A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2015 Feb 18, 18:43 -0800
You beat me to it in posting this but here are some additional thoughs and comments.
The 2 parameter least squares fit was obtained with the method given in the Nautical Almanac in section 11 entitled “Position from intercept and azimuth by calculation”. The result was checked independently using the minimization functionality available in the Excel Solver in the attached spreadsheet.
In this exercise I was also interested in seeing how well the 3 parameter fit described in http://fer3.com/arc/m2.aspx/Irregular-Quadrilateral-Center-Stuart-feb-2015-g30219 does. This assumes that there is an unknown constant offset, -D, present in all the sights. The results suggest that you have taken great care to eliminate any significant systematic error or offset. Note that if you add the same constant offset to all of the intercepts, the 3 parameter fit returns the same value for X, Y and adjusts D accordingly.
It might be an interesting to do a real double-blind experiment and introduce an unknown index error in the sextant perform a series of sights and then do the 3 parameter fit.