Specific features of the solution of problems of near-Earth inertial navigation are described for applications in which geodetic-class precision is required, the connection of problems of autonomous inertial navigation and satellite gravimetry, their complementary and contradictory character are considered, navigation support of modern projects of satellite geodesy is analyzed. The architecture of a precise strapdown inertial navigation system is considered, the mathematical model for its operation with account of errors is proposed. Error equations are obtained in a general nonlinear form. The specific features of the constructed model are the account of variations of velocity of the Earth's self rotation, the nonstationary character of the Earth's gravitational field, the gravitational influence of the Sun, the Moon, planets, and the account of tidal, tectonic, seasonal motions of the navigation coordinate system whose origin is situated at the point of the surface of the elastic Earth with respect to the Earth's geocentric coordinate system.
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