Error in loop closure algorithm?

[Mike McCombe]

----- Original Message ----- 
From: "John Halleck" <John.Halleck at utah.edu>
To: "Olly Betts" <olly at survex.com>
Cc: "Mike McCombe" <mikemccombe at btinternet.com>; "Survex User Group"
<survex at survex.com>
Sent: Thursday, August 12, 2004 12:06 AM
Subject: Re: Error in loop closure algorithm?

> > On Wed, Aug 11, 2004 at 11:04:43PM +0100, Mike McCombe wrote:
> > > Survex moves not only the survey legs in the "bad" loop but also
> > > adjusts the connecting leg (i.e. test.4 - test.5) and moves the
> > > station in the "good" loop (i.e. test.4) where the connecting leg
> > > joins. The "error" is only 1cm which wouldn't show in most cave
> > > surveys (with me using the instruments!) . However, the error is still
> > > 1cm if you scale the loops down to, say, 1m per leg - which becomes
> > > quite noticeable when the loops are small and generally well-closed.
>
>   Basicly, Least Squares, can smear a blunder all over everything.
>   Although whether or not it is very visible varies.

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.

> > I'm not seeing this on Linux with Survex 1.0.31.  If I run the second
> > example through cavern and then 3dtopos, I get these coordinates:
>
> > (    0.00,     0.00,     0.00 ) test.1
> > (   10.00,     0.00,     0.00 ) test.2
> > (   10.00,   -10.00,     0.00 ) test.3
> > (    0.00,   -10.00,     0.00 ) test.4
> > (  -10.00,   -10.00,     0.00 ) test.5
> > (  -10.00,    -0.42,     0.00 ) test.6
> > (  -20.00,    -1.50,     0.00 ) test.7
> > (  -20.00,    -8.92,     0.00 ) test.8
> >

When I do this I get:-
( Easting, Northing, Altitude )
(    0.00,     0.00,     0.00 ) test.1
(   10.00,     0.01,     0.00 ) test.2
(   10.00,   -10.00,     0.00 ) test.3
(    0.01,   -10.00,     0.00 ) test.4
(  -10.00,   -10.01,     0.00 ) test.5
(  -10.00,    -0.43,     0.00 ) test.6
(  -20.00,    -1.51,     0.00 ) test.7
(  -20.00,    -8.93,     0.00 ) test.8

Note the errors in test.2, test.4 and test.5
The errors are also visible in Aven which shows the bearing from test.5 to
test.4 as 89 degrees. (I suspect there's also a rounding issue here in
Aven).

> > What operating system are you using?  And which version of Survex?

Windows XP Pro (version 5.1.2600) with Survex 1.0.31

All the best,
Mike