With the "stratolites" (or whatever you want to call them) 400 miles away and no more than 100,000 ft high the geometry is very good for position measurements but very poor for height measurements.
At the extreme range of 400 miles the elevation angle is no more than 2.7° above the horizon. This would increase the height error by a factor of over 20.
The vertical errors of GNSS measurements are already somewhat worse than position errors but an extra factor of over 20 would be intolerable.
For reasonably accurate height measurements some transmitters should be more than 30° above the horizon, which doubles the expected errors.
If this were to be achieved using "stratolites" some would need to be no further than about 40 miles (about 60 km) away.
Since you continue to pester and harp about details of a conceptual system, and continue to ignore my suggestion that "Take this reply, rather, as an answer to the question "Is it possible to create -- at this point, say, imagine -- a positioning system using balloons rather than satellites?" in response to the thought "
There is no possible way for balloons to create a global positioning system," let's examine your objections.
"400 miles away and no more than 100,000 ft high" - Where did you get 400 miles as the the extreme range? My post said 100-200-300 miles apart for ground stations and balloons should be able to reach a station within a 400 mile
diameter circle. (Seems like you just
wanted it to be radius, so that's what you decided it was.) Did I ever say that there was only one balloon every 800 miles (to get your imagined extreme range to every balloon of 400 miles)? No. With one balloon at 400 miles distant, there's another one directly overhead if I've decided to place them only at that spacing. But did I? No. I have resources and I put balloons every 50 miles. No, 20 miles. No, 10 miles. As it is a conceptual system, I get to make the rules.
What about the oceans you say? It's impossible to cover the oceans!
No. My conceptual system uses an array of tethered buoys like the ones that already exist.
Oh, and by the way, who gets to say that 20 times the existing height error is intolerable? You? No. It's my conceptual system. As stated it's "a" positioning system, not "a recreation of the specifications of a system that exists today."
There's only one thing that's intolerable in this conversation.