Error in loop closure algorithm?

[John Halleck]

On Thu, 12 Aug 2004, John Halleck wrote:

> Date: Thu, 12 Aug 2004 08:44:34 -0600 (MDT)
> From: John Halleck <John.Halleck at utah.edu>
> To: Mike McCombe <mikemccombe at btinternet.com>
> Cc: John Halleck <John.Halleck at utah.edu>, Olly Betts <olly at survex.com>,
     Survex User Group <survex at survex.com>
> Subject: Re: Error in loop closure algorithm?
> 
> On Thu, 12 Aug 2004, Mike McCombe wrote:
> 
> > From: Mike McCombe <mikemccombe at btinternet.com>
> > [...]
> > I appreciate the significance of the "LMS vs Blunder" religious argument but
> > disagree with John's use of the word "everything". LMS algorithms distribute
> > errors according to the covariances of the observations. The covariance
> > between survey legs in loops which are not coupled is zero (i.e. they are
> > statistically independent) - hence errors in this example should not
> > propagate between the two loops.
> 
>   By the way, in order to sove the least squares problem at all you
>   have to tie down the location of at least one point.
> 
>   I think it obvious, but worth stating, that any shot between
>   a given loop, and the control point, is not statistically
>   independent of that blunder.  (Since all sections between
                        *******
     oops, make that 'not independent of that loop".

>   the control point and a given point contribute SOMETHING)
>   to the computation of the coordinates.
> 
>   And if I am between the control point and some other section of the
>   cave, that part of the cave isn't statistially independent of 
>   whatever loop I'm in.
> 
> 
>   Mike is right that it doesn't affect EVERYTHING (as I misspoke),
>   but it does affect all connected loops, and all shots downstream
>   (away from the control points) from blunders.
>