What
are the requirements for a successful position-determining system for you, me
and the millions of hikers, 4x4'ers, fishermen and paramedics? Certainly such a
system has to be affordable; it also needs to be accurate, easy to use, portable
and rugged. Very tough requirements to meet.

Distances between landmarks can be accurately measured by
different means. As kids we all used to count the seconds separating the
lightning flash and the arrival of the thunderclap. Since we know the speed of
sound in air (say 330m/s), we can easily work out the distance between the
origin of the flash and the observer. This reasoning of course depends on us
seeing the flash at the time that it was generated, which means that we accept
that the speed of light is infinite and that there is no delay between the flash
being generated and it being observed. In reality, the velocity of light (say
300 000 000 m/s), is high, but it is not infinitely so. If we have an accurate
enough timing device, it is possible to determine the time lapse between the
generation of a light signal and its reception.

The critical part in this is having a timing device that is
accurate enough for the purpose. Using a clock that is accurate to 0,001 second
(one millisecond) to determine the time-of flight of a light signal, leads to an
error of 300km. Nanosecond accuracy (0,000 000 001 sec) leads to an error of
0,0003km. This 300mm error is much more acceptable, but is totally dependent on
the availability of ultra accurate atomic clocks.

As an aside - in 1714 the British Parliament offered a prize
of 20 000 pounds to the first person to devise a method of finding longitude at
sea with an accuracy of 30 nautical miles. This sum was a great deal of money at
the time, but it was claimed only in 1762 by a certain John Harrison, who
constructed a clock, the chronometer, that was so accurate that navigators could
use it to attain the magic 30 mile precision.

Today we use radio signals instead of pulses of light as the
means of determining the distance between a receiver (your GPS equipment and a
signal source. Radio signals propagate at the speed of light, and precise
distance measurement is possible if very accurate clocks are available in both
the transmitter and the receiver. The signal source needs to radiate a signal
containing real time, an identification code and a position indicator. If the
signal source were an immovable ground station the positional information would
not be necessary. The receiver needs to keep its own accurate time so

that the time-of-flight of the signal can be determined, and
it also needs to know from which transmitter (where) the signal originated.
Since the US military started with the idea of GPS, they are understandably very
concerned about the safety and integrity of ground installations. Another
problem with ground stations is that there would need to be a very large number
to cover the whole earth. The decision was therefore to go with a satellite
system, and the Navstar system was born.

The satellites are big and expensive enough to each contain a
few atomic clocks (a few, since there have to be spares and they also need to be
checking each other), but your hand - held GPS receiver cannot make use of this
bulky and non-affordable timing technology. A timing device that is cheap and
small, however, is the ordinary quartz crystal oscillator - the same one that is
used in just about all wristwatches. The short term accuracy of such a timing
device can be of the order of a microsecond (1 000 nanoseconds), but this is not
nearly good enough to allow it to be used directly for computing the distance
between the receiver and the satellite. The success of the whole system depends
on the implementation of successful strategies to compensate for the receiver
clock errors.

Radar Radio Direction And Ranging also makes use of the time
that a signal takes to travel between target and antenna, but in this case the
process is straightforward. With radar the antenna radiates a strong microwave
signal which is bounced off the target and which is then reflected back to the
antenna. The process involves the determination of the time-of-flight of the
signal, dividing this value by two and then computing the distance. Here the
interval between sending and receiving a signal is determined by the sender -
accurate real-time clocks are not necessary at all. Trivial, compared to the
requirements for GPS.

Having more than one satellite available in the sky allows
your GPS receiver to compute the distance between itself and various 'visible'
satellites. Determining the distances to more than two satellites allows you to
plot your position accurately. Since each distance plot places you somewhere on
the surface of a sphere centered on a satellite, using data from three
satellites allows the position of the receiver to be calculated to being within
a three-sided volume of space. The size of this volume depends on the accuracy
of the data, and therefore primarily on the accuracy of the clocks. The
microsecond accuracy of the receiver clock does not lead to acceptable volume
sizes.

Solving the clock error problem is crucial. Determining a
position on earth requires values for three unknowns; x, y and z-positions. We
know from high school algebra that solving for three unknowns requires at least
three independent equations. Three satellites will give us x, y and z, but
imprecisely, since we do not know the value of a fourth variable, which is the
time error of the GPS receiver. This means that we have an equation with four
unknowns: x, y, z and the time error. Getting information from a fourth
satellite makes it possible to solve for this fourth unknown. The GPS receiver
makes use of an iterative, or repetitive, mathematical algorithm to determine
the time error.

