Effect of Observation Errors on Satellite Attitude Estimation

A study of the effect of observation errors on the best least squares estimate of satellite attitude based on two sets of direction measurements, where one set contains two independent measurements which are corrupted by zero-mean normally distributed additive errors, is summarized. Using Monte-Carlo techniques, the statistics of the estimated rotation of the satellite, from a known reference, were obtained. It was found that one of the parameterizations of the rotation, namely, the vector z, is best suited for estimation, since Δz is normally distributed with zero mean and its standard deviation is independent of the two direction measurements.