NavList:

Hi Josh,

You diagnosed the situation perfectly: two sights cannot tell us what uncertainty to use. We have to supply it somehow.

In theory, you can calculate an error ellipse for two sights if you assume a sight error. If each sight has a standard error of 1 NM, the shallow 5.2° intersection of the first two sights produces a one-sigma major semi-axis of about 15.6 NM (aligned along the bisector of the two LOPs, that is, extending right along the middle between them) and minor semi-axis of about 0.7 NM. The 95% ellipse uses the 2.45 sigma multiplier, giving about 38 NM and 1.7 NM respectively.

That enormous major axis is exactly why traditional navigation advice recommends an intersection close to 90°. With equal errors and a 90° intersection, the ellipse becomes a circle.

Hence, as you pointed out, the important distinction is between assuming the sight error and estimating it from the observations. With a least-squares solution, the observational variance is estimated from the residuals divided by N−2 degrees of freedom. With only two sights, the two LOPs intersect exactly, so there is no redundancy from which to estimate the observational scatter.

The software takes the purist approach: two sights give you the mathematical fix, and does not pretend to know its accuracy. Users can, of course, select a fix anywhere on the plot and make their own judgement.

I would not exclude adding an assumed error option in a future version. The user could supply their estimated sight error as a parameter in user settings, which the software then uses for the case of two-sight fixes.

Best,

Marco Suadoni

River Moth (Nauticat 33), Essex, UK

www.vincenta.co.uk