Starlink is an internet broadcasting service and is NOT designed to record or broadcast users location. The system is NOT GPS.
You have to know precisely where those 100s of satellites are to use them to determine your location. That is rather difficult to do when they are in a low Earth orbit. The reason GPS works is because the satellites are always above the exact same location. So your device knows exactly where is signal is coming from.
The accuracy is in the on-board Rubidium and Cesium clocks for GPS used to time the navigation signal...basic triangulation will not give you the nanometer accuracy you want. Triangulation uses the “TLAR” method...That Looks About Right. Also, GPS does not have just a navigation mission.
To my knowledge, StarLink does not have the time data programmed into the signal such that this is theoretically possible. Assume signal encoding does have the time data needed and that one has the homemade electronics to decode it out of the signal, the math is not trivial and takes awhile to work through. It would take multiple measurements and possibly needing a manual plot akin to using the advancing the plot technique used in dead reckoning.
Another mathematical method is via a sextant using time plus angle to the horizon. As with stars, this could be measured twice per day (unless it's cloudy) during nautical twilight. This would be a royal nightmare. Functionally, the StarLink satellites are moving at the speed of Ford GT vs a star moving like a VW Beetle speed. Big error is going to be introduced. The math is formidable to work through manually but is doable. Ship navigators would use an astrolabe, hour glass and many sheets of paper to do this for hundreds of years. In the 1700’s I believe it was, an English mathematician named Bowditch produced a very hefty book that shifted away from the complex math to look-up tables for each star, the moon and the sun.
With Bowditch, a mechanical chronometer on your wrist, star maps and a sextant, a skilled person on a boat can get their position within about 5-20 miles of error. On dry land that's not moving, accuracy is much better. Zero electronic anything. Perfect for the Zombie Invasion.
Also, keep in mind that the mathematics does not directly give you a point on a map and say you're standing here. Instead, it gives you a circle of position. That's because the math actually gives a position relative to the center point of the earth. When you project the point to the surface, this is a circle
Multiple measurements on multiple satellites give overlapping circles and your position is somewhere within the area where the circles overlap. Most of us have seen this on our cell phones or car nav system when driving in the mountains. Occasionally, a shaded circle appears around the car icon on the map. This is inducing that the number of satellites being tracked is less than the minimum needed to give the device's specified accuracy.
I've mentioned that the math is hard for any of the navigation options above. I've done math past basic calculus and candidly, when I got into celestial navigation I had trouble getting my brain around it. If I were to mechanically run the equations without understanding what was behind them I could certainly have just punched buttons on the calculator. My brain isn't wired that way though. Sidereal time is just plain weird to me. When I said the hell with the math detail and stuck with Bowditch, I was happy and functional.
Flash news or maybe not. For a number of years it has been well recognized that GPS satellites are increasingly vulnerable to antisatelite weapons in the event of major war. For maybe 10 years the US and EU have been talking about reactivating LORAN, which uses land based transmitters. The sides agree to the need and disagree on technical factors so no action. As an example, the US with LORAN-C had 4 or 5 transmitters in the continental US and these provided coverage for North America and for north of the equator, 3/4 of the Atlantic and 1/2 of the Pacific.