In Space Situational Awareness (SSA), it is crucial to assess the uncertainty related to thestate vector of resident space objects (RSO). This uncertainty plays a fundamental role in, forexample, collision risk assessment and re-entry predictions. A realistic characterization of thisuncertainty is, therefore, necessary.The most common representation of orbital uncertainty is through a Gaussian (or normal)distribution. However, in the absence of new observations, the uncertainty grows over timeand the Gaussian representation is no longer valid under nonlinear dynamics like spacemechanics. This study evaluates the time when the uncertainty starts becoming non-Gaussianin nature. Different algorithms for evaluating the normality of a distribution were implemented andMonte Carlo tests were performed on them to assess their performance. Also, the distancesbetween distributions when they are propagated under linear and nonlinear algorithms werecomputed and compared to the results from the Monte Carlo statistics tests in order to predictthe time when the Gaussianity of the distribution breaks. Uncertainty propagation using StateTransition Tensors and Unscented Transform methods were also studied. Among theimplemented algorithms for evaluating the normality of a distribution, it was found thatRoyston’s method gives the best performance. It was also found that if the Normalized L 2distance between the linear and non-linear propagated distributions is greater than 95%, thenuncertainty starts to become non-Gaussian. In the best case scenario of unperturbed two-bodymotion, it is observed that the Gaussianity is preserved for at least three orbital periods in thecase of Low-Earth and Geostationary orbits when initial uncertainty corresponds to the meanprecision of the space debris catalog. If the initial variances are reduced, then Gaussianity ispreserved for a longer period of time. Time for which Gaussian assumption is valid on orbitaluncertainty is also dependent on the initial mean anomaly. Effect of coordinatestransformation on Gaussianity validity time is also analyzed by considering uncertainty inCartesian, Keplerian and Poincaré coordinate systems. This study can therefore be used to improve space debris cataloguing.

<div> Space operations from the dawn of the Space Age have resulted in a large, and growing, resident space object population. However, the availability of sensor resources is limited, which presents a challenge to Space Situational Awareness applications. When direct communication with an object is not possible, whether that is due to a lack of access for active satellites or due to the object being characterized as debris, the only independent information source for learning about the resident space object population comes from measurements. Optical measurements are often a cost-effective method for obtaining information about resident space objects.<br></div><div> This work uses observability analysis to investigate the relationship between desired resident space object characteristics and the information resulting from ground-based optical measurements. Observability is a concept developed in modern control theory for evaluating whether the information contained within measurements is sufficient to describe the dynamical progression of a system over time. In this work, observability is applied to Space Situational Awareness applications to determine what object characteristic information can be recovered from ground-based optical measurements and under which conditions these determinations are possible. In addition, the constraints and limitations of applying observability to Space Situational Awareness applications are assessed and quantified.<br></div>

In this project, an algorithm has been proposed to detect a satellite’s maneuver by comparingthe orbital elements observed from the two line element data and the orbital elements propagatedwith the help of Simplified perturbations models. A set of TLE data for an object orbiting Earthcontains a specific set of orbital elements. Simplified perturbation are utilized to propagate theorbital velocity and position vector of the same object. By comparing the results obtained fromboth the methods, the maneuvers of a satellite are detected. This project outlines the workingmethodology and the implementation of the algorithm developed to detect the maneuvers. Thefunctioning of the technique is assessed with reference to two case studies for which the maneuverhistory is available by following the approach employed by Kelecy et al. (2007). The same methodis implemented to detect the orbit controlling maneuvers as well as the fine control maneuvers. Theresults derived from the analysis indicate that the maneuvers which has the magnitude of even aslow as cm/s has been detected when the detection parameters are calibrated properly.

This research introduces a satellite characterization method based on its light curve by utilizing and adapting the methodology of compressed sensing. Compressed sensing is a mathematical theory, which is established in signal compression and which has recently been applied to an image reconstruction by single-pixel camera observation. In this thesis, compressed sensing in the use of single-pixel camera observations is compared with a satellite characterization via non-resolved light curves. The assumptions, limitations, and significant differences in utilizing compressed sensing for satellite characterization are discussed in detail. Assuming a reference observation can be used to estimate the so-called sensing matrix, compressed sensing enables to approximately reconstruct resolved satellite images revealing details about the specific satellite that has been observed based solely on non-resolved light curves. This has been shown explicitly in simulations. This result implies the great potential of compressed sensing in characterizing space objects that are so far away that traditional resolved imaging is not possible.

The resident space object population in the near-Earth vicinity has steadily increased since the dawn of the space age. This population is expected to increase drastically in the near future as the realization of proposed mega-constellations is already underway. The resultant congestion in near-Earth space necessitates the availability of more complete and more accurate satellite tracking information to ensure the continued sustainable use of this environment. This work sets out to create an operational system for the delivery of accurate satellite tracking information by means of optical observation. The state estimates resulting from observation series conducted on a GPS satellite and a geostationary satellite are presented and compared to existing catalog information. The satellite state estimate produced by the system is shown to outperform existing two-line element results. Additionally, the statistical information provided by the processing pipeline is evaluated and found to be representative of the best information available for the satellites true state.

