Finding true north in UAVs
The accuracy when following lines of longitude via GPS is easy enough to calculate. It's just a question of how much cross-track error you have relative to how long your baseline is (the distance you fly along the line of longitude).

Specifically, suppose you have a GPS receiver with an RMS error of 5m. This is in any direction, so it affects both the cross-track error and the length of your baseline. If you fly a nominal 100m north along a line of longitude as reported by the GPS, you'll have a cross-track error of up to 5m &times; &radic;2 = 7m. (The &radic;2 is applied because you have error in your start position, and error in your end position, too. These are assumed to be independent.) There will be a length error of up to 7m, too, but we can ignore that since its effect on the final answer is much less.

So, the overall error in your direction is up to 7m for the 100m you traveled, so the error in your concept of due north is \$\sin^{-1}\frac{7}{100}\$, or approximately 0.07 radians = 4.2&deg; RMS.

Since the cross-track error remains constant regardless of the distance traveled, if you double the length of the baseline, the error in the angle will be halved, and so on. If you fly 500m north, then your error will be less than &plusmn;1&deg;.



If you use an RTK-capable GPS receiver, the measurement error will be reduced by about two orders of magnitude &mdash; centimeters rather than meters. This would allow you to achieve much higher accuracy for a given baseline distance, or to use a shorter baseline for a given level of accuracy.

If your drone/UAV is large enough, you can mount two receivers on it and use a technique known as "short-baseline interferometry" to get an accurate heading measurement directly without any motion at all. The receivers need to be capable of giving you carrier phase measurements, and their antennas need to be on the order of 24" apart. One of my consulting clients has done pioneering work in this area.