Inertial navigation equations for the apparent and gravitational velocities and their analytic solutions for an immovable object

Abstract

We propose new differential equations describing the perfect operation of strapdown intertial navigation systems (SINS) intended to determine the apparent, gravitational, and relative velocities of amoving object and the geographic coordinates of the object position. The superposition principle is used to construct the equations.

We construct analytical solutions of differential equations for the apparent and gravitational velocities in the case of an object immovable with respect to the Earth, which can be used to analyze the accuracy of operation of SINS mounted on an immovable base.