# NavList:

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

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Re: Symmedian point -earliest reference in navigation
From: Bill Lionheart
Date: 2018 Oct 14, 17:07 +0100

```Dave,
Three lines of position is an interesting case to teach to students
who will be in the future trying to deduce many unknowns from more
equations, and there are lots of useful lessons.  One extension of the
example is to include the DR position as a priori knowledge. This
leads (algebraically) to what is called Tikhonov regularization, or
Ridge Regression.

In matrices, instead of x = (A^TA)^-1 A^Tb  you have (A^TA+a^2 I )^-1
A^Tb where a is the ratio of the standard deviation of your "prior
distribution" which measures how much you trust DR and the errors in
the position lines. Here A^T is transpose and ^-1 means inverse and I
is the 2x2 identity matrix

I will eventually find a geometric construction for this I expect.

Bill
On Sun, 14 Oct 2018 at 14:24, David Pike  wrote:
>
> Bill
> Never being able to remember the definition of symmedian point for longer
than 30 minutes, I Googled it, and that led me to your tutorial
https://www.youtube.com/watch?v=pzDyi7ANoVA .  It extends well from a number
of connecting points from ‘A’ levels, which in my case was a long time ago.
On the whole, I think I preferred the geometrical solution although it does
explain why all the papers I attempt to read in the Journal of Navigation or
listen to at conferences are brim full of rows of matrices.
>
> I was pleased that you stressed that your position lines need to have equal
bands of error and that your solution is not necessarily what a ‘rule of
thumb’ kind of navigator might have used.  A useful thought which you could
have left for your potential students, who seemed unusually attentive, to go
away and think about is how they might have dealt with the fact they might
also have a lovingly worked out DR position to include in the casserole.
Should they ignore it, or should they seek a further MPP?  DaveP
>
> View and reply to this message
```
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