Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 27

Note: Circle tilted for illustration

Plane of intersection
Surface of
sphere 1

Surface of
sphere 2

SAT 2

SAT 1

Earth surface

(c) (d)

Plane of satellite
locations

(e)

Figure 2.6 (continued.)

receiver can be represented. In this formulation, it is typical to describe satellite and
receiver states in terms of position and velocity vectors measured in a Cartesian
coordinate system. Two principal Cartesian coordinate systems are inertial and
rotating systems. In this section, an overview is provided of the coordinate systems
used for GPS.

2.2.1 Earth-Centered Inertial Coordinate System
For the purposes of measuring and determining the orbits of the GPS satellites, it is
convenient to use an Earth-centered inertial (ECI) coordinate system, in which the
origin is at the center of the mass of the Earth and whose axes are pointing in fixed
directions with respect to the stars. A GPS satellite obeys Newton's laws of motion
and gravitation in an ECI coordinate system. In typical ECI coordinate systems, the
xy -plane is taken to coincide with the Earth's equatorial plane, the x -axisisper-

manently fixed in a particular direction relative to the celestial sphere, the

+

+ z -axis is

taken normal to the xy -plane in the direction of the north pole, and the y -axis

is chosen so as to form a right-handed coordinate system. Determination and subse-
quent prediction of the GPS satellite orbits are carried out in an ECI coordinate
system.

+