NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Navigator's Newsletter, and other forums.
From: James R. Van Zandt
Date: 2006 Oct 17, 22:45 -0400
From: James R. Van Zandt
Date: 2006 Oct 17, 22:45 -0400
Speaking of navigation forums, formal and printed and otherwise:
The sight reduction methods I have seen require an estimated position [1],
or give no error estimate [2], or both [3]. I think I have come up
with a new method.
I propose to use a three dimensional state and a *linear* Kalman
filter, with one update per sighting. If you have three sights, then
you don't need an estimated position at all. If you have only two
sights, you need only a very approximate estimate. Either way you can
get a proper error estimate so you can for example draw a 95 percent
error ellipse (assuming that you know the uncertainty of your
measurements).
(It does require inverting 3x3 matrices, so it's not well suited to
hand calculation.)
If someone remembers seeing something like this, I would appreciate a
reference. Otherwise I'll write it up in more detail.
- Jim Van Zandt
[1] C. De Wit, "Optimal Estimation of a Multi-Star Fix", Navigation v
21, n 4, Winter 1974-75, pp 320-325.
[2] M. F. A'Hearn and G. S. Rossano, "Two Body Fixes by Calculator",
Navigation v 24, n 1, Spring 1977, pp 59-66.
[3] altitude intercept method of Marcq St. Hilaire - i.e. one line of
position per sighting.
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