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This question and answer has got me thinking. Would one or more ground stations be necessary (or even just very beneficial) for a GPS-like system to operate around Mars?

The atmospheric issues are much smaller, but is a planet-fixed set of clocks still required or at least of strong benefit?

edit: I'm thinking that if a ground station is necessary computationally, then as long as the satellites could communicate amongst themselves in some way, they could construct a mathematical (virtual) ground station and solve for its location without it actually existing. Wouldn't the solution be unique? If not, what am I missing?

But if it's necessary observationally - I mean - if it's a fixed radar station measuring the position of the satellites, I still don't understand why they can't simply measure each other. It still seems like it would be sufficiently constrained to have a unique solution for all of their orbital elements. What is the unknown that a ground station is needed to find?

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    $\begingroup$ Yes, according to Mark Adler (and he would know) from another related thread: There will need to be a fixed ground station to update the orbital elements of the satellites to sufficient accuracy. He includes a links to Deep Space Atomic Clock (DSAC) regarding precision timekeeping and I'd add to it that there was recently a Von Kármán lecture on the topic that is worth watching, too. $\endgroup$
    – TildalWave
    Feb 8, 2016 at 2:52
  • $\begingroup$ This is fascinating reading - thank you for the links. The link to the Deep Space Atomic Clock page within that comment is also helpful. $\endgroup$
    – uhoh
    Feb 8, 2016 at 3:48
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    $\begingroup$ "A" ground station, as in just one? Just as multiple satellites are needed for a receiver to compute its position, wouldn't multiple fixed ground stations be needed to compute the positions/orbits of the satellites? $\endgroup$
    – Anthony X
    Feb 8, 2016 at 3:51
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    $\begingroup$ To get "GPS" accuracy, yes. As I recall, our current "map-tie" error, the uncertainty between inertial space coordinates and coordinates on a map of surface features, is a few hundred meters. You would need at least one ground station with a known location on a map to resolve that. If you're happy with an error of a few hundred meters, then you would not need a ground station. $\endgroup$
    – Mark Adler
    Jun 14, 2016 at 10:21
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    $\begingroup$ @MarkAdler OK I see I think - so the inertial system refers to what the satellites establish (which have been augmented with communication and computation capabilities, (and possibly some optics)). If I had a GPS-type receiver for this constellation, I might know "my place in the universe" (I mean ICRF), but not know my Global Position on Mars very accurately. So with these hypothetical, augmented satellites, the final task of the ground station is to establish where IT is - i.e. the ground! OK this is very helpful - thanks! $\endgroup$
    – uhoh
    Jun 14, 2016 at 13:31

1 Answer 1

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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.

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  • $\begingroup$ So are you saying "yes" or "no"? What is a "pivot station on the planet" and why is it different than a ground station? $\endgroup$
    – uhoh
    Jun 17, 2016 at 23:25
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    $\begingroup$ @uhoh: A pivot station would serve as a receiver location with a "known" location. Say you place a pivot receiver at planetary coordinates 0N0E. The SEF is slowly drifting around, so for that location you get SEF coordinates depending on time. Distribute the difference between to the other receivers and they can convert beck from SFE to planetary coordinates. So why is this not a ground station? Because a ground station would be controlling the satellites (update their clocks or ephemeris data in their navigation signals). A pivot station may simply broadcast directly to the other receivers. $\endgroup$
    – datenwolf
    Jun 17, 2016 at 23:55
  • $\begingroup$ @uhoh: So the difference between a pivot station and a ground station is: Does it control the operational parameters of the navigation satellites themself? If it does (by adjusting the clocks, measuring their orbital parameters and updating their transmission), in short does the whole system hinge on its proper operation, then it's a ground station. If it's simply acting as a point of reference but is passive against the satallite system, then it's a pivot station. Either way, you need some piece of equipment that provides a relation between the reference frame of the satellites and the ground $\endgroup$
    – datenwolf
    Jun 17, 2016 at 23:59
  • $\begingroup$ OK so the pivot station is, roughly speaking, at minimum, GPS receiver and a radio (or optical) transmitter that sends the solution back to the satellite network. The "net" can calculate the drift and difference. This is to fix the "earth-tie" error @MarkAdler mentions. And 0N0E means 0.0N, 0.0E - i.e. near the equator so you can reconstruct the planets rotation. Have I got it essentially right? $\endgroup$
    – uhoh
    Jun 18, 2016 at 0:04
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    $\begingroup$ @uhoh: Yes, you got it. Technically you could equip the navigation satellites with star alignment optics to fix their coordinate system against the sky – and it would make a lot of sense. But for planetary coordinates you'd still have to measure the alignment of the planet against the sky then, or have some planet reference frame establishing pivot stations (which could be located at arbitrary locations, of course). $\endgroup$
    – datenwolf
    Jun 18, 2016 at 8:22

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