Quaternion Regular Equations and Algorithms of Space Inertial Navigation

This paper proposes the new quaternion equations of perfect functioning for strapdown inertial navigation systems and for spatial inertial navigation systems with azimuthally stabilized platform and with the gyrostabilized platform which retains its orientation in an inertial reference frame. These equations use the regular four-dimensional variables proposed by the author of this paper. These INS equations are dynamically analogous to the quaternion regular equations of perturbed spatial two-body problem in four-dimensional Kustaanheimo-Stiefel variables, which makes it possible to use the results, obtained in the theory of regular celestial mechanics and astrodynamics, in space inertial navigation. This paper discusses the development of INS algorithms using the proposed quaternion equations of INS perfect functioning. This paper develops the results derived in [1]–[5].