# Browsing by Subject "Space situational awareness"

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Item Analytical approach to the design of optimal satellite constellations for space-based space situational awareness applications(2011-12) Biria, Ashley Darius; Marchand, Belinda G.; Lightsey, E. GlennShow more 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.Show more Item Applications of random finite set-based multi-target trackers in space situational awareness(2022-08-18) Ravago, Nicholas; Jones, Brandon A.; Zanetti, Renato; Jah, Moriba; Russell, Ryan P; Weisman, RyanShow more Space situational awareness, the ability to accurately characterize and predict the state of the space environment, has become a topic of interest as the population of operational satellites increases. This trend is being driven by the deployment of large constellations of satellites that could consist of tens of thousands of satellites when fully deployed. Tracking space objects accurately is important for predicting and preventing collisions between objects, which can result in catastrophic damage to operational satellites and create debris clouds that endanger other satellites. However, tracking space objects is complicated due in part to the uncertain origins of measurements, a problem known as data ambiguity. While multiple target tracking algorithms that can handle data ambiguity exist, tracking in the space environment presents other challenges. The number of available observations per object is generally low due to the large number of objects relative to available sensor resources, and many observations are left uncorrelated due to the aforementioned data ambiguity problem. The recent rise of large constellations presents another problem in that the involved satellites will utilize low thrust propulsion systems to maintain formation, requiring maneuvering target tracking capabilities for optimal performance. In this dissertation we will analyze two problems that are representative of the space object tracking challenges that operators will face in the near future. We will show how applicable algorithms can developed using finite set statistics, a mathematical framework that allows a top-down approach to be employed in developing rigorous Bayes-optimal multi-target filters with desired functionalities. The first problem we analyze is a large constellation tracking problem. We simulate a constellation of over 4,500 satellites in low Earth orbit and track them using a network of twelve ground-based myopic sensors. These sensors are tasked using a cost function that combines an information-theoretic reward. We also leverage tactical importance functions to enable the incorporation of mission-based objectives, like prioritization of objects at risk of collision, into the tasking logic. The collected data are processed using a labeled multi-Bernoulli filter. The state catalog estimate produced by the filter is used to motivate the next round of sensor tasking, resulting in an autonomous closed loop system for integrated tasking and tracking. After a five-day tracking period, the state catalog estimate is used to perform a conjunction analysis. We combine existing methods to produce a computationally efficient workflow for the filtering of close approaches between satellites and the quantification of risk. The second problem we analyze is tracking multiple targets when maneuvering targets are present. Maneuvering targets deviate from their natural trajectories in unpredictable ways and generally require specialized tracking algorithms for best performance. A common method for tracking such targets is the interacting multiple model filter which maintains a bank of models to represent the possible dynamics of a target. Unknown dynamics can be represented as white noise processes through the concept of equivalent noise. This allows maneuvering space objects to be tracked efficiently, but this algorithm lacks the ability to characterize maneuvers. Using finite set statistics, we are able to develop a formulation of the generalized labeled multi-Bernoulli filter that allows for the integration of arbitrary dynamical models. This allows us to utilize data-adaptive methods that model unknown dynamics more specifically, allowing the filter to perform maneuver characterization in addition to maneuvering target tracking. We also develop a consider-based least squares maneuver estimation algorithm that models unknown dynamics using a single impulsive velocity change. The timing of this maneuver is estimated through a multiple hypothesis method. This method is integrated with our formulation of the generalized labeled multi-Bernoulli filter and applied to a simulated constellation of geostationary Earth orbiting satellites that includes a satellite performing an unknown maneuver. Results in our large constellation tracking work showed that our integrated tasking and tracking algorithm was able to maintain custody of all simulated satellites. We were able to improve the accuracy of risk analysis by incorporating a measure of collision risk in the sensor tasking logic, but the improvement was marginal. We hypothesize that a more generalized optimization algorithm or different sensor architecture may allow mission objective-based tasking to exert greater influence. Our results for the maneuvering target tracking problem showed that we were able to characterize the maneuver dynamics with an acceptable level of accuracy. The