Vector methods for determination of rigid body orientation

Vector methods for determining the orientation of a rigid body using information about vectors in the reference and body-related coordinate systems are considered. The analysis is based on the least squares method in vector-matrix form. This approach allows us to consider the application of different methods of solving the problem from a single standpoint: matrix (using the directional cosine matrix), geometric (using the Gibbs vector), quaternion (using the quaternion of rotation). Numerical evaluation of the accuracy of eight orientation determination algorithms obtained on the basis of these methods was performed.