Inertial navigation in space using quaternion regular equations of astrodynamics

The new quaternion equations of perfect functioning of the spatial inertial navigation systems with azimuthally stabilized platform and with gyrostabilized platform which retains its orientation in an inertial reference frame, and the quaternion equations of perfect functioning of the strapdown inertial navigation systems in regular four-dimensional Kustaanheimo-Stiefel variables are proposed. These INS equations have a dynamic analogy with the quaternion regular equations of the perturbed spatial two-body problem, 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, 2].