NavList:

Antoine C, you wrote:
"By the way, an almost similar problem has already been submitted ..."

That was an occultation puzzle. Of course, there is some common ground in any navigation puzzles involving the Moon. Then again, you could just as easily say that the problem that I have described here is completely analogous to every two-body star fix ever posted, and we NavList folks are blind, dumb fools for not seeing it! After all, the limb of the Moon is nothing more than the "horizon" of the Moon viewed from a great distance. In this photographic puzzle we are measuring angular altitudes above the Moon's horizon --clearly, that's just like any two-body fix with a pair of altitudes above the sea horizon. Therefore this is trivial, and any child with a slide rule should be able to get a position fix after a few moments of reflection. 

And maybe that's the whole point?? Conceivably that's why I brought it up: to compare so that we see the benefits of the similarity and to contrast so we recognize the practical limits of that similarity. :)

Antoine, you added:
"I differ from your view-point in the sense that the cones "apexes" are the centers of the stars themselves and not the Moon Center. Hence such cones are virtually not different from cylinders since the stars are so far away. "

It depends on how we look at things. What do we choose to include as part of the observation, and what can we choose to see as a correction to the observation? Of course normally when we think about occultations, it's convenient to imagine the Moon casting a sort of shadow with each star as an exceedingly distant point-like light source. Those shadows are effectively cylinders. Occultations lend themselves easily to this "cylindrical" perspective. But lunar distance angles can be interpreted as cones of position, and this, you will find, can be a fruitful, productive point of view for several reasons. I won't belabor it. You'll see for yourself, of course.

You concluded:
"this "worsens" the situation and we are facing a most unfavorable environment with a problem quite ill-conditioned here. Nobody's fault, just the environment here."

I think you'll find it's not as bad as it first appears. Give it a go. Or you could look at the very nice error analysis in the PDF that Modris Fersters has created. The error ellipse, assuming his diagram is what it appears to be (and no doubt, it is), would be about 2.5 times longer in the direction towards the Moon as it is in the perpendicular dimension. Not great, but not terrible either. :) Do you agree with his position fix, nearly enough? Do you agree with his error analysis?

Frank Reed