The third point can be misinterpreted to make it sound like gps involves a steady tone generated from a known location like more traditional navigation aids used in aviation, rather than clocks taking advantage of our understanding relativistic effects.
While Earth is in the Martian sky, and if the signal were strong enough, a viewer could average receiving signals from over half of the constellation rather than only half a dozen. Furthermore the time signals would originate from many of the satellites moving less orthogonally to the viewer and instead moving toward and away from the viewer.
Compared to measuring the sun relative to a changing horizon, it seems plausible that an extremely precise direction and altitude relative to Earth could give even more precise location on Mars.
While Earth is in the Martian sky, and if the signal were strong enough, a viewer could average receiving signals from over half of the constellation rather than only half a dozen. Furthermore the time signals would originate from many of the satellites moving less orthogonally to the viewer and instead moving toward and away from the viewer.
Compared to measuring the sun relative to a changing horizon, it seems plausible that an extremely precise direction and altitude relative to Earth could give even more precise location on Mars.