The paper considers the use of vector measurements of the Earth's magnetic field for the correction of low-grade inertial navigation systems based on microelectromechanical sensors. It is proposed to use global geomagnetic models for navigation of short-lived moving objects flying at high altitudes. The paper presents the numerical simulation results of such a navigation system based on low-grade inertial sensors, a fluxgate magnetometer and the global magnetic field model EMM2017.