Constraint Estimation of Spacecraft Positions

Abstract

The Constraint Kalman Filter is implemented for spacecraft formation ying absolute positions estimation. The orbital motion of a spacecraft is characterized by two range extrema (perigee and apogee). At the extremum, the rate of change of a spacecraft's range vanishes. This motion constraint can be used to improve the position estimation accuracy. The application of the Constrained Kalman Filter at only two points in the orbit causes lter instability. Two variables, α and β are introduced into the Constraint Kalman Filter to maintain the stability and improve the estimation accuracy. An Extended Kalman Filter is implemented as a benchmark for comparison with the Constrained Kalman Filter. Simulation results show that, with proper selection of α and β values, the Constraint Kalman Filter provides better estimation accuracy as compared to the Extended Kalman Filter. In this paper, two scenarios are studied. In the rst scenario, a spacecraft's absolute position is estimated by assuming the availability of radar measurements. In the second scenario, spacecraft formation absolute positions are estimated. It is assumed that the spacecraft formation is equipped with a wireless localization positioning system. The WLPS provides the relative position measurements between spacecraft in the formation. Only relative measurements are assumed in this paper.