Direct quaternion determination from BARS measurements

The output data from the Band Angle Readout System IMU (under consideration for use in missile and submarine guidance systems) include six 'band angles', four of which can be used to determine the missile's guidance. This can be accomplished by computing the 9-parameter direction cosine transformation matrix from a reference set of axes to the missile body set of axes. In the present paper, it is shown that the attitude band angles are intimately related to Euler angles, and that quaternion determination is a relatively straightforward matter. Since 12 conventions exist for defining Euler angles, several direct determination algorithms can be developed. These algorithms are briefly compared, and one routine is discussed in detail.