In the end it always boils down to inertial frames of reference. Every object in free fall has it's own inertial frame of reference and any motion outside of that frame will be a relative measurement. For a system based on the GPS principle to work at least 4 satellites are required (details on how GPS works go to a different question please).
Each of these satellites carries its own inertial frame but you want to know your position in a frame of reference that's different from each of the satellites' ones. The first step to do this is to define an "global" frame of reference all the satellites can be referenced against. There are different ways to do this. A ground station would be the most straightforward one. But there are other ways too, and for a mission to an not yet inhabited planet these may be more interesting.
One possible method would be, that the satellites are communicating with each other (the GPS satellites currently in operations don't do this) establishing a frame of reference between them (let's call that Satellite Established Frame (SEF)), that's not strictly aligned to anything on the planet below. All location would then happen in that frame of reference. Pivot stations on the planet would constantly sample their position and from that derive a SEF to planetary coordinates mapping, which in turn would be distributed to mobile navigation receiver stations. Why do it that way? Because it gives you a working navigation system right at the moment you arrive at the planet's surface. It may be off by a few arcminutes until the exact location of the pivot station could be determined from astronomic measurements. With a system like GPS that depends on a working ground station you get reliable navigation only after the ground station has been established. With a self-establishing frame of reference, that is allowed drift you can use plain old, reliable Rubidium clocks on the satellites and nothing more. If a ground station is required, then a Cesium fountain clock or better has to be put into operation for the whole thing to be accurate.