Initial relative orbit determination analytical error covariance and performance analysis for proximity operations

This research furthers the development of a closed-form solution to the anglesonly initial relative orbit determination problem for close-in proximity operations when the camera offset from the vehicle center-of-mass allows for range observability. Emphasis is placed on developing closed-form error covariance equations for the initial relative orbit state solution and verification of the analytic covariance equations through systematic nonlinear Monte Carlo simulation of typical rendezvous missions with the International Space Station. Closedform analytic estimates of the relative state error covariance based on angle measurement errors, attitude knowledge errors and camera center-of-mass offset uncertainties for three and more observations are obtained. A two-body Monte Carlo simulation system is used to evaluate the performance of the closed-form relative state estimation algorithms and associated closed-form covariance equations. The sensitivity of the solution accuracy to spacecraft trajectories, camera offset, camera accuracy, attitude knowledge, and the time-interval between measurements is presented and discussed.