In inertial navigation and geodesy, the ellipsoid is a mathematical model that represents the shape of the Earth in a simplified, precise, and usable way. Instead of treating the Earth as a perfect sphere, professionals and navigation systems model it as an oblate ellipsoid, slightly flattened at the poles and bulging at the equator due to Earth’s rotation. This representation provides a consistent geometric surface on which positions, heights, and motions can be defined accurately.
The ellipsoid provides the fundamental reference surface for GNSS and coupled inertial navigation systems. It uses key parameters, including the semi-major axis and the flattening factor. The semi-major axis represents the equatorial radius. The flattening factor describes how much the Earth deviates from a perfect sphere.
Common global reference ellipsoids, such as WGS-84, ensure worldwide consistency for positioning, navigation, and mapping.
In inertial navigation, the ellipsoid plays a critical role in expressing position. Professionals define latitude and longitude geometrically on the ellipsoid rather than on the true physical Earth surface. When an INS integrates accelerations and angular rates to compute velocity and position, it relies on an Earth model to project motion correctly in a curved reference frame. The ellipsoid enables accurate transformation between body, navigation, and Earth-centered coordinate frames, while accounting for Earth curvature and rotation.
The ellipsoid defines ellipsoidal height as the vertical distance between a point and the ellipsoid surface. This height differs from physical height above sea level. Navigation systems use it for precise positioning, sensor fusion, and GNSS/INS integration.
Using the ellipsoid ensures mathematical continuity and stability, which are critical for Kalman filtering and error propagation models.