Satellites commonly use onboard digital cameras, called star trackers. A star tracker determines the satellite's attitude, i.e. its orientation in space, by comparing star positions with databases of star patterns. In this thesis, I investigate the possibility of extending the functionality of star trackers to also detect the presence of resident space objects (RSO) orbiting the earth. RSO consist of both active satellites and orbital debris, such as inactive satellites, spent rocket stages and particles of different sizes. I implement and compare nine detection algorithms based on image analysis. The input is two hundred synthetic images, consisting of a portion of the night sky with added random Gaussian and banding noise. RSO, visible as faint lines in random positions, are added to half of the images. The algorithms are evaluated with respect to sensitivity (the true positive rate) and specificity (the true negative rate). Also, a difficulty metric encompassing execution times and computational complexity is used. The Laplacian of Gaussian algorithm outperforms the rest, with a sensitivity of 0.99, a specificity of 1 and a low difficulty. It is further tested to determine how its performance changes when varying parameters such as line length and noise strength. For high sensitivity, there is a lower limit in how faint the line can appear. Finally, I show that it is possible to use the extracted information to roughly estimate the orbit of the RSO. This can be accomplished using the Gaussian angles-only method. Three angular measurements of the RSO positions are needed, in addition to the times and the positions of the observer satellite. A computer architecture capable of image processing is needed for an onboard implementation of the method.

<p>Ballistic and chemical trajectory options to Uranus are investigated for launch dates spanning 50 years. Trajectory solutions are found using STOUR, a patched conic propagator with an analytical ephemeris model. STOUR is heritage software developed by JPL and Purdue, written in FORTRAN. A total of 89 distinct gravity-assist paths to Uranus are considered, most of which will allow for a deep space maneuver (DSM) at some point along the path. For each launch year, the most desirable trajectory is identified and cataloged based on time of flight (up to 15 years), total $\Delta$V cost (DSM and capture maneuver), arrival $V_\infty$, and delivered payload. The Falcon Heavy (Recoverable), Vulcan VC6, Falcon Heavy (Expendable) and SLS Block 1B are considered to provide a range of low- to high-performance launch vehicle capabilities. A rough approximation of Starship's performance capabilities is also computed and applied to select years of launch dates. A flagship mission that delivers both a probe and an orbiter at Uranus is considered, which is approximated as a trajectory capable of delivering 2000 kg. Jupiter is unavailable as a gravity-assist body until the end of the 2020s but alternative gravity-assist paths exist, providing feasible trajectories even in years when Jupiter is not available. A rare Saturn-Uranus alignment in the late 2020's is identified which provides some such trajectory opportunities. A probe-and-orbiter mission to Uranus is feasible for a Vulcan VC6 with approximately 13 year flight times and for a Recoverable Falcon Heavy with approximately 14.5 year flight times. An Expendable Falcon Heavy reduces the time of flight to around 12.5 years and opens up `0E0U' as a gravity-assist path, while the SLS Block 1B typically offers trajectories with 10 to 11 year flight times and opens up more direct `JU' and `U' solutions. With the SLS, flight times as low as 7.5 years are possible.</p> <p>  </p> <p>A new, rapid grid search tool called GREMLINS is also outlined. This new software is capable of solving the same problems as STOUR, but improves on it in three crucial ways: an improved user-experience, more maneuver capabilities, and a more easily maintained and modified code base. GREMLINS takes a different approach to the broad search problem, forgoing $C_3$ matching in favor of using maneuvers to patch together tables of pre-computed Lambert arcs. This approach allows for vectorized computations across data frames of Lambert solutions, which can be computed much more efficiently than the for-loop style approach of past tools. Through the use of SQL tables and a two-step trajectory solving approach, this tool is able to run very quickly while still being able to handle any amount of data required for a broad search. Every line of code in GREMLINS is written in Python in an effort to make it more approachable and easier to develop for a wide community of users, as GREMLINS will be the only only grid search tool available as free and open source software. Multiple example missions and trajectory searches are explored to verify the output from GREMLINS and to compare its performance against STOUR. Despite using a slower coding language, GREMLINS is capable of performing the same trajectory searches in approximately 1/5 the runtime of STOUR, a FORTRAN-coded tool, thanks to its vectorized computations.</p>

<p dir="ltr">This research considers orbit maintenance strategies for multi-body orbits in the context of the Earth-Moon Circular Restricted Three Body Problem (CR3BP). Dynamical requirements for successful long-term orbit maintenance strategies are highlighted.</p>

