The Exact Solution of the Riccati-Type Approximate Kinematic Equation and its Application to Construct a Quaternion Algorithm for Determining Orientation of a Strapdown INS

The exact solution of the Riccati-type approximate quaternion 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 (the truncated Darboux problem is actually solved). Proceeding from this solution, the following approach to the design of a new algorithm for computation of strapdown INS orientation is proposed.