ERROR ANALYSIS OF DIRECTION COSINES AND QUATERNION PARAMETERS TECHNIQUES FOR AIRCRAFT ATTITUDE DETERMINATION

Matrix differential equations for the determination of aircraft attitu de orientation and the associated errors equations are developed in a four-dimensional space for both the direction cosines and quaternion p arameter approaches. In this four-dimensional space, the corresponding algorithms, using accumulated gyro outputs, are developed and evaluat ed for the case of classical coning motion with time-varying angular v elocity direction vector. Computation using symbolic algebra is consid ered in finding a closed-form solution for error propagation for a tim e-varying angular velocity direction vector. Examining the coning moti on case shows that the true (analytic) scale and skew errors generated by the gyro drift are negligibly small in the direction cosines appro ach, Further, the true (analytic) scale errors in the quaternion techn ique are smaller than the computed (numerical) errors. Graphically ill ustrated are the true and computed errors in both the direction cosine s and quaternion techniques for comparison.