As resident space object populations grow, and satellite propulsion capabilities improve, it will become increasingly challenging for space-reliant nations to maintain space situational awareness using current human-in-the-loop methods. This dissertation develops several real-time adaptive approaches to autonomous sensor network management for tracking multiple maneuvering and non-maneuvering satellites with a diversely populated Space Object Surveillance and Identification network. The proposed methods integrate suboptimal Partially Observed Markov Decision Processes (POMDPs) with covariance inflation or multiple model adaptive estimation techniques to task sensors and maintain viable orbit estimates for all targets. The POMDPs developed in this dissertation use information-based and system-based metrics to determine the rewards and costs associated with tasking a specific sensor to track a particular satellite. Like in real-world situations, the population of target satellites vastly outnumbers the available set of sensors. Robust and adaptable tasking algorithms are needed in this scenario to determine how and when sensors should be tasked. The strategies developed in this dissertation successfully track 207 non-maneuvering and maneuvering spacecraft using only 24 ground and space-based sensors. The results show that multiple model adaptive estimation coupled with a multi-metric, suboptimal POMDP can effectively and efficiently task a diverse network of sensors to track multiple maneuvering spacecraft, while simultaneously monitoring a large number of non-maneuvering objects. Overall, this dissertation demonstrates the potential for autonomous and adaptable sensor network command and control for real-world space situational awareness. / Ph. D. / As the number of spacecraft in orbit increase, and satellite propulsion capabilities improve, it will become increasingly difficult for space-reliant nations to keep track of every object orbiting earth using human-in-the-loop methods. Already, the population of target satellites vastly outnumbers the available set of sensors. At any given time, a given network of sensors cannot observe every satellite in orbit, and must manage the available sensors effectively to keep track of every object of interest. The ability to maintain actionable knowledge of every orbiting object of interest is known as space situational awareness. Conventional tracking processes have generally not changed for decades, and were designed when there were far fewer satellites in orbit with little or no ability to maneuver. These methods involve large numbers of operators and engineers who schedule a network of sensors under the assumption that the satellites will not unexpectedly change their orbits for long periods of time. In the near future, traditional space surveillance approaches will become insufficient at maintaining space situational awareness, particularly if more satellites conduct unanticipated maneuvers. This dissertation develops several real-time approaches for controlling a diverse network of ground and space-based sensors that remove the need for human intervention. These fully computer-based command and control processes adapt to dynamic situations and automatically task sensors to rapidly track multiple maneuvering and non-maneuvering satellites. The decision processes used to determine which sensors should be tasked to observe a particular spacecraft compare the amount of information that can be collected in a single observation and the workload a sensor must execute to collect the observation. The command and control strategies developed in this dissertation successfully track 207 non-maneuvering and maneuvering spacecraft using only 24 ground and space-based sensors. The results show that adaptive, fully autonomous sensor network control processes can effectively and efficiently task a diverse set of sensors to track multiple maneuvering spacecraft, while simultaneously monitoring a large number of non-maneuvering objects. Overall, this dissertation demonstrates the potential for adaptive, computer-based sensor network command and control for real-world space situational awareness. This research was supported by the Virginia Tech New Horizons Graduate Scholar Program, the Ted and Karyn Hume Center for National Security and Technology, the DARPA Hallmark program, and the U.S. Joint Warfare Analysis Center.

With the increase in space traffic, proliferation of inexpensive launch opportunities, and interest from many countries in utilizing the space domain, threats to existing space assets are likely to increase dramatically in the coming years. The development of a system that can identify potential threats and alert space operators is vital to maintaining asset resiliency and security. The focus of this thesis is the design and evaluation of such a system. The design is comprised of the development of a classification hierarchy and the selection of machine learning models that will enable the identification of anomalous object behavior. The hierarchy is based on previous examples applied to object classification while reconsidering the assumption that a satellite may perform only one mission. The selected machine learning models perform both supervised classification of actively maneuvering objects and unsupervised identification of anomalous behavior within large satellite constellations. The evaluation process considers the independent adjustment of model hyperparameters to achieve optimal model settings. The optimal models perform both classification functions and return moderate accuracy. The system is applied to several case studies examining edge cases and what factors constitute a threatening object and what factors do not. Suggestions for improvement of the system in the future are presented. / Master of Science / The increase in space traffic, proliferation of inexpensive launch opportunities, and interest from many countries in utilizing the space domain represent existential threats to existing spacecraft and operations in low-Earth orbit. Threats to the safe operation of spacecraft are likely to increase dramatically in the coming years. The development of a system that can identify potential threats and alert space operators is vital to maintaining asset resiliency and security. The focus of this thesis is the design and evaluation of such a system. This is accomplished by identifying a system architecture through evaluating current assumptions of what missions satellites are capable of performing. Following the system-level design, modules are proposed that utilize machine learning to identify satellite behavior that is abnormal. These modules are tested and tuned with optimal parameters to deliver improved identification performance. The system is applied to several case studies examining edge cases and what factors constitute a threatening object and what factors do not. Suggestions for improvement of the system in the future are presented.