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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Pub.249 Epoch 2020 is available.
From: Robin Stuart
Date: 2018 Nov 24, 05:35 -0800

Rafal,

The order parameter you use, c.3 = |1/3 Sum(exp(3*i*Zn))|,  seems rather ad hoc. Is it based on the mathematical realization of some principle or requirement or is it just something constructed to have a maximum when the azimuths are separated by 120°? If the latter how can you be sure it gives the correct ranking when sights are not at the ideal separation?

There is no unique way to quantify the quality of a round of sights but a couple of good candidates might be the area of confidence ellipse (at some confidence level) that the sights produce or the root-mean-square distance of the observer’s possible position from the MPP. I have looked into this recently and find that for 3 LoP’s, with azimuths Z1, Z2 and Z3 each having the same Gaussian errors in their intercepts these measures are both inversely proportional to the square root of

Q=sin2(Z1-Z2)+sin2(Z3-Z1)+sin2(Z2-Z3).

In other words when comparing rounds of sights a bigger value of Q means better. From a purely statistical standpoint the azimuths 0°, 60°, 120° are just as good as 0°, 120°, 240°. The measure Q shows this whereas your c.3 does not. The latter set is preferable if there might be some systematic error such an incorrect I.C. or height of eye as pointed out in Bowditch 2017 https://msi.nga.mil/MSISiteContent/StaticFiles/NAV_PUBS/APN/Chapt-18_Sight_Planning.pdf

The quantity Q generalizes in the obvious way for more than 3 LoP’s,

Regards,

Robin Stuart

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