NavList:

In the thread "The Future of Celestial Navigation: A British Viewpoint", Paul Dolkas commented on navigating on the surface of Mars and the Moon:

"If/when manned trips to the Moon & Mars take place, surface vehicles will need a celestial navigation system (automated or not)"

Well, for both places, since there's near perfect visibility from orbit, there's another option: air traffic control. Just stick a couple of satellites with good telescopes in orbit and photograph the targets on the ground to get their positions.

This ATC approach is an option that also exists for ships at sea down here on Earth (though not photographically and not in any unclassified program). Paul, I imagine you're familiar with this, but for anyone else, there are groupings of artificial satellites known as "NOSS trios". Originally this name referred to triangular grouping of satellites which spysat enthusiasts identified as "National (or Naval) Ocean Surveillance System" satellites. It is believed that these record all manner of radio emissions including "noise" from everyday electrical systems on ships at sea. By using three satellites and comparing the arrival delay, it's believed that these satellites could determine accurate positions for practically anything with a functioning electrical system out on the ocean. These satellites are observed as triangular groupings moving across the sky. They're fun to watch, and they've apparently spawned quite a few "UFO" reports. While the "NOSS trio" name was originally applied exclusively to trios of US intelligence satellites, it's also now applied to their US successors, which are pairs instead of trios, and also to similar groupings from other countries including especially various Chinese "NOSS trios" which have been launched recently. Navigation in a world of satellite "ATC" would consist of "requesting" your current position from the eyes in the sky.

Another option just turns the tables again. If you can observe a known satellite on a known orbit at a known time, your position on the ground is fixed exactly. On Earth visual observation of satellites suffers from many of the problems of celestial navigation --the biggest two being that you can't see them in daylight or when it's cloudy. But on the Moon and Mars, you can see satellites nearly all day long. So while building a lunar GPS system might be a bit too expensive, launching a dozen inert balloons would not be, and you could pin down your position with great accuracy and no horizon or artificial horizon required. It would work on Mars, too, and of course there we've got a little help from a natural satellite. The martian moon Phobos orbits in a relatively low orbit and simply observing its position relative to background stars will give an excellent position fix (except in the high arctic regions where Phobos is never visible). In fact, there's a nice little demo of this making the news this week. Here's Phobos transiting the Sun:
http://www.skyandtelescope.com/news/home/An-Annular-Eclipse-on-Mars-222074771.html

-FER
PS: The S&T editors have also just published a very good, basic guide to satellite observing for anyone new to the game:
http://www.skyandtelescope.com/observing/home/Sat-seeing_Tour.html

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