The exact solution of the Bortz approximate equation and construction of the quaternion orientation algorithm of strapdown INS on its basis

The exact solution of the Bortz approximate linear equation 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 design of a new algorithm for computation of strapdown INS orientation is proposed.