ABSTRACT
Chapter 6 is about the spacecraft attitude determination, which is based on the solution of Wahba’s problem. In principle, spacecraft attitude can be determined by a set of observed (measured) astronomical vectors and corresponding ephemeris astronomical vectors at the given time. An important problem is to find some fast, accurate, and robust algorithms to calculate the spacecraft attitude. That information is very important for spacecraft attitude control. Many algorithms are developed for this purpose. This chapter will discuss some important algorithms. Section 6.1 formulates the mathematical formula for the attitude determination problem, which is now named Wahba’s problem. Section 6.2 derives the famous Davenport’s formula which reduces Wahba’s problem to a much easier eigenvector problem and quaternion becomes a part of the solution. Most efficient and effective attitude determination algorithms are based on Davenport’s formula. Section 6.3 presents the solutions of QUEST and FOMA methods. Section 6.4 reveals an analytic solution for a special case when two vector measurements are available. Section 6.5 introduces a general analytic solution. Section 6.6 describes a method using optimization on Riemannian manifold, which is probably the most efficient and accurate method in the author’s opinion. Section 6.7 discusses a method of estimating rotational rate using only vector measurement.
