LINEARIZED ORBIT COVARIANCE GENERATION AND PROPAGATION ANALYSIS VIA SIMPLE MONTE CARLO SIMULATIONS
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Monte Carlo simulations are used to explore how well covariance represents orbit state estimation and prediction errors when fitting to normally distributed, zero mean error observation data. The covariance is generated as a product of a least-squares differential corrector, which estimates the state in either Cartesian coordinates or mean equinoctial elements, and propagated using linearized dynamics. Radar range and angles observations of a LEO satellite are generated for either a single two-minute radar pass or catalog-class scenario. State error distributions at the estimation epoch and after propagation are analyzed in Cartesian, equinoctial, or curvilinear coordinates. Results show that the covariance is representative of the state error distribution at the estimation epoch for all state representations; however, the Cartesian representation of the covariance rapidly fails to represent the error distribution when propagated away from epoch due to the linear nature of the comparison coordinate system, not the linearization of the dynamics used in the covariance propagation. Analysis demonstrates that dynamic nonlinearity ultimately drives the error distribution to be non-Gaussian in element space despite the fact that sample distribution second moment terms appear to remain consistent with the propagated covariance. Lastly, the results show the importance of using as much precision as possible when dealing with ill-conditioned covariance matrices.
