GPS Overview Part 3 - GPS System Operation
The original theory behind Location-Based Services -
or LBS - is to help you find out where you are or where something
else is.
One part of LBS is the GPS satellite
constellation. The following overview describes the history and workings
of GPS, as well as its uses and the future for it.
The basic idea behind GPS is to use satellites
in space as reference points for locations on earth. With GPS, signals
from the satellites arrive at the exact position of the user and are
triangulated. This triangulation is the key behind accurate location
determining and is achieved through several steps.
Suppose we measure our distance from a satellite and
find it to be 11,000 miles (how it is measured is covered later). Knowing
that we're 11,000 miles from a particular satellite narrows down all the
possible locations we could be in the whole universe to the surface of a
sphere that is centred on this satellite and has a radius of 11,000 miles.
Next, say we measure our distance to a second
satellite and find out that it's 12,000 miles away. That tells us that
we're not only on the first sphere but we're also on a sphere that's
12,000 miles from the second satellite, i.e. somewhere on the circle where
these two spheres intersect. If we then make a measurement from a third
satellite and find that we're 13,000 miles from that one, that narrows our
position down even further, to the two points where the 13,000 mile sphere
cuts through the circle that's the intersection of the first two spheres.
The two possible locations
So by ranging from three satellites we can narrow
our position to just two points in space. To decide which one is our true
location we could make a fourth measurement. But usually one of the two
points is a ridiculous answer (either too far from Earth or moving at an
impossible velocity) and therefore can be rejected without a measurement.
How the satellites actually measure the distance is
quite different from determining your position and essentially involves
using the travel time of a radio message from the satellite to a ground
receiver. To make the measurement we assume that both the satellite
and our receiver are generating the same pseudo-random code at exactly the
same time. This pseudo-random code is a digital code unique to each
satellite , designed to be complex enough to ensure that the receiver
doesn't accidentally sync up to some other signal. Since each satellite
has its own unique Pseudo-Random Code this complexity also guarantees that
the receiver won't accidentally pick up another satellite's signal. So all
the satellites can use the same frequency without jamming each other. And
it makes it more difficult for a hostile force to jam the system, as well
as giving the DOD a way to control access to the system.
By comparing how late the satellite's pseudo-random
code appears compared to our receiver's code, we determine how long it
took to reach us. Multiply that travel time by the speed of light and you
obtain the distance between the receiver and the satellite. However this
calls for precise timing to determine the interval between the code being
generated at the receiver and received from space. On the satellite side,
timing is almost perfect due to their atomic clocks installed within each
satellite. However as it would be extremely uneconomical for receiver to
use atomic clocks a different method must be found.
GPS solves this problem by using an extra satellite
measurement for the following reason: If our receiver's clocks were
perfect, then all our satellite ranges would intersect at a single point -
our position. But with imperfect clocks, a fourth measurement, will not
intersect with the first three satellite ranges. So the receiver's
computer will then calculate a single correction factor that it can
subtract from all its timing measurements that would cause them all to
intersect at a single point. That correction brings the receiver's clock
back into sync with universal time , ensuring (once the correction is
applied to all the rest of the receivers’ measurements) precise
positioning.
As would be expected, a variety of different errors
can occur within the system, some of which are natural, whilst others are
artificial. First of all, a basic assumption, the speed of light, is not
constant as this value changes as the satellite signals travel through the
atmosphere. As a GPS signal passes through the charged particles of the
ionosphere and then through the water vapour of the troposphere it gets
slowed down, and this creates the same kind of error as bad clocks. This
problem is tackled by attempting to use modelling of the atmospheric
conditions of the day, and using dual-frequency measurement, i.e.
comparing the relative speeds of two different signals. Another problem is
multipath error , this is when the signal may bounce off various local
obstructions before it gets to our receiver. Sophisticated signal
rejection techniques are used to minimize this problem.
There are also potential problems at the satellites.
Minute time differences can occur within the on-board atomic clocks, and
sometimes position (ephemeris) errors can occur. These other errors
can be magnified by a high GDOP "Geometric Dilution of Precision"
This is where a receiver picks satellites that are close together in the
sky, meaning the intersecting circles that define a position will cross at
very shallow angles. That increases the grey area or error margin around a
position. If the receiver picks satellites that are widely separated the
circles intersect at almost right angles and that minimises the error
region. Obviously good receivers determine which satellites will give the
lowest GDOP.
