Depends on the system. Typically, the older systems do not work like this. The GPS satellites only transmit a signal that contains their location information and the time. The device must collect several of these signals and then use trigonometry to calculate your real location in time and position. Yes there are relativistic effects due to the distance to the satellites and gravity.

For instance, in home lab electrical engineering, if a person wants a really good reference clock but cannot afford a cesium atomic reference, they can use a relatively cheap GPS system to build a referenced oscillator that is disciplined by the reference clock on these satellites. I think they are cesium too, but it has been awhile since Dave Jones made YT uploads on the eevblog about it. A Garmin bicycle computer is another example. It is triangulating the signals and plotting periodic waypoints with some basic averaging.

That said, WiFi routers and cellular towers are possible to use for similar triangulation. Maybe check out Hak5 if they are still around. It has been awhile since I looked them up, but they used to make pen testing red team stuff that will infer much about vulnerabilities.