Attitude Determination Using Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. TRIAD, the earliest published algorithm for determining spacecraft attitude from two vector measurements, has been widely used in both ground-based and onboard attitude determination. Later attitude determination methods have been based on Wahba's optimality criterion for n arbitrarily weighted observations. The solution of Wahba's problem is somewhat difficult in the general case, but there is a simple closed-form solution in the two-observation case. This solution reduces to the TRIAD solution for certain choices of measurement weights. This paper presents and compares these algorithms as well as sub-optimal algorithms proposed by Bar-Itzhack, Harman, and Reynolds. Some new results will be presented, but the paper is primarily a review and tutorial.