Covariance Estimation and Autocorrelation of NORAD Two-Line Element Sets

This thesis investigates NORAD two-line element sets (TLE) containing satellite mean orbital elements for the purpose of estimating a covariance matrix and formulating an autocorrelation relationship. Orbit propagation is performed using Simplified General Perturbations Number 4 (SGP4) analytical model as implemented within Satellite Took Kit. For a given satellite, TLEs from a span of two weeks are used to calculate position and velocity differences of estimated state vectors in order to characterize their variance behavior and compute a covariance matrix for the most recent TLE. Six satellites and eight time spans are investigated, with all state vector differences evaluated in satellite-based coordinate systems. An autocorrelation relationship for each satellite is generated to characterize confidence levels of the orbit predictions. Trends in the deterministic dynamics and errors in the model are observed and discussed. Covariance matrix estimates and associated TLEs are presented.