Earth-Centered, Earth-Fixed Coordinate System - Fundamentals of Global Positioning System Receivers: A Software Approach - page 51

CHAPTERFOUR

Earth-Centered, Earth-Fixed
Coordinate System

4.1 INTRODUCTION

In the previous chapter the motion of the satellite is briefly discussed. The true
anomaly is obtained from the mean anomaly, which is transmitted in the navi-
gation data of the satellite. In all discussions, the center of the earth is used as a
reference. In order to find a user position on the surface of the earth, these data
must be related to a certain point on or above the surface of the earth. The earth
is constantly rotating. In order to reference the satellite position to a certain point
on or above the surface of the earth, the rotation of the earth must be taken into
consideration. This is the goal of this chapter.
The basic approach is to introduce a scheme to transform the coordinate sys-
tems. Through coordinate system transform, the reference point can be moved
to the desired coordinate system. First the direction cosine matrix, which is used
to transform from one coordinate system to a different one, will be introduced.
Then various coordinate systems will be introduced. The final transform will
put the satellite in the earth-centered, earth-fixed (ECEF) system. Finally, some
perturbations will be discussed. The major portion of this discussion is based on
references 1 and 2.
In order to perform the transforms, besides the eccentricity e s and mean
anomaly M , additional data are obtained from the satellite. They are the semi-
major of the orbit a s , the right ascension angle , the inclination angle i ,andthe
argument of the perigee ω . Their definitions will also be presented in this chapter.