There are many problems with the traditional ground based compass swinging:
- should be done at cruise power but cruise RPM often can't be achieved on the ground
- hard to line up the plane accurately
- a hassle to do in bad weather, or at grass locations when the grass is soft
- compasses can be heavily affected by electrics e.g. alternator load, which lights are on, etc. Wingtip-mounted fluxgate magnetometers tend to be a lot better but all these things are affected by e.g. a steel hangar 50-100m away.
As a result most compasses are way off, notwithstanding the deviation card carrying impressive figures like 1 degree max error.
It is intuitively obvious one could use the highly accurate GPS track for this. Suprisingly, I did not find much on google... there is the usual "TAS from GPS" stuff like
this, which is commonly used for calibrating one's speedo.
In zero wind, track=heading. But how can you be sure there is no wind aloft? Fly two reciprocal headings, and if this yields reciprocal tracks, then either wind=0 or you are flying in line with the wind, and in both cases track=heading.
If there is wind, it will usually be unknown, but if one flies reciprocal headings and increases them (say 15 degree increments) until one is seeing reciprocal tracks, then you have nailed the above case.
Unfortunately, a compass has one screw for N-S adjustment and another screw for E-W adjustment, so one really wants a method which yields more or less direct N-S and E-W headings.
It is hard to explain without a diagram, but it is fairly obvious that if you fly N-S reciprocal headings, and (assuming there is wind) you get
non-reciprocal tracks, then your compass error will be determined from the assymetry between the non-reciprocity of the tracks and the headings being flown, and you can set this error directly on the compass. Then repeat this for E-W.
Example:
Fly 360 and 180.
If the track is 360 and 180, you have no (relevant) wind so set the compass to 360/180 (the easy case).
If the track is 010 and 170 (obviously a westerly wind from 270) then the non-reciprocity is symmetrical about the heading, so set the compass to 360/180 as before.
If the track is 008 and 168 (obviously a slight southerly component in the above wind) then your actual heading is 358.
I hope I got that right, but it seems a useful method.
The above works to a first order accuracy i.e. the wind effect is small relative to your TAS. If you fly at 50kt and the wind is 50kt, the geometry becomes quite complex, and possibly needs and iterative solution.