I had always assumed that GPS satellites were geo-synchronous, and that the process of resolving your location was simple trigonometry.
It turns out that GPS satellites are non-geo-synchronous - being in a medium earth orbit.
The following description of the calculation states:
GPS satellites transmit data continuously which contains their current time and position. A GPS receiver listens to multiple satellites and solves equations to determine the exact position of the receiver and its deviation from true time. At a minimum, four satellites must be in view of the receiver in order to compute four unknown quantities (three position coordinates and clock deviation from satellite time).
So then they have another go at explaining it:
Although usually not formed explicitly in the receiver processing, the conceptual TDOAs define the measurement geometry. Each TDOA corresponds to a hyperboloid of revolution. The line connecting the two satellites involved (and its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect.
Then they provide a picture:
Now it seems that my phone is doing all that.
My question is: Is there a simple way to explain GPS resolution? Something at the level of High School Physics, Calculus and Algebra.
The book "Exploring Black holes: an introduction to general relativity" contains a chapter with a project devoted to the GPS system. The book only uses basic Calculus and Algebra, but makes a few assumptions which can only be fully explained using the full theory of general relativity. But the necessary assumptions and physics are explained at a basic level in the book.
That particular chapter is based on two articles
Carroll O. Alley, "Proper Time Experiments in Gravitational Fields with Atomic Clocks, Aircraft, and Laser Light Pulses"
and
Neil Ashby,"Relativistic Effects in the Global Positioning System".