The new and known strapdown INS algorithms for high-precision estimation of the orientation parameters of a moving object (Rodrigues–Hamilton (Euler) parameters) in the inertial frame are nvestigated. The new algorithms are based upon using the classical Hamilton rotation quaternion, quaternion with zero scalar part, which is correlated to the classical rotation quaternion via the quaternion equivalent of Cayley formula, and also the new quaternion differential equation for the inertial orientation of a moving object.
