The New Analytical Algorithm for Determining the Strapdown INS Orientation

Abstract

The analytical solution of an approximate (truncated) equation for the vector of a rigid body finite rotation has made it possible to solve the problem of determining the quaternion of orientation of a rigid body for an arbitrary angular velocity and small angle of rotation of a rigid body with the help of quadratures. Proceeding from this solution, the following approach to the construction of the new analytical algorithm for computation of a rigid body orientation with the use of strapdown INS is proposed: 1) By the set components of the angular velocity of a rigid body on the basis of mutually — unambiguous changes of the variables at each time point, a new angular velocity of a rigid body is calculated; 2) Using the new angular velocity and the initial position of a rigid body, with the help of the quadratures we find the exact solution of an approximate linear equation for the vector of a rigid body finite rotation with a zero initial condition; 3) The value of the quaternion orientation of a rigid body (strapdown INS) is determined by the vector of finite rotation. During construction of the algorithm for strapdown INS orientation at each subsequent step the change of the variables takes into account the previous step of the algorithm in such a way that each time the initial value of the vector of finite rotation of a rigid body will be equal to zero. Since the proposed algorithm for the analytical solution of the approximate linear equation for the vector of finite rotation is exact, it has a regular character for all angular motions of a rigid body).