NavList:

Robin

You wrote   
that 1 LoP defines a Confidence Ellipse with an infinite axis

I respectfully submit that I do not agree with your assertion.  A LoP is not an infinite line.  It is merely an approximation of a segment of a circle of equal altitude.  This circle cannot have infinite circumference.  Further, we must not ignore the very item which permits the LoP to be approximated with a line.  That is the azimuth to the body.   That further restricts the length to a segment of the circumference.  Yes, that is still fairly lengthy ellipse, but certainly not infinite. The axis along the LoP defined by the uncertainty in azimuth, the axis perpendicular defined by the uncertainty in altitude

Alex:  unless each of your LoPs has absolutely zero error (I do not see how this can be), then there is uncertainty which will yield an ellipse (albeit not infinite) of probability.  We cannot know the precise altitude, we cannot know the precise azimuth.  When we have two such LoPs, we can combine those uncertainties.  Surely, Alex, you cannot mean that there is no probability of your position being anywhere other than the crossing of the LoPs. Perhaps this discussion should be tailored to exactly what you mean by "Ellipse of Confidence".  

Brad