Typical algorithms for processing unresolved space imagery from optical systems make broad assumptions about the expected behavior of the sensors during collection. While these techniques are often successful at data reduction for a particular mission, they rarely extend to sensors in different operating modes. Such specialized techniques therefore reduce the number of sensors able to contribute imagery. By approaching this problem with analysis of the fundamental dynamic equations and geometry at play, we can gain a deeper understanding into the behavior of both stars and space objects viewed through optical sensors. This type of analysis has the potential to enable data collection from a wider variety of sensors, increasing both the quantity and quality of data available for space object catalog maintenance. This dissertation will explore the implications of this approach to unresolved data processing. Sensor-level motion descriptions will be derived and applied to the problem of space object discrimination and tracking. Results of this processing pipeline as applied to both simulated and real optical data will be presented. / Ph. D.

<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>

<p dir="ltr">Characterizing unknown space objects is an important component of robust space situational awareness. Estimating the shape of an object allows analysts to perform more accurate orbit propagation, probability of collision, and inference analysis about the object’s origin. Due to the sheer distance from the camera combined with diffraction and atmospheric ef- fects, most resident space objects of interest are unresolved when observed from the ground with electro-optical sensors. State of the art techniques for object characterization often rely on light curves — the time history of the object’s observed brightness. The brightness of the object is a function of the object’s shape, material properties, attitude profile, as well as the observation geometry. The process of measuring real light curves is complex, involv- ing the physics of the object, the sensor, and the background environment. The process of recovering shape information from brightness measurements is known as the light curve shape inversion problem. This problem is ill-posed without further assumptions: modern direct shape inversion methods require that the attitude profile and material properties of the object is known, or at least can be hypothesized. This work describes improvements to light curve simulation that faithfully model the environmental and sensor effects present in true light curves, yielding synthetic measurements with more accurate noise characteris- tics. Having access to more accurate light curves is important for developing and validating light curve inversion methods. This work also presents new methods for direct shape inver- sion for convex and nonconvex objects with realistic measurement noise. In particular, this work finds that improvements to the convex shape inversion process produce more accurate, sparser geometry in less time. The proposed nonconvex shape inversion method is effective at resolving singular large concave feature.</p>

<p dir="ltr">With the increase in planned space missions in cislunar space, it is necessary to study the ability of observers to observe and track objects in this regime. This thesis focuses on creating a sensor tasking algorithm for constellations of optical observers to efficiently observe cislunar objects. The circular restricted three body problem is used for the dynamics of the objects while the bi-circular restricted four body problem is used to approximate the position of the sun.</p><p dir="ltr">A new way of discretizing the field of regard is proposed that respects the observers field of view on the unit sphere. A method for providing feedback to the observer in a delayed feedback environment is applied to mean state, single Gaussian, and particle representations of uncertainty. The method of determining a scaling coefficient for Sanson’s probability of detection is recorded. Sanson’s probability of detection is studied for determining the correct effective aperture dimensions of an optical observer. An approximation is presented for expediting calculations of Sanson’s probability of detection. An uncertainty propagation analysis shows there is an efficient number of particles to use for particle uncertainty far below the required number for a full Monte Carlo particle uncertainty representation. </p><p dir="ltr">Mean state, single Gaussian and particle methods of uncertainty characterization are compared in a cislunar simulation showing the benefits of the particles solution over other forms of uncertainty characterization. Particles are not only an effective uncertainty representation in a delayed feedback environment, they are computationally feasible for the sensor tasking problem. The performance of the particle algorithm for a constellation of observers is evaluated in a simulated small satellite breakup in a Lyapunov orbit and a simulated breakup of the proposed Lunar Gateway. The performance of observers in direct retrograde, low lunar, geosynchronous, and northern Halo orbits are evaluated in the breakup simulations. Results from these simulations show that observers in low lunar and Halo orbits can be valuable observation standpoints in breakups around the near-Moon region of cislunar space.</p>

As near-Earth space becomes increasingly crowded with spacecraft and debris, the need for improved space situational awareness has become paramount. Contemporary ground-based systems are limited in the detection of very small or dim targets. In contrast, space-based systems, above most atmospheric interference, can achieve significant improvements in dim target detection by observing targets against a clutter-free space background, i.e. targets above the horizon (ATH). In this study, numerical methods for the evaluation of ATH coverage provided by constellations of satellites are developed. Analysis of ATH coverage volume is reduced to a planar analysis of cross-sectional coverage area in the orbit plane. The coverage model performs sequences of boolean operations between polygons representing cross-sections of satellite sensor coverage regions and regions of interest, returning the coverage area at the desired multiplicity. This methodology allows investigation of any coverage multiplicity for planar constellations of any size, and use of arbitrary sensor profiles and regions of interest. The implementation is applied to several constellation design problems demonstrating the utility of the numerical ATH coverage model in a constellation design process. / text

