Fright level
Educate me.
I hope I have, else Google is your friend.
Well, sort of. It would appear that your model of GPS - of which I know nothing - is relying on a representation of a magnetic compass needle - albeit maybe a computer generated image of a needle - built in to it, which seeks Magnetic North just like the old E2B that hung from the windscreen pillar of the Boeing 747, and has actually nothing whatsoever to do with orbiting satellites, or obtuse mathematical equations ? Is this right ?
If so, then it is no better than the old alcohol filled compass bolted in front of the stick of the Harvard, or hung upside down from above the windshield of some aircraft, and read with a mirror, and I agree that it doesn't need to be actually bolted to the fore and aft axis of the aircraft, just occasionally aligned with it by holding it in a wavering hand, which might occasionally get it spot on. The heading it depicts is relative to its lubber line, as you correctly say, but only if the its lubber line and the aircrafts lubber line are parallel will you know the aircraft heading correctly. No ?
If this is not the case, then we are back to the the original question - How Does A GPS Work Out Heading ? and the question was HEADING, not Track Made Good. ?? HEADING is relative to North, either True or Magnetic, not movement over the ground, which is what the GPS computes.
Knowing ones heading, and track made good, and groundspeed and airspeed, then one can work out the wind.
A GPS uses the satellites to work out where it is, then a few milli-seconds, minutes or whatever units it is programmed to accept, it works out where it is again - then Bingo ! it now knows which way it was moving, and what speed it has achieved between the two points over the time it has taken to make the two points, i.e. groundspeed, and you know what airspeed you were flying,and what heading you were maintaining, and so the rest is just maths.
Using a sextant in a Boeing 707 I would fix a position using the stars, maybe half an hour later I would fix my new position by the same means, and providing the pilot had maintained a steady compass heading, the difference between where I now knew I was, versus the position where I had worked out that I would have been had there been no wind ( or more accurately the forcast wind that I has applied ) - the Air Plot - provided the correct wind vector to apply to the next required track to arrive at the next turning point ( 'waypoint' in Yuppiespeak )
The basics of navigation are no different now, the only difference is that I might slave away for 7 hours, producing a 'fix' by sextant every 30 minutes - and barely have time for a coffee - whereas the GPS does it in a nano-second, and continuously,whereas I drew a graphical representation on a chart - and actually created a visible triangle of velocities that could be seen, and measured.
Not a lot new under the Sun - all that's new is the means by way the information is derived.
Thanx.
P.s. Between the sextant and the GPS was INS ( inertial navigation ). The INS couldn't work out where it was, it had to be told where it was starting from, after which it used acceleration changes to work out where it was next - and hence calculated the same formulas to reach the same results. The Powers that Rule Our Lives could turn off the satellites at a whim - then where would you be ? INS was totally self contained, the World could be destroyed by a Nuclear Holocaust between leaving New York and arriving overhead London, and the INS would calmly continue to navigate blissfully unaware !! Happy Days.