# NavList:

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

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Re: Fix Maximum Probability Positions
From: Hanno Ix
Date: 2013 Mar 19, 22:33 -0700
John:

I stumbled already over EQ 1. Your explanation for that one was a little short.
A flag went up.

Not sure I see things right right, but:

There is one circle around the substellar point SSP1
that has a mean radius R1 plus 'noise' N(0, sigma1). You did the CelNav on this one.
You do not know your azimuth as of yet so you can be anywhere on that circle
with the same probability.

There is another circle around SSP2; radius R2 + same  'noise' N(0,sigma).;
I did the CelNav on that one. I can be anywhere because I don't know my azimuth either.
Same thing.

EQ 1 , i.e. the multiplication of probabilitues, works if just one of us can be on both circles with equal probablity
but without knowledge of azimuths. In that case, the most frequent points that you visit are the
intersections and EQ1 is correct. No problem here.

However that is there is two of us. Since each of us can be somewhere on his circle as measured
there very little chance we meet but we  occasionally do.

I am wondering  therefore: Is the intersection not the point where the distance between is
must frequently zero? This way we would find the intersection without any knowledge about azimuths
which neither one has anyway a-priory? Knowing now the intersection the azimuths follow.

However, in that case EQ 1 would not apply.

h

From: John Karl <jhkarl---.net>
To: hannoix---.net
Sent: Tuesday, March 19, 2013 11:14 AM
Subject: [NavList] Fix Maximum Probability Positions

Attached is my latest contribution to the endless fix/MPP question. I hope we all agree that these discussions are interesting. And even useful at sea, but only to a degree where all of us would consider not the MPP, but the opposite -- the largest possible error when it comes to risking life and property.
Happy armchair navigating.
May you find your beer at its MPP,
JK
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