Nonlinear orbit uncertainty prediction and rectification for space situational awareness

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Title: Nonlinear orbit uncertainty prediction and rectification for space situational awareness
Author: DeMars, Kyle Jordan
Abstract: 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 .
URI: http : / /hdl .handle .net /2152 /ETD -UT -2010 -12 -2596
Date: 2011-02-07

Citation

Nonlinear orbit uncertainty prediction and rectification for space situational awareness. Doctoral dissertation, University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2010 -12 -2596 .

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