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Sat Nav group test
I read with interest your article on satellite navigation (PCW January 2006 issue). I have been using Tom-Tom Mobile with my Nokia 6680 phone for a while now, I have it mounted exactly between the two dials in my car where it doesn't obstruct the window view and is inline with my view of the instuments.
I have built a Bluetooth GPS receiver into the dashboard, it sits under the plastic, and comes on with the ignition so that it cannot be seen. I always take my phone with me, so that aids the security and the fiddling with things that stops people using such a system after a while.
However, probably not the first to point this one out, but the process of determining your position with satellites is Trilateration. It differs from Triangulation because as you correctly point out, you know only the distance and not the direction of the satellite. Triangulation works by knowing where the lines cross, and to do that you need the direction.
A nice way I find to illustrate GPS and Trilateration is to think of it this way. If you know how far you are from something in 3d, you can be at any point on a sphere. If you also happen to know how far another satellite is, then you will have two spheres and this will provide you with a circle at the point where they overlap. So now you know that you are somewhere on that circle. If you add another satellite, you will find that it will intersect that circle in two points. So know you know that you are in one of two points. GPS can cheat and bet that you are on one rather than the other by guessing that you are on the surface of the earth. (rather than in a 200 mile hole or in space!) So it can cheat by using the earth as a sphere (for 2d).
Finally you'd need another satellite in order to get your 3D fix, as this would cross only one of the points. In practice, you cannot send a signal faster than light to say when you are transmitting and thus working out how far away the satellites are, so you need another satellite in order to factor this out. (its like 4 equations and 4 unknowns, you need a 5th to solve it). Unless its all gone horribly wrong, if you add more satellites, they should just reassure you that the equations were right, and you can start estimating accuracy and stuff.
I have built a Local Positioning System, which is very similar and works using sound for indoor positioning. We using this to help determine where people are for wearable computing and crime scene stuff etc.
James Cross
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