absolute errors in our characterization were relatively high compared to the actual maneuvers, but we were able to maintain custody of all objects. Consistency metrics were stable through the occurrence of the maneuver, indicating accurate quantification of the estimated maneuver error uncertainty. Future work remains to scale this work up to a larger-scale scenario where maneuver detection will become a greater factor due to its impact on computational efficiency. Further work would also required to extend our algorithm to non-Gaussian state representations that are often utilized in low-Earth orbit tracking scenarios.Show more Item Nonlinear orbit uncertainty prediction and rectification for space situational awareness(2010-12) DeMars, Kyle Jordan; Bishop, Robert H., 1957-; Akella, Maruthi R.; Marchand, Belinda G.; Crain, Timothy P.; Jah, Moriba K.Show more 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.Show more Item Numerical analysis and design of satellite constellations for above the horizon coverage(2010-12) Takano, Andrew Takeshi; Marchand, Belinda G.; Fowler, Wallace T.Show more 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.Show more Item On the application of credibilistic filtering to uncertainty quantification and assessment in the operational space domain(2020-08-13) Bever, Marcus Jonathan; Jah, Moriba K.Show more The local space environment is a rapidly changing political and commercial landscape. There is a tremendous need for informed operational decisions in a regime that is fundamentally a collaborative and interconnected domain. These choices must be made not in spite of inaccurate and imprecise knowledge, but accounting for such restrictions in reasoning, thereby enabling the most realistic and actionable conclusions to be drawn in the realm of space traffic. A survey of hierarchical uncertainty methods yields a class of outer probability measures that is particularly well-suited to an adaptation of the Bayesian framework. Examples of an elementary nature are first explored where the delineations between aleatory and epistemic uncertainty is apparent. Potential and proven applications to the field of space situational awareness serve as the more complex realization of and motivation for such efforts. This study culminates in the formulation, demonstration, and analysis of the credibilistic Gaussian mixture filter in the context of space trackingShow more Item Space object translational and rotational state prediction and sensitivity calculation(2016-12) Hatten, Noble Ariel; Russell, Ryan Paul, 1976-; Akella, Maruthi R; Bettadpur, Srinivas V; Jones, Brandon A; Weisman, Ryan MShow more While computing power has grown monumentally during the space age, the demands of astrodynamics applications have more than kept pace. Resources are taxed by the ever-growing number of Earth-orbiting space objects (SOs) that must be tracked to maintain space situational awareness (SSA) and by increasingly popular but computationally expensive tools like Monte Carlo techniques and stochastic optimization algorithms. In this dissertation, methods are presented to improve the accuracy, efficiency, and utility of SO state prediction and sensitivity calculation algorithms. The dynamical model of the low Earth orbit regime is addressed through the introduction of an upgraded Harris-Priester atmospheric density model, which introduces a smooth polynomial dependency on solar flux. Additional modifications eliminate singularities and provide smooth partial derivatives of the density with respect to SO state, time, and solar conditions. The numerical solution of the equations of motion derived from dynamics models is also addressed, with particular emphasis placed on six-degree-of-freedom (6DOF) state prediction. Implicit Runge-Kutta (IRK) methods are applied to the 6DOF problem, and customizations, including variable-fidelity dynamics models and parallelization, are introduced to maximize efficiency and take advantage of modern computing architectures. Sensitivity calculation -- a necessity for SSA and other applications -- via RK methods is also examined. Linear algebraic systems for first- and second-order state transition matrix calculation are derived by directly differentiating either the first- or second-order form of the RK update equations. This approach significantly reduces the required number of Jacobian and Hessian evaluations compared to the ubiquitous augmented state vector approach for IRK methods, which can result in more efficient calculations. Parallelization is once again leveraged to reduce the runtime of IRK methods. Finally, a hybrid special perturbation/general perturbation (SP/GP) technique is introduced to address the notoriously slow speed of fully coupled 6DOF state prediction. The hybrid method uses a GP rotational state prediction to provide low-fidelity attitude information for a high-fidelity 3DOF SP routine. This strategy allows for the calculation of body forces using arbitrary shape models without adding attitude to the propagated state or taking the small step sizes often required by full 6DOF propagation. The attitude approximation is obtained from a Lie-Deprit perturbation result previously applied to SOs in circular orbits subject to gravity-gradient torque and extended here to SOs in elliptical orbits. The hybrid method is shown to produce a meaningful middle ground between 3DOF SP and 6DOF SP methods in the accuracy vs. efficiency space.Show more