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Daniel Guggenheim School of Aerospace Engineering
Daniel Guggenheim School of Aerospace Engineering
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ItemUninformative Prior Multiple Target Tracking Using Evidential Particle Filters(Georgia Institute of Technology, 2017-09) Worthy, Johnny L., III ; Holzinger, Marcus J.Space situational awareness requires the ability to initialize state estimation from short measurements and the reliable association of observations to support the characterization of the space environment. The electro-optical systems used to observe space objects cannot fully characterize the state of an object given a short, unobservable sequence of measurements. Further, it is difficult to associate these short-arc measurements if many such measurements are generated through the observation of a cluster of satellites, debris from a satellite break-up, or from spurious detections of an object. An optimization based, probabilistic short-arc observation association approach coupled with a Dempster-Shafer based evidential particle filter in a multiple target tracking framework is developed and proposed to address these problems. The optimization based approach is shown in literature to be computationally efficient and can produce probabilities of association, state estimates, and covariances while accounting for systemic errors. Rigorous application of Dempster-Shafer theory is shown to be effective at enabling ignorance to be properly accounted for in estimation by augmenting probability with belief and plausibility. The proposed multiple hypothesis framework will use a non-exclusive hypothesis formulation of Dempster-Shafer theory to assign belief mass to candidate association pairs and generate tracks based on the belief to plausibility ratio. The proposed algorithm is demonstrated using simulated observations of a GEO satellite breakup scenario.
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ItemDempster-Shafer Theory Applied to Admissible Regions(Georgia Institute of Technology, 2017-02) Worthy, Johnny L., III ; Holzinger, Marcus J.The admissible region approach is often used a bootstrap method to initialize a Bayesian state estimation scheme for too-short-arc measurements. However, there are ambiguities in how prior probabilities are assigned for states in the admissible region. Several approaches have proposed methods to assign prior probabilities, however there are inconsistencies in how the prior probabilities can be manipulated. The application of Dempster-Shafer evidential reasoning theory to the admissible region problem can avoid these ambiguities by eliminating the need to make any assumptions on the prior probabilities. Dempster-Shafer theory also enables the testing of the validity of the assumptions used to construct the admissible region. This paper introduces Dempster-Shafer theory and formulates the admissible region in terms of plausibility and belief which reduce to traditional Bayesian probability once there is sufficient information in the system.
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ItemProbability Density Transformations on Admissible Regions for Dynamical Systems(Georgia Institute of Technology, 2015-08) Worthy, Johnny L., III ; Holzinger, Marcus J.The admissible region as used for initial orbit determination is often expressed as a uniform multivariate probability density function (PDF). A multivariate PDF may be transformed and expressed in an alternate state space if the total probability is preserved over the transformation. This paper applies the general multivariate PDF transformation method to an admissible region to develop the conditions required for such a transformation. Because the probability must be preserved, it is shown that in general an admissible region PDF may not be transformed by a nonlinear transformation unless specific mapping conditions are met over all the state space volume. If this condition is not met then the transformation of an admissible region PDF yields incorrect probabilities over the state space. Further, it is also shown that if each state in an admissible region is locally observable then the constant gradient condition is lifted.
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ItemUncued Satellite Initial Orbit Determination Using Signals of Opportunity(Georgia Institute of Technology, 2015-08) Worthy, Johnny L., III ; Holzinger, Marcus J.This paper investigates the application of signal of opportunity based multilateration to generate initial orbit estimates. Using at least 4 observer stations, the time differential of arrival of signals of opportunity can be measured and used to determine a 3D position estimate of the source of the signal with some associated covariance on the position estimate. While this solution gives the position of the object, admissible region theory may be applied to bound the possible velocity states belonging to a particular source. Two constraints are considered and analytically derived for the time differential of arrival problem to constraint the possible velocity solutions for a given position estimate. Once a joint admissible region is formed from these constraints, it may be sampled and used as an initial distribution for a particle filter. This work shows an example application of particle filter initiation with a time differential of arrival measurement based admissible region.
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ItemIncorporating Uncertainty in Admissible Regions for Uncorrelated Detections(Georgia Institute of Technology, 2014-08) Worthy, Johnny L., III ; Holzinger, Marcus J.Admissible region methods for initial orbit determination are generally implemented without considering uncertainty in observations or observer state. In this paper a generalization of the admissible region approach is introduced that more accurately accounts for uncertainty in the constraint hypothesis parameters used to generate the admissible region. Considering the uncertainty to have Gaussian distributions, the proposed relationship between provided information uncertainty and admissible region uncertainty results directly in an analytical approximate probability density function. The methodology is extended to account for admissible regions with multiple overlapping constraint hypothesis. The proposed approach is applied to an example optical detection to demonstrate the quality of the approximation and the sensitivity of the resulting distribution to typical errors.