Better algorithm for relative positioning and posing based on quaternion and spacecraft orbit and attitude information

Aim. There already exists Hall algorithm for positioning and posing according to Ref.3 by X.A. Quintana. We now propose a new algorithm that we believe is better than Hall's. In the full paper, we explain in some detail our algorithm; in this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: quaternion based method for determining position and attitude. Its two subtopics are: the quaternion based description of the rotational transformation for three dimensional bodies (subtopic 1.1), the camera model and the basic equation for machine vision for determining position and attitude (subtopic 1.2) and the quaternion based model for determining position and attitude by machine vision (subtopic 1.3). In subtopic 1.3, the initial position values are calculated by eq.(16) in the full paper; eq.(16) is based on Taylor expansion and least squares method. The second topic is: the algorithm for relative positioning and posing based on quaternion and spacecraft orbit and attitude information. Finally we give an example of numerical simulation, whose results are given in Figs.2 through 8 in the full paper. These results show preliminarily that our proposed algorithm is much faster than Hall's.