Finally up to recently there was another ,
man-made source of errors. The U.S. was very mindful of the fact that
terrorists and unfriendly governments could use the accurate positioning
provided by GPS and so intentionally degraded GPS’s accuracy. This
policy is called Selective Availability or SA. This involves the
DOD introducing some "noise" into the satellite's clock data
which, in turn, adds noise (or inaccuracy) into position calculations. The
DOD may also has been sending slightly erroneous orbital data to the
satellites which they transmit back to receivers on the ground as part of
a status message. Together these factors made SA the biggest single source
of inaccuracy in the system. Military receivers used a decryption key to
remove the SA errors and so they were considerably more accurate.However,
effective May 2, 2000 selective availability has been eliminated. The
recent terrorist attacks on America have not changed this position. This
is due to the fact that civilian uses of GPS have become critical across
the world, and because the United States Department of Defence now has the
technology to localise the control system to deny GPS signals to selected
areas.
Using a modified form of GPS called Differential
GPS (originally initiated by the U.S. Coast Guard to counter the
accuracy degradation caused by Selective Availability) can significantly
reduce the above errors. Even with SA eliminated, DGPS continues to be a
key tool for highly precise navigation on land and sea. DGPS can yield
measurements accurate to a couple of meters in moving applications and
even better in stationary situations. Differential GPS involves the
co-operation of two receivers, one that's stationary and another that's
roving around making position measurements.
As each GPS receivers use timing signals from at
least four satellites to establish a position then each of those timing
signals is going to have some error or delay depending on what sort of
problems have occurred it on its journey down to Earth. Since each of the
timing signals that go into a position calculation has some error, that
calculation is going to be a compounding of those errors.
However if two receivers are fairly close to each
other, say within a few hundred kilometres, the signals that reach both of
them will have travelled through virtually the same slice of atmosphere,
and so will have virtually the same errors
This means that you could use have one receiver to
measure the timing errors and then provide correction information to the
other receivers that are roving around. This allows virtually all errors
to be eliminated from the system.
The reference station operates by receiving the same
GPS signals as the roving receiver but instead of working like a normal
GPS receiver it uses its known position to calculate timing, rather than
using timing signals to calculate position. Essentially determining what
the travel time of the GPS signals should be, and compares it with what
they actually are. The difference is an "error correction"
factor. The receiver then transmits this error information to the roving
receiver so it can use it to correct its measurements.
Since the reference receiver has no way of knowing
which of the many available satellites a roving receiver might be using to
calculate its position, the reference receiver quickly runs through all
the visible satellites and computes each of their errors. Then it encodes
this information into a standard format and transmits it to the roving
receivers. The roving receivers can then apply the corrections for
particular satellites they are using. The United States Coast Guard and
other international agencies are establishing reference stations all over
the place, especially around busy harbours and waterways.
There are also different kinds of DGPS, for use when
users don’t need precise positioning immediately. This is termed Post
Processing DGPS, and is used when the roving receiver just needs to
record all of its measured positions and the exact time it made each
measurement. Then later, this data can be merged with corrections recorded
at a reference receiver for a final clean-up of the data, meaning you
don’t need the radio link required in real-time systems. Another form of
DGPS, called Inverted DGPS, which is used to save money when
operating a large fleet of users. With an inverted DGPS system the users
would be equipped with standard GPS receivers and a transmitter and would
transmit their standard GPS positions back to the tracking station (the
main office). Then at the tracking station the corrections would be
applied to the received positions.
This is a new version of GPS that can eliminate
errors even better than other forms. Recall that a GPS receiver determines
the travel time of a signal from a satellite by comparing the pseudo
random code it's generating, with an identical code in the signal from the
satellite. The receiver slides its code later and later in time until it
syncs up with the satellite's code. The amount it has to slide the code is
equal to the signal's travel time. The problem is that the bits (or
cycles) of the pseudo random code are so wide that when the signals sync
up there is room for error. Survey receivers are better as they start with
the pseudo random code and then move on to measurements based on the
carrier frequency for that code. This carrier frequency is much higher so
its pulses are much closer together and therefore more accurate. At the
speed of light the 1.57 GHz GPS signal has a wavelength of roughly twenty
centimetres, so the carrier signal can act as a much more accurate
reference than the pseudo random code by itself. And if it can get to
within one percent of perfect phase like you expect with code-phase
receivers you can (theoretically) obtain 3 or 4 millimetre accuracy.
In essence this method is counting the exact number
of carrier cycles between the satellite and the receiver. The problem is
that the carrier frequency is hard to count because it's so uniform. Every
cycle looks like every other. The pseudo random code on the other hand is
intentionally complex to make it easier to know which cycle you're looking
at. But Carrier-phase GPS tackles this problem by using code-phase
techniques to get close. If the code measurement can be made accurate to
say, a meter, then we only have a few wavelengths of carrier to consider
as we try to determine which cycle really marks the edge of our timing
pulse. Resolving this carrier phase ambiguity for just a few cycles is a
much more tractable problem and as the computers inside the receivers
increase in processing power and functionality it's becoming possible to
make this kind of measurement without all the steps that survey receivers
go through.
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