Earth-Centered, Earth-Fixed Coordinate System - Fundamentals of Global Positioning System Receivers: A Software Approach - page 58

This last frame is often referred to as the earth-centered inertia (ECI) frame. The
origin of the ECI frame is at the earth's center of mass. In this frame the z 4 -axis
is perpendicular to the equator and the x 4 -axis is the vernal equinox and in the
equator plane. This frame does not rotate with the earth but is fixed with respect
to stars. In order to reference a certain point on the surface of the earth, the
rotation of the earth must be taken into consideration. This system is referred to
as the earth-centered, earth-fixed (ECEF) frame.

4.5 EARTH ROTATION ( 1,2 )

In this section two goals will be accomplished. The first one is to take care of the
rotation of the earth. The second one is to use GPS time for the time reference.
First let us consider the earth rotation. Let the earth turning rate be ˙ ie and
define a time t er such that at t er = 0 the Greenwich meridian aligns with the
vernal equinox. The vernal equinox is fixed by the Greenwich meridian rotates.
Referring to Figure 4.6, the following equation can be obtained

− ˙ ie t er er = ( 4 . 15 )

where er is the angle between the ascending node and the Greenwich meridian,
the earth rotation rate ˙ ie = 7 . 2921151467 × 10 − 5 rad/sec. When t er = 0, er =
, this means that the Greenwich meridian and the vernal equinox are aligned.

FIGURE 4.6 Rotation of the earth.