Orbital debris is a current and growing threat to reliable space operations and new space vehicle traffic. As space traffic increases, so does the economic impact of orbital debris on the sustainability of systems that increasingly support national security and international commerce. Much of the debris collision risk is concentrated in specific high-density debris clusters in key regions of Low Earth Orbit (LEO). A potential long-term solution is to employ a constellation of observation satellites within these debris clusters to improve monitoring and characterization efforts, and engage in Laser Debris Removal (LDR) as means of collision mitigation. Here we adapted and improved a previous methodology for evaluating such designs. Further, we performed an analysis on the observer constellations' effectiveness over a range of circular, elliptical, and self-maneuvering designs. Our results show that increasingly complex designs result in improved performance of various criteria and that the proposed method of observation could significantly reduce the threat orbital debris poses to space operations and economic growth. / Master of Science / Orbital debris is defined as all non-operational, man-made objects currently in space. US national space regulations require every new satellite to have a de-orbit plan to prevent the creation of new debris, but fails to address the thousands of derelict objects currently hindering space operations. As space traffic increases, so does the economic impact of orbital debris on the sustainability of systems that increasingly support national security and commercial growth. While orbital debris is usually assessed by looking at the full volume of space, most massive debris objects are concentrated in high-density clusters with a higher than normal probability for collision. A potential solution to the growing orbital debris problem is to place a group of observation satellites within these debris clusters to both improve monitoring capabilities and provide a means for preventing potential collisions by engaging with debris via Laser Debris Removal (LDR). This research presents a methodology for comparing and contrasting different observer satellite constellation designs. Our results show that increasingly complex orbit designs improve various performance criteria, but ultimately orbits that more closely match those of the debris objects provide the best coverage. The proposed method of observation and engagement could significantly reduce the threat orbital debris poses to space operations and economic growth.

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>

In recent years, the accumulation of space debris has become an increasingly pressing issue, and adequately monitoring it is a formidable task for designated ground-based sensors. Supplementing the capabilities of these ground-based networks with orbiting sensing platforms would dramatically enhance the ability of such systems to detect, track, identify, and characterize resident space objects -- the primary goals of modern space situational awareness (SSA). Space-based space situational awareness (SBSSA), then, is concerned with achieving the stated SSA goals through coordinated orbiting sensing platforms. To facilitate the design of satellite constellations that promote SSA goals, an optimization approach is selected, which inherently requires a pre-defined mathematical representation of a cost index or measure of merit. Such representations are often analytically available, but when considering optimal constellation design for SBSSA applications, a closed-form expression for the cost index is only available under certain assumptions. The present study focuses on a subset of cases that admit exact representations. In this case, geometrical arguments are employed to establish an analytical formulation for the coverage area provided as well as for the coverage multiplicity. These analytical results are essential in validating numerical approximations that are able to simulate more complex configurations. / text

Modern space situational awareness entails the detection, tracking, identification, and characterization of resident space objects. Characterization is typically accomplished through the use of ground and space based sensors that are able to identify some specific physical feature, monitor unique dynamical behaviors, or deduce some information about the material properties of the object. The present investigation considers the characterizaiton aspects of situational awareness from the perspective of a close-proximity formation reconnaissance mission. The present study explores both relative translational and relative rotational motion for deployment of a spacecraft and observation of a resident space object. This investigation is motivated by specific situations in which characterization with ground or fixed space based sensors is insufficient. Instead, one or more vehicles are deployed in the vicinity of the object of interest. These could be, for instance, nano-satellites with imaging sensors. Nano-satellites offer a low-cost and effective technological platform, which makes consideration of the proposed scenario more feasible. Although the motivating application is rooted in space situational awareness, the techniques explored are generally applicable to flight in the vicinity of asteroids, and both cooperative vs. non-cooperative resident space objects. The investigation is initially focused on identifying the key features of the relative dynamics that are relevant to space situational awareness applications. Subsequently, effective spacecraft control techniques are considered to achieve the reconnaissance goals. / text

A new method for predicting the uncertainty in a nonlinear dynamical system is developed and analyzed in the context of uncertainty evolution for resident space objects (RSOs) in the near-geosynchronous orbit regime under the influence of central body gravitational acceleration, third body perturbations, and attitude-dependent solar radiation pressure (SRP) accelerations and torques. The new method, termed the splitting Gaussian mixture unscented Kalman filter (SGMUKF), exploits properties of the differential entropy or Renyi entropy for a linearized dynamical system to determine when a higher-order prediction of uncertainty reaches a level of disagreement with a first-order prediction, and then applies a multivariate Gaussian splitting algorithm to reduce the impact of induced nonlinearity. In order to address the relative accuracy of the new method with respect to the more traditional approaches of the extended Kalman filter (EKF) and unscented Kalman filter (UKF), several concepts regarding the comparison of probability density functions (pdfs) are introduced and utilized in the analysis. The research also describes high-fidelity modeling of the nonlinear dynamical system which drives the motion of an RSO, and includes models for evaluation of the central body gravitational acceleration, the gravitational acceleration due to other celestial bodies, and attitude-dependent SRP accelerations and torques when employing a macro plate model of an RSO. Furthermore, a high-fidelity model of the measurement of the line-of-sight of a spacecraft from a ground station is presented, which applies light-time and stellar aberration corrections, and accounts for observer and target lighting conditions, as well as for the sensor field of view. The developed algorithms are applied to the problem of forward predicting the time evolution of the region of uncertainty for RSO tracking, and uncertainty rectification via the fusion of incoming measurement data with prior knowledge. It is demonstrated that the SGMUKF method is significantly better able to forward predict the region of uncertainty and is subsequently better able to utilize new measurement data. / text