Hi I have a specific problem of accuracy of one GPS relative to another GPS over a distance of 30 - 50 metres apart. I suppose the radical change of thinking is that I dont need its location on the surface of the earth but its relative position to another point over this short distance. Can I achieve accuracy of <2cm? The maths is simple as I dont have to account for spherical modelling but can accept it as a flat surface.
Cheers
Good luck.
If you have a standalone GPS receiver your positioning error is on the meter level.
If you have surveying-quality equipment, maybe if you stand still for a long time you can get the distance down to 2 cm.
There are many reasons that you may get differences in readings even by two identical models.
There are augmentation systems that typically allow for 3cm accuracy. See this section of the Wikipedia article on GPS.
So you have two separate GPS receivers that are communicating with each other (or with a 3rd party), and you want to know how far apart they are. How similar are the GPS receivers? How far apart, timewise, do the two take their position measurements? How much control do you have over the receivers?
If you care about <2cm accuracy in a 30-50m range, GPS may not be the best solution for you. It'd take a bit more effort (and the equipment would probably cost more), but you could do 2d triangulation terrestrially rather than going all the way to space...
<2 cm, might be difficult, because the GPS might not even provide data with that kind of resolution.
So, you've got to have about 7 digits of precision below the decimal point to even be possible.
That puts it at about 0.000646790757 seconds (3600th of a degree). So, if your GPS doesn't provide that much precision, you can't even tell the difference between 2cm, regardless of whether the error is relative or not.
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So, sure, there's a lot of limitations in this analog system, there's lots of room for error to creep in. The article Eric J. linked is trying to reduce that error, but that's talking about the error of the system and such. But look at your GPS, it probably gives lat long coordinates. There's two principles involved here, Accuracy and Position. If I told you that my current position was 40 degrees north, and 112 degrees west, that would be an accurate, but imprecise position.
If I told you that my current position was 21.2212541341213432134512311312312312 degrees north and 65.1231340980193809810938049801980980 degrees west, that would be a precise, but inaccurate position. Both are potential issues here. How much precision does the GPS give you?
Lets say the GPS gives you a position of 32.4423 N (lets ignore East/West for now). In an ideal world this information would be perfectly accurate, but what the hardware is really saying is that the value is somewhere between 32.44225 and 32.4435. This isn't a limitation of accuracy, but that of precision. The variability in this system is .0001 degrees, which is http://www.google.com/search?hl=en&q=.0001+%2F+360++radius+of+the+earth++2+*+pi&aq=f&oq=&aqi= 11 meters. On the other hand, if the position is 32.4422934561, that's a variability of .0000000001 degrees, which is about a thousandth of a centimeter. So, if your GPS hardware did have that much precision, it would probably give you a similar accuracy error that you have now "10 meters" or something like that. That's because of the previously mentioned problems with the analog system (air density, humidity...).
The GPS system can't tell you how close it is, because it doesn't know. It's trying to tell you the absolute position.
But, if we have two GPS devices, that are presumably the same, we can assume (and that's probably pretty safe) that the error is probably the same between the two GPS devices. If say, they're 50 meters apart, the accuracy reported by the GPS software might be in the neighborhood of 10 meters, but we can probably get the relative distance between the two, as long as the GPS units report enough precision.
How much money do you have?
RTK-GPS will give you sub-cm relative accuracy between the two units but isn't cheap.
To get better than m accuracy you need to use the carrier phase to compare the actual radio wave between two receivers, this takes some fancy electronics and a fast data link between the units - you are probably looking at >$20K, but all the major survey GPS companies make units.
Or you can always build your own
It sounds like differential GPS might be what you're looking for. The idea is that you establish a base station, whose location is known very accurately (within centimeters). Then you take simultaneous readings at the base station and at the (nearby) "roving" point you're trying to measure. Then calculate the error in the base station GPS measurement, and apply that correction to the GPS reading at the roving station. The idea is that the atmospheric corrections for two nearby sites will be similar, so the correction needed at the base station should be close to that required at the roving station.
In theory, if the receivers are seeing exactly the same satelites then the relative distance between them should be fairly accurate shouldn't it? Otherwise, you'll have to use differential GPS or some other means.
If I'm not wrong, height variations might be more the problem. So I am doubting the accuracy. Differential GPS is probably your only option if you're going to use GPS.