Satellite Constellation - Fundamentals of Global Positioning System Receivers: A Software Approach - page 30

CHAPTERTHREE

Satellite Constellation

3.1 INTRODUCTION

The previous chapter assumes that the positions of the satellites are known.
This chapter will discuss the satellite constellation and the determination of the
satellite positions. Some special terms related to the orbital mechanics, such as
sidereal day, will be introduced. The satellite motion will have an impact on
the processing of the signals at the receiver. For example, the input frequency
shifts as a result of the Doppler effect. Such details are important for the design
of acquisition and tracking loops in the receiver. However, in order to obtain
some of this information a very accurate calculation of the satellite motion is not
needed. For example, the actual orbit of the satellite is elliptical but it is close
to a circle. The information obtained from a circular orbit will be good enough
to find an estimation of the Doppler frequency. Based on this assumption the
circular orbit is used to calculate the Doppler frequency, the rate of change of
the Doppler frequency, and the differential power level. From the geometry of
the satellite distribution, the power level at the receiver can also be estimated
from the transmission power. This subject is presented in the final section in
this chapter.
In order to find the location of the satellite accurately, a circular orbit is insuf-
ficient. The actual elliptical satellite orbit must be used. Therefore, the complete
elliptical satellite orbit and Kepler's law will be discussed. Information obtained
from the satellite through the GPS receiver via broadcast navigation data such as
the mean anomaly does not provide the location of the satellite directly. However,
this information can be used to calculate the precise location of the satellite. The
calculation of the satellite position from these data will be discussed in detail.