This work presents a measurement model designed for multiple observers (space-based and/or ground-based) for cislunar orbit determination and estimation for space domain awareness (SDA). The measurement model is able to rely solely on angles-only measurements by defining the line between the observer and the target object as the intersection of two non-parallel planes. There are two primary applications for the measurement model related to cislunar SDA: (1) It provides a new initial orbit determination (IOD) technique that does not require any knowledge of the dynamical environment, and (2) It is adopted into a sequential estimation scheme to provide continuous orbit tracking. The present measurement model is studied and demonstrated for both Earth orbits and cislunar space applications. While the goal is to operate in cislunar space, evaluating the measurement model in Earth orbits allows for the comparison against established IOD and estimation methods, resulting in a more rigorous analysis of the performance. Within this work, several different aspects of the present measurement model are studied, both analytically and computationally, to understand their effect on the orbit determination and estimation problems. By methodically varying the location of the observers, relative to the target, it is shown that the error produced by the IOD solution to the measurement behaves in a predictable manner. The IOD solution model can then be compared against similar IOD methods for Earth orbit. For orbit estimation, the measurement model is used in a modified extended Kalman filter that incorporates Analytic Continuation, allowing it to propagate the perturbed orbit dynamics to increase estimation accuracy. The measurement model is then incorporated in both an extended Kalman filter and unscented Kalman filter, comparing the resulting accuracy and computational time as the measurement frequency and nonlinearity of the dynamics are varied. For cislunar space, the measurement model is used to perform IOD and tracking of objects in orbits with relevance to future space missions. Finally, the present measurement model is shown to be capable of fusing other measurement methods from heterogeneous sensors to perform accurate orbit estimation. Overall, it is shown that the measurement model produces highly accurate results for IOD and orbit estimation. The results of the IOD solution have the same level of accuracy as other Earth orbit IOD methods and is shown to be able to easily translate to cislunar orbits without any modification, while maintaining that accuracy. For orbit estimation, the measurement model is shown to converge to an accurate estimate quickly and maintain that level of accuracy even in the absence of measurements, which is to be expected due to the vastness of cislunar space. The present approach will have future applications in space-based space surveillance networks for on-orbit cislunar SDA operations.

Geosynchronous Equatorial Orbit (GEO) is critical to Earth communications, weather monitoring, and national defense. Orbit estimation of GEO objects is difficult due to physical constraints placed on ground-based tracking devices such as weather, object range, and tracking frequency restrictions. These constraints are commonly mitigated through the use of two-way signaling devices for cooperative GEO satellites. However, determining the position and velocity of uncooperative GEO satellites and/or objects is more challenging. The objective of this dissertation is to quantify the increased orbital accuracy of objects in the GEO catalog when the Air Force Space Command Space Surveillance Network (AFSPC SSN) is augmented with space-based angles-only measurements from a sensor in a unique near-GEO orbit. Linear covariance theory and analysis provides an efficient method to determine the covariance of the position and velocity of an uncooperative GEO object, while incorporating uncertainties in the dynamics and sensor errors. Once this covariance is determined, an error budget analysis is performed to determine the major sources of uncertainty contributing to position errors of objects in the GEO catalog. As a result, it is shown through linear covariance analysis that incorporating measurements from a space-based sensor in a near-GEO orbit increases the orbital accuracy of GEO objects when compared to the orbital accuracy achieved with AFSPC SSN measurements alone.

This thesis will focus on the performance of angles only initial orbit determi- nation (IOD) methods on observational data of low Earth orbit (LEO) CubeSats. Using data obtained by Lockheed Martin’s Space Object Tracking (SpOT) facil- ity, four methods: Gauss, Double-R, Gooding and Assumed Circular, will use different amounts of orbital arc to determine which methods perform the best in the short arc regime of less than 10 degrees of orbital arc. Once the best method for estimating the orbit is determined, there will be analysis on whether these IOD methods are accurate enough to predict a secondary observation session. Finally non-linear regression will be performed to determine if the error metrics follow a predictable trend based on how much orbital arc is seen by the observer. It was determined that above a certain amount of orbital arc, angles only IOD methods can reliably predict a secondary observation session to facilitate more observations. Below 4 degrees of orbital arc, which is around 60 seconds of ob- serving time for LEO objects, none of the methods were able to reliably predict a secondary observation session. The Assumed Circular method was the best method for observing LEO CubeSats because it forces the IOD solution to be circular, which limits the error in the shape of the orbit as the amount of orbital arc decreases. Finally, many metrics follow an exponential trend when compared to the orbital arc. Thus, the amount of orbital arc seen is a strong predictor for the accuracy of the angles only IOD solutions.

Tradition spacecraft proximity operations require large and expensive on-board sensors and significant ground support. Relative angle measurements can be obtained from small, simple, and inexpensive on-board sensors, but have not traditionally been used for proximity operation because of difficulty generating rang information. In this thesis it is shown that useful relative range data can be generated provided that the spacecraft is experiencing a small continuous thrust such as would be provided by a low-thrust propulsion system.