This value is then used to re-compute distances to all four
(or more) satellites. As a bonus, in addition to the positional information, the
GPS system therefore provides time signals accurate to within about 200
nanoseconds. This then also is

the reason why the time readout of a GPS-receiver cannot be
re-set by the user - it is continually being computed from the information
received from at least three independent atomic clocks, and this is why it
always extremely accurate. If your GPS time readout differs from that given by
the SABC, the SABC is wrong and you are right!

Signals from four satellites provide 3D (x, y and z) and time
information. Three satellites lead to 2D information - x, y and time, while the
z or altitude information cannot be computed.

The above description makes all this sound rather easy. If
the satellites were fixed in space it would in actual fact be so. But, the
satellites are not fixed in space. They circle the earth at 14000 km/h at a
distance of 20 190 km, in orbits that take 11 hours 58 minutes to complete, so
that they seem to drift, like the stars, four minutes per day. In contrast to
this, geostationary satellites (like many communications satellites), are at 36
000 km from the earth and circle the earth once in exactly 24 hours so that they
always stay over the same spot on the surface of the earth. Geostationary
satellites have one attribute that makes them unsuitable for GPS-use, and that
is the fact that they can only be launched into equatorial orbits, which would
give very poor visibility from high and low latitudes. It would also mean that
they are all in the same plane, making for very poor positional accuracy.

To give good coverage to GPS receivers anywhere on earth,
there are always at least 24 satellites (or Space Vehicles, SV's, as they are
often referred to) in orbit. Of these, three are spares. Four SV's travel in
each of six orbits, each inclined at 55° to the equator so that four or more of
the SV's are at all times visible from any point on the surface of the earth. In
addition to the atomic clocks and the communications equipment each satellite
also contains fuel for its small manoeuvring engines, giving it a limited
capability of orbit adjustment.

In addition to the Navstar satellites in space (the 'Space
Component'), there is also a ground support system (the 'Control Segment') with
a master control station and a number of monitoring stations around the world.
The last component of the system is the 'User Segment', which includes us with
our GPS receivers.

Once a SV is in space, it does not stay in exactly the same
orbit from day to day. There are factors that influence the orbit unpredictably,
such as pressure from the solar wind, and predictably, like the gravitational
effects of the moon and planets. The ground stations of the Control Segment need
to determine the speed and position of each satellite with great accuracy so
that it can predict and describe the satellite's orbit unambiguously. Such a
description of the satellite clock parameters and its orbital characteristics is
called an ephemeris, and this information is uploaded to each individual
satellite. The ephemeris information can be updated twice per day as the
satellite passes over a ground station. When or if the ground station finds that
a satellite has wandered from its predicted position in orbit, the orbit is
re-computed and the data uploaded to the satellite. Since there is limited fuel
on board, it is only as a last resort that the satellite is physically moved
with the aid of its own engines. This happens when the orbit deviates so much
from the desired path that accurate prediction is no longer possible. When your
GPS receiver acquires information from a satellite, the ephemeris data is
received, and this is what allows

it to measure the time difference between when the signal was
broadcast and when it was acquired, so that it is possible to compute the
distance between satellite and receiver.

All the satellites broadcast information continuously on the
same two frequencies, the L1 frequency at 1575.42MHz, and L2 at 1227.6MHz. Cost
and bulk considerations cause most or all small receivers to utilise only the L1
frequency. The radiated power of a satellite transmission is not much more than
500W. Compare this with the radio in your microlight, putting out 5W. The
difference being that the satellite is at least 20 000 km distant, and if it
appears to be low on the horizon, it is much further away than this. The signal
arriving at your receiver is therefore barely distinguishable above the
background electronic noise.

The small non-directional antenna on the GPS receiver
recovers this extremely low level, noisy signal) and passes it to the receiver
where spread spectrum technology deciphers the signal. The advantage of
spread-spectrum is that it can extract a very low-level signal from background
noise, but it can only do so at the expense of speed. Data rates of 50 bits per
second are the norm. If a receiver needs to acquire all the information that a
satellite broadcasts, which includes ephemeris data and 'almanac' data, the
process will take more than 1 0 minutes to complete. Normally the receiver only
needs the ephemeris information from the satellite.

So, what influences the signal during the transit between
satellite and GPS receiver?