Can a half-arsed method of picking time from a randomly chosen satellite and then using it to complete the work of triangulation / tetrahedrongulation / hyper-tetrahedrongulation, actually work?
I'm glad you asked. The delay in the transmission of GPS timestamps ought to be between about 67 ms (directly overhead) and maybe 85 ms (a satellite near the horizon, so add the radius of our planet). With a random pick you should expect up to +/-18 ms of error. And that makes the sides of your triangles +/-5400 km in error. That is to say, you're going to miss that airport.
Surely, one will quickly start averaging the incoming timestamps from all satellites, instead. But with just 12 sats in view, this isn't going to improve this method hugely. And hugely is what we need. Taking a few extra minutes is also no good. The sats take 12 hrs to cross the sky. Given only a few minutes, the constellation and the error of its averaged time will not change. With 12 hrs we are onto something, but then an annoying problem of the varying drift of our local timekeeper props up.
I'm afraid that the methods for multiple-equations for multiple unknowns is pretty much unavoidable, with time one of the unknowns.
Last edited by balsa model; 11th Jun 2020 at 13:29.
Reason: (added ", actually work?" to complete the opening question)