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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