A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2018 Oct 19, 11:17 -0700
It's June 15, 2019. You're sailing from New England to Bermuda, and you have chosen to use celestial navigation. To start with an easier case, let's suppose you are becalmed and you are not in the Gulf Stream or an eddy (so currents are minimal).
At 1540 the Sun bears 135° true. You get a fair altitude and then wait for local noon. Around 1640, you get a noon altitude, and you're very happy with it. Then an hour later at 1740 you get another decent altitude when the Sun bears 225°. That's a full 90° change in azimuth from the first to the third sights so you can plot a nice fix. But let's throw a wrinkle into this. At the times of the first and third sights, your boat was bouncing around in some swells and you have much less confidence in those sights. You are able to assign "confidence weights" to your sights: you rate the noon sight as a ten (solid confidence) but the other sights are only fives.
So how do you process these sights? How do you get a fix from them? In this case it's relatively easy because the geometry is trivial. You would have a nice symmetrical triangle, and you would nudge the fix closer to the noon line side of the triangle. But what's the general case? Assuming you're familiar with the standard least-squares methodology as detailed in the Nautical Almanac, there's a simple generalization. Double up (or otherwise multiply) the lines of position in proportion to the confidence weight. In the case at hand, if you like the noon sight twice as much as either of the other two, then treat it as two identical sights at noon. It's not a three-sight fix with one LOP at double weight -- it's a four-sight fix with all LOPs treated equally. The math will then move the fix closer to the noon-derived latitude in a mathematically consistent fashion. It's just that simple. And this works with much less obvious geometry than my simple symmetrical example.