A new approximative method for attitude correction in inertial navigation systems

In this paper, a novel algorithm for correcting the error of attitude in inertial navigation systems is introduced. Since the oftenly used differential equations of the navigation errors show the small rotation angles instead of the error of Euler angles, the nonlinear equation between the small rotation angles and the error of Euler angles, are derived. To obtain an approximative solution for the derived equations, third order multiplication of the small rotation angles are ignored and error of Euler angles are expressed explicitly as functions of the Euler angles and the small rotation angles. Based on the obtained solution, a new algorithm for attitude correction in inertial navigation is developed. A comprehensive numerical simulation is performed and superiority of the proposed algorithm than the usual method used for attitude correction, is shown. The proposed algorithm has smaller error in calculation of Euler angles. Also, the proposed method saves the orthogonality and normality conditions of the transformation matrix.