Error in loop closure algorithm?
John.Halleck at utah.edu
Thu Aug 12 15:44:34 BST 2004
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
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.
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