Error analysis of direction cosines and quaternion parameters techniques for aircraft attitude determination

Matrix differential equations for the determination of aircraft attitude orientation and the associated errors equations are developed in a four-dimensional space for both the direction cosines and quaternion parameter approaches. In this four-dimensional space, the corresponding algorithms, using accumulated gyro outputs, are developed and evaluated for the case of classical coning motion with time-varying angular velocity direction vector. Computation using symbolic algebra is considered in finding a closed-form solution for error propagation for a time-varying angular velocity direction vector. Examining the coning motion case shows that the true (analytic) scale and skew errors generated by the gyro drift are negligibly small in the direction cosines approach. Further, the true (analytic) scale errors in the quaternion technique are smaller than the computed (numerical) errors. Graphically illustrated are the true and computed errors in both the direction cosines and quaternion techniques for comparison.