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

This research furthers the development of a closed-form solution to the angles-only 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. Closed-form 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 or 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.