Angles-only navigation is simple, robust, and well proven in many applications. However, it is sometimes ill-conditioned for orbital rendezvous and proximity operations because, without a direct range measurement, the distance to approaching satellites must be estimated by firing thrusters and observing the change in the target's bearing. Nevertheless, the simplicity of angles-only navigation gives it great appeal. The viability of this technique for relative navigation is examined by building a high-fidelity simulation and evaluating the sensitivity of the system to sensor errors. The relative performances of square-root filtering methods, including Potter, Carlson, and UD factorization filters, are compared to the conventional and Joseph formulations. Filter performance is evaluated during closed-loop "station keeping" operations in simulation.

The proposed thesis of this dissertation has both a practical element and theoretical component which aim to answer key questions related to the use of angles-only navigation for autonomous orbital rendezvous. The first and fundamental principle to this work argues that an angles-only navigation filter can determine the relative position and orientation (pose) between two spacecraft to perform the necessary maneuvers and close proximity operations for autonomous orbital rendezvous. Second, the implementation of angles-only navigation for on-orbit applications is looked upon with skeptical eyes because of its perceived limitation of determining the relative range between two vehicles. This assumed, yet little understood subtlety can be formally characterized with a closed-form analytical observability criteria which specifies the necessary and sufficient conditions for determining the relative position and velocity with only angular measurements. With a mathematical expression of the observability criteria, it can be used to 1) identify the orbital rendezvous trajectories and maneuvers that ensure the relative position and velocity are observable for angles-only navigation, 2) quantify the degree or level of observability and 3) compute optimal maneuvers that maximize observability. In summary, the objective of this dissertation is to provide both a practical and theoretical foundation for the advancement of autonomous orbital rendezvous through the use of angles-only navigation.

Space travelers in science fiction can drop out of hyperspace and make a pinpoint landing on any strange new world without stopping to get their bearings, but real-life space navigation is an art characterized by limited information and complex mathematics that yield no easy answers. This study investigates, for the first time ever, what position and velocity estimation errors can be expected by a starship arriving at a distant star - specifically, a miniature probe like those proposed by the Breakthrough Starshot initiative arriving at Proxima Centauri. Such a probe consists of nothing but a small optical camera and a small microprocessor, and must therefore rely on relatively simple methods to determine its position and velocity, such as observing the angles between its destination and certain guide stars and processing them in an algorithm known as an extended Kalman filter. However, this algorithm is designed for scenarios in which the position and velocity are already known to high accuracy. This study shows that the extended Kalman filter can reliably estimate the position and velocity of the Starshot probe at speeds characteristic of current space probes, but does not attempt to model the filter’s performance at speeds characteristic of Starshot-style proposals. The gravity of the target star is also estimated using the same methods.

The expansion of space activities has led to an increase in congestion. With this increase, there has been a growing emphasis on the importance of space situational awareness. Without it, the space environment can become hazardous, with increasing threats of collision and debris generation. As the utilization of space continues to grow, effective methods for tracking objects to maintain situational awareness must also be considered. One approach to tracking objects in space involves a series of steps, including optical observations and orbit estimations using initial orbit determination methods, followed by additional observations and continuous tracking. However, a challenge with this tracking method is the low quality and quantity of observational data, which can impact the accuracy achieved from these methods. This thesis will study two new and two traditional methods of initial orbit determination, analyzing improvements in accuracy with limited data for each method. Additionally, the impact of observation elevation will be analyzed to assess its effects on the quality of data, and how this, along with a limited amount of data, can affect the overall initial orbit determination accuracy.

The probability of satellite collisions and disintegrations cluttering the near-Earth orbital environmentis ever-growing. This is especially true for the congested Low Earth Orbit (LEO) regime; once a critical density of objects is reached, a collisional cascading is projected to generate runaway growth of theorbital population. Comprehensive tracking of Resident Space Objects (RSO) is a requisite precursor to conjunction forecasting and avoidance; a strategy for active debris mitigation. Conducted at Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) Andøya Space, this work presents a means through which a passive optical observation station can be established using only an off-the shelf Canon EOS-1300 camera for uncued detection. A custom processing pipelinewas developed to perform data reduction on the retrieved images and initialisation of the object orbit was accomplished via implementations of the classic Initial Orbit Determination (IOD) algorithms of Laplace and Gauss. RSO identification was performed by reconstruction of the overpass and comparison against objects in a Two Line Elements (TLE) database. The complete script initiates the tracking process, and requires no inputs other than the image, and the geodetic coordinates of the ground station. The processing pipeline was demonstrated to perform robustly on the collected images and the algorithms were tested for different orbital regimes using precision angular data extracted from literature, with the retrieved results corresponding closely to the available reference values for all orbital regimes. Their performance as predictors of satellite position was compared for a variety of test cases, withthe Gauss algorithm producing more consistent results. However, orbits could not be initialised from the images, due to insufficient angular and timing precision. Various adaptations and extensions are suggested in order to achieve the requisite accuracy in the optical data and improve the data collection.