Single-point position estimation in interplanetary trajectories using star trackers

Abstract

This study provides a single-point position estimation technique for interplanetary missions by observing visible planets using star trackers. Closed-form least-squares solution is obtained by minimizing the sum of the expected object-space squared distance errors. A weighted least-squares solution is provided by an iterative procedure. The weights are evaluated using the distances to the planets estimated by the least-squares solution. It is shown that the weighted approach only requires one iteration to converge and results in significant accuracy gains compared to simple least squares approach. The light-time correction is taken into account while the star-light aberration cannot be implemented in single-point estimation as it requires knowledge of the observer velocity. The proposed method is numerically validated through a statistical scenario as follows. A three-dimensional grid of test cases is generated: two dimensions sweep through the ecliptic plane and the third dimension sweeps through time from January 1, 2018 to January 1, 2043 in 5-year increments. The observer position is estimated at each test case and the estimate error is recorded. The results obtained show that a large majority of positions are well suited to position estimation by using star trackers pointing to visible planets, and reliable and accurate single-point position estimations can be provided in interplanetary missions. The proposed approach is suitable to be used to initiate a filtering technique to increase the estimation accuracy.