From: John Halleck (John.Halleck_at_utah.edu)
Date: Mon Feb 12 2001 - 17:30:32 CET
Received: (from mdom_at_localhost) by karto.ethz.ch (8.9.3/8.9.3/SuSE Linux 8.9.3-0.1) id RAA09025 for cavexml-outgoing; Mon, 12 Feb 2001 17:30:34 +0100 Received: from cor.oz.cc.utah.edu (nahaj_at_cor.oz.cc.utah.edu [155.99.2.2]) by karto.ethz.ch (8.9.3/8.9.3/SuSE Linux 8.9.3-0.1) with ESMTP id RAA09021 for <cavexml_at_cartography.ch>; Mon, 12 Feb 2001 17:30:33 +0100 Received: from localhost (nahaj_at_localhost) by cor.oz.cc.utah.edu (8.9.2/8.9.2) with ESMTP id JAA21994 for <cavexml_at_cartography.ch>; Mon, 12 Feb 2001 09:30:32 -0700 (MST) Date: Mon, 12 Feb 2001 09:30:32 -0700 (MST) From: John Halleck <John.Halleck_at_utah.edu> To: cavexml_at_cartography.ch Subject: Re: Other areas that haven't been discussed. In-Reply-To: <3A87F448.8000501_at_aic.nrl.navy.mil> Message-ID: <Pine.GSO.4.05.10102120925090.19817-100000@cor.oz.cc.utah.edu> Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: owner-cavexml_at_karto.baug.ethz.ch Precedence: bulk Reply-To: cavexml_at_cartography.ch
On Mon, 12 Feb 2001, Ralph Hartley wrote:
> Date: Mon, 12 Feb 2001 09:33:44 -0500
> From: Ralph Hartley <hartley_at_aic.nrl.navy.mil>
> Reply-To: cavexml_at_cartography.ch
> To: cavexml_at_cartography.ch
> Subject: Re: Other areas that haven't been discussed.
>
> John Halleck wrote:
>
> >
> >>
> >> From: Ralph Hartley <hartley_at_aic.nrl.navy.mil>
> >>
> >>> > If a measurement is marked reliability="godgiven" any program should
> >>> > treat it as fixed, and apply no corrections, adjustments, etc. to it.
> >>> > Loop closures should consider its variance to be zero. It is the users
> >>
> >> > If you have more than one point with variance zero, then the least
> >> > squares adjustment has a singular matrix, and the adjustment is
> >> > therefore invalid.
> >>
> >> > I don't think you understand the ramifications of zero variance.
> >>
> >> I think I do. I don't think there are any problems unless there is at least one loop.
> >
> >
> > Matrices with zero rows are singular.
> > Inverting such a matrix is invalid.
> > Zero weight shots give zero rows. (Whether or not they are in a loop, if they are in
> > the adjustment.
>
> Shots marked reliability="godgiven" would (if just plugged blindly into
> a matrix, which is not a good idea) be infinitely weighted, not zero. Of
Sorry, I misspoke. Yes, it makes an infinite weight... which you can't
solve in the matrix.
> course, if one is not careful, that could be just as bad. If one insists
> on just dropping everything into one big matrix, one could use an
> arbitrary large factor instead. You would have to worry about numerical
> stability problems, but you should be doing that anyway.
Whether or not dropping them all into one matrix is "bad", depends a lot
on the method that is going to be used to solve it. Probably not a topic
> It's the reliability="error" shots that should be given zero weight. The
> reasonable thing to do with them is to leave them out of the matrix
> altogether, not to add zero rows.
> While it is true that a singular matrix has no inverse, there are
> actually a number of techniques for getting useful information in a
> situation that calls for the inverse of a matrix, but where the matrix
> may be singular. In fact, least squares itself is the oldest of those,
> but there are others.
LS is for over determined NON-SINGULAR systems.
Psudo-inverses are for singular systems.
However, if you follow standard survey practice you won't have a singular
matrix to begin with.
> >> I should have said that loops specified as goodgiven should not be closed.
> >
> > If they are good given, why would they missclose to begin with?
> [...]
>
> >
> >> You would use this, for example, to set the
> >> coordinates of the datum to (0,0,0), which by definition is exact. It
> >> should be used very sparingly.
> >
> > If you have a single control point, then the weighting of it is
> > going to cancel out, and a numerically stable adjustment is not
> > going to move it anyway.
>
> This is true. But if you have more than one point who's coordinates are
> given, one of them has to be singled out as fixing the coordinates,
> while the others would be subject to adjustment.
Not true.
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