sensitivity of resulting fragment motion to the orbit and location of origination, but there are some general features and trends that can aid in providing insights to owner-operators and the development of debris mitigation guidelines.</p>

<p><br></p><p dir="ltr">Achieving high optical resolution imaging is one of the most important goals in the history of optics. However, due to finite aperture sizes, a diffraction limit is imposed on optical imaging. Therefore, the Rayleigh limit, which describes the minimum separation at which two point sources are resolvable, has served as a critical limit in optical resolution. Many methods have been studied to break the limit and succeed in resolving nearby sources below the Rayleigh criterion but only beyond a certain distance. Furthermore, it has been demonstrated that quantum-inspired optics techniques maintain consistent variance in estimating the separation of point sources even at low separations, but only with prior information like a known number of sources and equal brightness. Therefore, achieving the ultimate optical resolution remains an open question. This thesis will conclusively address this challenge considering real-world scenarios, i.e., no prior information or controlled lab environment as well as low signal-to-noise ratio (SNR), turbulence, and other practical challenges.</p><p><br></p><p dir="ltr">In information theory, the estimation variance of a random parameter can be quantified using the inverse of Fisher information. By maximizing the Fisher information, one can minimize the variance in estimation. In my thesis, we have shown that the measurement can be accelerated without sacrificing optical resolution using the adaptive mode so that quantum Fisher information per detected photon is maximized. The notable attribute that sets it apart from other quantum-inspired methods is that it does not require any prior information, making it more feasible for practical application. We have further shown that the space domain awareness (SDA) challenge can be effectively handled with the aforementioned approach with a very limited photon budget and even in the presence of turbulence. Toward solving the challenges, we designed a photon statistics-based direct imaging method that can also serve as a baseline method for quantum optics. In my thesis, atmospheric turbulence is also deeply explored and the effect is mitigated using reinforcement learning.</p><p><br></p>