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Richard Reed wrote, about my test-to-destruction of the least-squares 
algorithm in the almanac, by starting it off from, not the DR position, but 
from its antipode-

"Thanks George and Peter for the education.  My little plane geometry 
demonstration didn't use real sights or spherical triangles, and I didn't 
suspect a navigation triangle that stretched halfway around the world would 
still work!

I had a look at a sun sight from a book and soon saw that George's trial, as 
I understand it, couldn't be done in Pub. 249 tables using that sight 
because large negative calculated altitudes are not listed, so I guess this 
would be done using a calculator, which I'll work on out of curiosity.  If 
this comes out as I expect, the first intercept will place the LOP nearly as 
far back as DR was displaced, 180 degrees."

Well, it's not really a practical task for doing by calculator, in my view. 
First few iterations would, at a guess, produce immense cocked-hats, from 
which you would have to estimate, each time, a best new starting-position 
for the next iteration. And Richard is right, the first few iterations would 
involve large negative altitudes, which tables are not designed to cope 
with. Though you can get round these things, often, by working out the 
altitude of an antipode of the point you really wanted, and subtracting it 
from 180º. Or something like that. Such tricks exist. But it would be an 
awful lot of slog.

What I've wondered is this: say you offered the least-squares algorithm a 
collection of six assorted position lines, three clustered round a 
cocked-hat in one part of the World, the inconsistent contact George 
Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.others around 
another cocked-hat in an entirely different area. Would it home in on one or 
the other, or would it choose to produce a solution that was somewhere in 
no-man's land, between the cocked hats, with an immense error-ellipse? My 
guess is, the latter.

By the way, included with the AstroNavPC booklet, from the UK Nautical 
Almanac Office, but not within the back pages of the Almanac itself, is the 
algorithm for calculating the error-ellipse which that software displays. I 
think it has a minor error in its text, but more important, in my view the 
whole concept of deducing an error-ellipse from a single cocked-hat is 
fundamentally flawed. Anyone like to take up that question?

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 

   

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