Delete comment from: Ken Shirriff's blog
In your first footnote, you say "First, ranging only determined distance, while GPS determines position in three dimensions and also the exact time"
Fundamentally, GPS also only determines distances, which it calls pseudoranges. Where it gets weird, and the reason for the "pseudo," is that they're distances in spacetime - each distance is affected by the difference between the satellite's clock and your clock.
With four of those pseudoranges (one for each dimension) and information about the locations of all of the satellites (which is transmitted continuously by the satellites themselves) you can do a bunch of math and determine your position in four dimensions. The geometric relationship between the satellites that you use in your computations has a huge impact on precision, though, so having more pseudoranges to choose from is always better.
Back when GPS wasn't a household word and the constellation was a lot smaller, there were frequently periods where there simply weren't four satellites in view, but you could still compute a fix from three pseudoranges if you had a geoid model and some non-GPS-derived knowledge of your altitude. The precision was pretty terrible, though, so in practice it made more sense to plan your GPS usage for times you could expect to see more signals.
May 5, 2022, 6:27:58 PM
Posted to The digital ranging system that measured the distance to the Apollo spacecraft