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The second integral of acceleration in locally level coordinates should result in the estimated vehicle position. This integral is somewhat less than straightforward when longitude and latitude are the preferred horizontal location variables.

The rate of change of vehicle altitude equals its vertical velocity, which is the first integral of net (i.e. including gravity) vertical acceleration. The rates of change of vehicle longitude and latitude depend on the horizontal components of vehicle velocity, but in a less direct manner. The relationship between longitude and latitude rates and east and north velocities is further complicated by the oblate shape of the Earth.

Figure 3.8 Equipotential surface models for Earth.

The rates at which these angular coordinates change as the vehicle moves tangent to the surface will depend upon the radius of curvature of the reference surface model. Radius of curvature can depend on the direction of travel, and for an ellipsoidal model there is one radius of curvature for north–south motion and another radius of curvature for east–west motion.