Side note: How would Cell phone location detection work for US troops in the Gulf War?
Well, I haven't had the pleasure of knowing many soldiers who served in the Gulf War.
So I couldn't say.
While I haven't either, I have had the pleasure of talking to people who are experienced with GNSS, cell phone location detection and/or satellite communication.
So I can say: It wouldn't have worked.
Cell phone location detection is (to a large part) done on the network side, i.e. location data can easily be refused - quite likely if you don't have your own or at least a "friendly" network at your location.
See my earlier post:
3. Being independent of ground installation (it was originally a military system - one usually neither relies on enemy cell towers nor does one get the chance to build own cell towers in enemy territory)
The same is true for any other type of signal - if you don't control the transmitter, you can be denied service.
This might change in the future, but so far (and even more so when the US set up GPS) satellites were safe in orbit.
And unlike any ground-based transmitter they can be used in hostile territory as they don't need to actually be there.
=> "Ground-based GPS" wouldn't have worked for US troops
Just as it wouldn't work for e.g. seagoing vessels, as there's simply is no ground to base anything on.

I never wrote that GPS devices like Garmin, TomTom, or Magellan, require cell phone location devices to operate.
Indeed, as far as I recall, you didn't. However, if they don't ...
what would they need to operate? The OP's question was, after all:
if there is no satellite how GPS works?
There was a lot of - logically sound - explanation how it would work
with satellite based GNSS.
GNSS is well documented and the math/physics would be the same for round or flat earth.
Pick a smartphone app like GPSTest. It's open source on github, so you can verify, that it's actually doing what's it claims it's doing.
It will list and graphically display the available GNSS signals and the corresponding location.
As it's performing the calculations based on satellite positions and signal characteristics, it can only get a correct location fix if the satellites are where they are reporting to be in orbit.
It provides correct locations => satellites, not ground-based transmitters.
Still im curious ... does anyone have a sound explanation how GPS would work without satellites?
(i.e. GPS as we actually experience it, not other positioning methods)
I surmise that signal broadcasting positions are in much the same locations as cell phone towers.
Do have any more information to substantiate your conjecture?
iC