Pass notes on the basics of GPS - an informal tutorial.
So, what does GPS stand for?
Global Positioning System. It's a way of pin pointing where you are without having to work it out using a map, compass, the stars and so on. The main thing you need is a GPS receiver, which can be hand-held or fitted into a vehicle. It gives you your latitude and longitude, with an accuracy of down to less than a centimetre in some cases.
But I know where I am, so what's the problem?
GPS is used by all sorts of people in situations where knowing
your location is important and not always easy. A boat at sea,
for example, needs to avoid dangerous rocks and stay in the right
shipping channels. If it's dark and cloudy, it can be difficult
to use traditional methods of navigating, so GPS is vital.
Who else uses GPS?
Planes, trains and automobiles, for a start. The emergency services. Hikers can use it to stay on the right route, and satellite navigation in cars uses it, so the driver doesn't have to keep looking at a map. It can also be used to automatically monitor the position of a vehicle, so that its movements can be tracked. The whole GPS system was set up for military purposes by the US Department of Defence.
So, it involves satellites?
Right. There are 24 GPS satellites in orbit around the earth. Usually there are a few more, as spares in case one breaks down.
And just where are they, these satellites?
They orbit around the Earth at a height of about 11,000 miles. They are arranged in 6 different orbits, with 4 satellites in each orbit. Each of the orbits is tilted at 55 degrees to the Equator.
Explain that bit, if you would...
It means that a satellite's path might cross the Equator over Brazil, say, then reach a latitude of 55 degrees North somewhere around Moscow. Then it crosses the Equator at the opposite point on the Earth's surface to the last time, which in this case would be Indonesia, and continues to 55 degrees South - over the South Pacific - before passing over Brazil again.
Must take a while...
Not really. A complete orbit takes about 12 hours. They go like a rat up a drainpipe, at more than 7000 miles an hour.
Hang on a minute - how do you use something that's moving that fast to find your location? I know you can work out your position by taking compass bearings to some fixed points on a map, like a church or a mountain.
That's called triangulation.
I haven't finished yet. I also know you can use the position of stars to navigate, if you take account of the Earth's rotation. Is that how it works?
No. GPS doesn't work by taking bearings, it works by comparing your precise distances from several satellites at any one moment in time, which is called trilateration.
That's easy for you to say - what's the idea?
Let's say you woke up by the side of the road in a strange place, with no idea at all where you were...
That did happen to me once, actually.
Yes, maybe we shouldn't go into that. You get the picture anyway - you've got a map with you, but you need to work out where you are on it. Using your skill and judgement, you notice a road sign that says "Birmingham 70 miles". That's helpful, because it puts you somewhere in England or Wales, 70 miles from Birmingham. You could use a pair of compasses to draw a circle on your map with its centre at Birmingham and a radius of 70 miles. Now you know you must be somewhere on the circumference of that circle. That could mean you were near Llanidloes, Manchester, Lincoln, Huntingdon, Hemel Hempstead, or Bath, for example.
It's not a lot to go on, is it?
It's a start. Now let's say you see another road sign that says "York 100 miles".
I'm not in Bath, am I?
Clearly not. If you draw another circle on your map, with the centre at York and a radius of 100 miles, you'll see that it crosses the first one in only two places, near Chester and near Peterborough. You must be in one of those two places.
I'm impressed. I've got a feeling I should be looking for another road sign.
Absolutely. Let's say you see one saying "London 80 miles". Another circle on the map...
...centred on London, radius 80 miles.
Right. You'll see that it makes your location near Peterborough.
This is brilliant. A map and pair of compasses seems a bit low tech, though.
As long as you know the coordinates the latitude and longitude of the other places and the distances to them, you can calculate your coordinates using the mathematics of trigonometry.
Aha! But these satellites are in space, not on the ground. That must be more tricky.
Same idea, extra dimension. Imagine fixing a point in three dimensions in a room - perhaps it's where a particularly intelligent fly is hovering. If the fly works out that it is two metres from the light bulb, then it knows it must be somewhere on the surface of a sphere, radius two metres, centred on the bulb. If it's also two metres from the light switch, it must be somewhere that the first sphere intersects the second, which gives a circle in the air.
This is some fly you've got here...
Stay with me on this... A measurement of three metres from the TV on/off button narrows it down to two points on that circle and a fourth measurement, perhaps from the electric socket in the corner, tells it exactly where it is.
I get it. But tell me this, if you're so smart. Measuring distances to major cites and light bulbs is one thing. If I've got a GPS receiver, how does it measure the distance to a satellite that's buzzing along at 7000 miles an hour? Ha!
Ready for the really clever bit?
Is this the "Here comes the science" moment?
Could be. What happens is that the satellite constantly sends out pulses of information as radio waves, and the receiver picks these up.
I'm with you 100% so far.
Each pulse contains details of the satellite's exact location in three dimensions at the moment it sent the pulse, and also the exact time the pulse was sent. The receiver compares the time the pulse was sent from the satellite with the time it arrived at the receiver. The difference tells it how long the journey took. Radio waves, like all electromagnetic radiation, travel at the speed of light, which 186,000 miles per second. This means the receiver can calculate its exact distance from the satellite, based on the length of time the radio waves took to arrive.
What sort of travel times are we talking about here?
A satellite right overhead would be about 11,000 miles from the receiver, so the radio waves would take around 0.06 that's six hundredths - of a second. Satellites over other places will be further away, so their signal takes slightly longer to arrive.
So it does this for several satellites?
Oh yes. As long as it can get information from 3 satellites it can calculate latitude and longitude reasonably well. A fourth fix allows it to calculate altitude as well that's your height above sea level and make a more accurate calculation of the coordinates.
Very clever. Sounds like a case of "synchronise watches".
Yes, the time measurements have to be very accurate indeed. The satellites have atomic clocks on board, accurate to within 3 billionths of a second. The receiver needs to be accurate too, but atomic clocks are hugely expensive, so GPS receivers contain quartz clocks, which are less accurate. However, the information that the satellites send out includes signals that help keep the quartz clocks in the receivers synchronised with the atomic clocks. Even so, the software in the receiver has to perform a few tricks to compensate for errors that can occur. The receiver also has stored data about where the satellites should be at any moment.
OK. And what makes the satellites so sure of where they are all the time?
The satellites' orbits and the information they send out are monitored by five ground stations around the world. They look for any signs of inaccuracies in the satellites' data and upload any necessary corrections to the satellites via four large antennae. The master control station is in the USA, at Schriever Air Force Base, near Colorado Springs, Colorado.
Well thank you for that. I have to say I have developed a burning thirst for more knowledge about GPS satellites. What can I do?
You could have a look at the satellite fact sheet and the links list for more resources, and see the
case studies on this site, for examples of how GPS technology is being used
in vehicle tracking.