NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: John Karl
Date: 2013 Mar 20, 14:51 -0700
Hanno,
The fix problem that we've all (I think all) been discussing uses St. Hilaire LOPs. In this method the azimuths are known, and are exact (as accurate as the almanac). The only uncertainty is in the altitude measurements, equivalently the intercepts. (There is the departure of the straight-line LOP approximation from the circular LOP, but that's negligible for our topic).
But you do raise an interesting point: What is the probability distribution for the two-body fix which solves directly for the fix's lat & lon (as discussed in my book on p. 101, Revised & Expanded Ed.)?? Because we'd assume circular distributions for each of the two altitude measurements, I expect the resulting distribution to be circular also -- quite different from the cocked hat (shown below).
Maybe I'll think about calculating that -- and maybe not....
Interesting....
JK
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