They could use UWB positioning systems. Accuracy is still not the best, but power consumption is very low and range more than adequate for a small base camp like the landing area. Solar power alone should be enough to power each beacon during Mars' daytime.
Not sure what techniques exactly you’re referring to, but the commonly used techniques for GPS enhancement (e.g. RTK [1]) are not simple distance measurements between GPS receivers and base stations but rather both stations measuring the satellite signal and using the difference of the signal in both locations to improve position estimates.
I imagine it’s possible to set up a ground-based network, but you would need a high density to cover large surfaces (you want to see at least four stations from every position). I also imagine that it would be difficult to get accurate vertical positions if the stations are all in the same horizontal plane.
https://www.firaconsortium.org/discover/how-uwb-works