In this work, sensor tasking refers to assigning the times and pointing directions for a sensor to collect observations of cataloged objects, in order to maintain the accuracy of the orbit estimates. Sensor tasking must consider the dynamics of the objects and uncertainty in their positions, the coordinate frame in which the sensor tasking is defined, the timing requirements for observations, the sensor capabilities, the local visibility, and constraints on the information processing and communication. This research focuses on finding efficient ways to solve the sensor tasking optimization problem. First, different coordinate frames are investigated, and it is shown that the observer fixed Local Meridian Equatorial (ground-based) and Satellite Meridian Equatorial (space-based) coordinate frames provide consistent sets of pointing directions and accurate representations of orbit uncertainty for use by the optimizers in solving the sensor tasking problem. Next, two classical optimizers (greedy and Weapon-Target Assignment) which rely on convexity are compared with two Machine Learning optimizers (Ant Colony Optimization and Distributed Q-learning) which attempt to learn about the solution space in order to approximate a global optimal solution. It is shown that the learning optimizers are able to generate better solutions, while the classical optimizers are more efficient to run and require less tuning to implement. Finally, the realistic scenario where the optimization algorithm receives no feedback before it must make the next decision is introduced. The Predicted Measurement Probability (PMP) is developed, and employed in a two sensor optimization framework. The PMP is shown to provide effective feedback to the optimization algorithm regarding the observations of each sensor.<br>

<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>

<p>    </p> <p>Space has become ever more crowded since the launch of Sputnik. The need for predictions of possible collisions between space objects has only ever grown. The development of space, particularly around Earth, increases the density of space objects and skyrockets the number of close approaches between these objects, called conjunctions. This investigation is conducted in the context of probability dilution, a phenomenon leading to a false negative collision prediction where increasing positional uncertainty decreases the predicted likelihood of a collision. Dilution is investigated along two avenues: how to generate accurate collision predictions in an efficient manner and how to obtain better input data with which to make these predictions. Along the first avenue, this research presents a novel analytical rectan- gular probability of collision expression as well as a variety of new covariance scale factor formulations for maximum collision probability that indicate the maximum possible collision risk for any conjunction. Along the second avenue, this research tests new sensor tasking regimes to mitigate dilution, ultimately showing that while dilution can be reduced, shrink- ing the positional covariance through optimal measurement updates may not be enough to avoid false negatives in orbital conjunctions. </p>

<pre>Because of the increasing population of space objects, there is an increasing necessity to monitor and predict the status of the near-Earth space environment, especially of critical regions like geosynchronous Earth orbit (GEO) and low Earth orbit (LEO) regions, for a sustainable future. Space Situational Awareness (SSA), however, is a challenging task because of the requirement for dynamically insightful fast orbit propagation models, presence of dynamical uncertainties, and limitations in sensor resources. Since initial parameters are often not known exactly and since many SSA applications require long-term orbit propagation, long-term effects of the initial uncertainties on orbital evolution are examined in this work. To get a long-term perspective in a fast and efficient manner, this work uses analytical propagation techniques. Existing analytical theories for orbital perturbations are investigated, and modifications are made to them to improve accuracy. While conservative perturbation forces are often studied, of particular interest here is the orbital perturbation due to non-conservative forces. Using the previous findings and the developments in this thesis, two SSA applications are investigated in this work. In the first SSA application, a sensor tasking algorithm is designed for the detection of new classes of GEO space objects. In the second application, the categorization of near-GEO objects is carried out by combining knowledge of orbit dynamics with machine learning techniques.</pre>

<div>As the number of Resident Space Objects around Earth continues to increase, the need for an optimal sensor tasking strategy, specifically with Ground-Based Optical sensors, continues to be of great importance. This thesis focuses on the single and multi-sensor tasking problem with realistic optical sensor modeling for the observation of objects in the Geosynchronous Earth Orbit regime. In this work, sensor tasking refers to assigning the specific?c observation times and viewing directions of a single or multi sensor framework to either survey for or track new or existing objects. For this work specifically, the sensor tasking problem will seek to maximize the total number of Geosynchronous Earth Orbiting objects to be observed from a catalog of existing objects with a single and multi optical sensor tasking framework. This research focuses on the physical assumptions and limitations on an optical sensor, and how these assumptions affect the single and multi sensor tasking scenario. First, the concept of the probability of detection of a resident space object is calculated based on the viewing geometry of the resident space object. Then, this probability of detection is compared to the system that avoids the computational process by implementing a classical heuristic minimum elevation constraint to an electro-optical charged coupled optical sensor. It is shown that in the single and multi-sensor tasking scenario if the probability of detection is not considered in the sensor tasking framework, then a rigid elevation constraint of around 25^o-35^o is recommended for tasking Geosynchronous objects. Secondly, the topic of complete geo-coverage within a single night is explored. A sensor network proposed by Ackermann et al. (2018) is studied with and without the probability of detection considerations, and with and without uncertainties in the resident space objects' states. (then what you have). For the multi-sensor system, it is shown that with the assumed covariance model for this work, the framework developed by Ackermann et al. (2018) does not meet the design requirements for the cataloged Geosynchronous objects from March 19th, 2019. Finally, the concept of a variable repositioning time for the slewing of the ground-based sensors is introduced and compared to a constant repositioning time model. A model for the variable repositioning time is derived from data retrieved from the Purdue Optical Ground Station. This model is applied to a single sensor scenario. Optimizers are developed using the two repositioning time functions derived in this work. It is shown that the constant repositioning models that are greater than the maximum repositioning time produce results close to the variable repositioning solution. When the optimizers are tested, it is shown that there is a small increase in performance only when the maximum repositioning time is significant.</div>