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Thanks Brad.
1) We don't. As in many experimental techniques if you calibrate
everything you can, practice making the measurement enough, and
average over a number of measurements the BEST you can expect at the
end is independent, identically distributed, zero mean and
approximately normal. Also this is the only assumption that makes it
easy to calculate the most probable position, pretty much anything
more sophisticated and you will need a computer.

I am sure more experienced CelNav practitioners will come in on this,
but of course if you take a series of sights of the same body you also
get some information about the errors.

2) If there are no immediate dangers yes I recommend the symmedian
point - however the time spent finding it might be better spent taking
a few more sights! As to an update on the corner nearest danger
principle, I have something to say on that, but not finished writing
it yet. The take home message is that the symmedian is close to the
short edge!

I agree these are good things to consider. I generally give this talk
to 6th form students who have come for an interview at the University
of Manchester. It is just a popular talk to entertain and enthuse
them, and if they develop an interest in geometry or navigation that
is a bonus. I would quite enjoy talking about this to an audience who
care about navigation but I have not done that yet.

Bill
On Mon, 15 Oct 2018 at 20:19, Brad Morris  wrote:
>
> Bill, you wrote
>
>
> I have searched through the NavList archives, I followed most of the 
references in David Burch's helpful blog post 
http://davidburchnavigation.blogspot.com/2016/07/most-likely-position-from-3-lops.html
>
>
> From David Burch Navigation
>
> Begin quote
>
> "Practicing navigators have tended to choose the best position within the 
triangle of intersecting LOPs (cocked hat) as some central value of their 
choice, based on their experience and the actual sights at hand. In most 
cases this is an adequate solution, but in rare cases ...
>
> ...It can be shown that if the standard deviations of the sights are all the 
same (no one LOP better than another), and there is no systematic error that 
applies to all of them, then the most likely position is located at what is 
called the symmedian point"
>
> End quote, emphasis added.
>
> -----
>
> By following this advice, we may "improve" our fix, but only under certain 
circumstances.  At the end of the geometric construction (or the matrix 
manipulations, if so inclined), the symmedian point is found.  It will likely 
be different from the "by eye" dot.  It will certainly be a different fix 
than that found by following Admiralty advice, particularly with danger 
nearby.
>
>
> Bill, please answer the following questions for practical navigators.
>
> 1)  How are we to know, with certainty, that
>     [a] the standard deviations of the sights are all the same, and
>     [b] there is no systematic error
> Most importantly, the method by which we are to know.   Do you expect 
navigators to determine the statistical distribution of the observations of 
each body, so as to know that the standard deviations for each body are all 
the same?
>
> 2) Please justify why using the symmedian point is better than Admiralty 
advice on the cocked hat.  Or do you only recommend the symmedian point when 
there is no danger nearby and all of the conditions met?
>
> Aside from the pure exercise of applied mathematics, answering these 
questions should improve the focus and rationale for the symmedian point 
lecture.
>
> Brad
>
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> 

   

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