An introduction to the Global Positioning System
GPS navigation
Tracking Code Phase
In standard GPS navigation, each GPS receiver produces “replicas” of the code
transmitted by the various satellites.
These replicas represent the code the
receiver expects to receive from any given
satellite. A satellite is located and verified
when a replica of the code matches up
with the code received (a process known
as code phase tracking). At the beginning
of each individual signal is a sort of time
stamp. When the two signals are
examined by the receiver (called
“correlation”), the time stamps of the two
signals are compared and a time difference is ascertained. Given this time difference
and the rate of propagation of the signal, the GPS receiver uses the simple formula of
Rate times Time equals Distance (R*T=D) to compute the distance to each satellite.
Due to the uncertainties introduced by the many variables this distance to each satellite
is only an estimate, and is known as the pseudo-range.
Pseudo-Range Navigation
The pseudo-range from each satellite can be seen as a radius of a large sphere, and the
location of the GPS receiver is one point on that sphere. When several pseudo-ranges
from several satellites are used in conjunction, the position of the receiver is simply the
intersection of these spheres at a given time. The position is first determined in what is
known as the Earth-Centered, Earth-Fixed (ECEF) coordinate system, which describes
the receiver’s position relative to the center of the earth. From this ECEF location the
receiver then easily deduces the latitude, longitude, and altitude, which of course
describes the receiver’s position on the surface of the earth.
In solving for the ECEF position the receiver needs to examine four variables (three
dimensions and time), and a minimum of four
satellites is required. In the event that only three
satellites are available, a two-dimensional fix
can be calculated by assuming a certain
altitude. The greater the number of satellites
visible to the receiver the greater the level of
GPS accuracy, as five or more satellites can
provide position, time and redundancy.
