Geography
is about maps, history is about chaps, runs the old school saying. However,
chaps often have a good deal of difficulty with maps, and ladies even more so.
(This is not entirely a sexist remark; there is some scientific evidence for
this.) At any rate, deciding on a strange road where one has got to is one of
those situations which can cause a rift in the most happy of marital blisses.
For this reason alone it may be worthwhile considering the cost of a gizmo to
solve the mystery. Of course, it may also be useful to reach the intended
destination in time for dinner.
The
gizmo is a GPS (Global Positioning System) device, which may come as a small,
hand-held and relatively cheap contraption, or as a grand's worth of built-in
console with map display in colour and voice instructions as to where to go
next. How does it work and is it really worth it? More particularly, does it
mean that one can abandon buying all those Ordnance Survey maps?
My
declared interest in the subject is that I have an awful lot of Ordnance Survey
maps in the cupboard. This interest stems from my school days, where I reached
the dizzy heights of Colour Sergeant in the Combined Cadet Force. I was not
entirely soldier material, but our officers recognized that not all the cadets
were going to Sandhurst, so there was considerable indulgence for activities
which did not involve cleaning rifles. Thus after I had exhausted the advantages
of being camp cook I founded the Survey Section to map the school nature
reserve. In this pursuit I visited the Ordnance Survey printing press to gawp at
the amazing machines which generated these fantastically beautiful and accurate
maps.
A
surveyor knows that if you can determine your distance from known fixed points,
you can work out where you are. If, for example, you know that you are 300 km
(188 miles) from Plymouth and 140 km (88 miles) from London, you draw a circle
of radius 188 miles around Penzance on the map, and another of radius 88 miles
around London, and see where the two circles intersect. This turns out to be
either Coventry or the English Channel. If you are in a car, you will probably
opt for Coventry, but it is nice to make sure by confirming in addition that you
are 27 km (17 miles) from Birmingham.
The
fixed points are a number of satellites put into precisely specified orbits by
the American Department of Defense. There are 4 in each of 6 orbital planes
around the earth at a height of about 12,000 miles, with some spares available.
The arrangement is such that at least 5 satellites are always visible from any
point on the surface of the earth, which is as well for the pilot of an
aeroplane, who, by the same geometrical reasoning, needs the distance from a
fourth known point to determine whether he is 10,000 feet above the surface of
the earth or below it. It is logical to point out that three will do, if one is
prepared to calculate that some locations are obviously daft and therefore can
be eliminated. Bear with me a little longer, and the advantage of the fourth
will become clear.
The
key to finding your position in space on or around the earth is therefore
finding the distances from 4 satellites of known position, which is done by
timing how long it takes to send a signal from the satellite to your receiver.
Each satellite has its own signal pattern, which it sends at known times. The
receiver times the delay and converts it into distance, based on the signal's
travelling at the speed of light. Clearly, for this to work the clocks in the
satellite and the receiver must be synchronized. The satellite clocks are atomic
clocks, with errors of one second in a squillion years, but these cost tens of
thousands of pounds each, and are too big to fit in a hand-held device. What
happens next is a clever trick. The receiver, which has only a cheap quartz
clock, calculates that the 4 distances do not meet at any single point in space,
so it resets the clock, thereby shortening or lengthening all the calculated
distances, until a single meeting point is reached. When it has done this, you
have not only your exact position, but also the atomically exact time. Quite
amazing.
Inaccuracies
can creep in at any stage. The satellites may deviate from their assigned orbit,
so there are 5 ground stations which track their precise position and transmit
this information and any clock corrections to the satellites, which broadcast
this along with their identification code. The speed of light, which we need to
know in order to translate signal delay into distance, is less in the atmosphere
than in the vacuum of space. There are also errors due to the signal bouncing
off nearby cliffs or skyscrapers. Finally the Department of Defense built in a
randomness factor to increase the inaccuracy for civilians. This has now
officially been switched off, but the American military reserves the right to
switch it on again. The satellites actually transmit on 2 frequencies, one of
which is encoded and for the military only. The positional interpretation from a
dual frequency signal is so accurate that you could practically map the carrots
in your vegetable patch. For the rest of us an accuracy of within a few meters
is entirely acceptable. It has to be, because that is all we are going to get.
The exact accuracy is a matter of probability. For a single reading, the
probability is 95% that the indication is within 100 meters of the true
location. For readings over 12 hours, that comes down to less than 5 meters. The
accuracy can even be improved by comparing the signal at your position with the
signal at a known fixed point on the earth (differential GPS). Similarly, the
measurement of speed of movement can be very accurate, and GPS is a good way of
calibrating a speedometer.
Should
you buy a GPS receiver? If you don’t like maps, and if it is important to you
not to get lost, and if you don’t mind spending £200 to £1000, and if it is
important to keep ahead of the Joneses, then what are you waiting for? Myself, I
shall just go on collecting Ordnance Survey maps, and, when I plan to go abroad,
I shall buy the same maps there too.
Copyright PHP Harris 2003
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