A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Hakel
Date: 2017 Jan 19, 12:58 -0800
I did convergence tests like these when I first coded the NA sight-reduction method into the spreadsheet many_body_fix.xls. I created a simple symmetric example with two equal-sized LOPs crossing at 45° west at ~25° north and south, which are calculated directly (see attached lops.png). Then you can enter the same two LOP data into the many-body spreadsheet, vary the AP, and see how the solution changes. It remains remarkably stable (I hardcoded 4 iterations). As the AP latitude approaches the equator the results get crazy for a while but eventually, once you move the AP to the the southern hemisphere, they start to converge to the other crossing. This method is also nice to tell you that you can trust the result when the residual distance in the yellow cell is small enough.