Short Communication: Determining the average attitude of a rigid body

Three-dimensional angular kinematics exist on the surface of a unit hypersphere, therefore the average attitude cannot always be accurately computed by averaging Cardan angles. This study derives and evaluates a method for determining average body attitude, by exploiting the singular value decomposition of the average of a set of attitude matrices. To test the method 1000 criterion attitudes were determined, and for each attitude 10 noisy attitude matrices generated. The new method and the averaging of Cardan angles extracted from the 10 noisy attitude matrices were evaluated for their ability to estimate the criterion attitude. At low attitude variance the two approaches provided equivalent results, but with increasing attitude variance levels the new procedure was superior. The method provides superior estimates of average attitude compared with averaging Cardan angles, by accounting for the geometric distribution of rigid body attitudes on the surface of a unit hypersphere.