Error in loop closure algorithm?

[Olly Betts]

On Thu, Aug 12, 2004 at 08:44:34AM -0600, John Halleck wrote:
>   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.

Survex will fix the first station mentioned at the origin if no points
are fixed.  So station 1 will have coordinates (0,0,0).

The rationale is that it's fairly common to have a cave survey which
hasn't (yet) been tied into any point for which coordinates are known,
and it's convenient for the software to pick an arbitrary coordinate
system rather than force the user to pick one.

>   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.

I don't follow what you're trying to say here at all.  I suspect you
must mean something other than "statistically independent" in its
normal mathematical sense...

The example Mike gave (with the implicit fixing of station 1) has a loop
with a control point and a single leg linking this to a second loop with
a blunder in.  That's rather different to the linked loops example you
gave in an earlier mail.

Mike's network has articulation points at either end of the single
linking leg so solving the first loop (and fixing the coordinates of all
the stations in it) then solving the second loop should be equivalent to
solving the whole system.  Hence nothing in the second loop should
affect the coordinates of stations in the first loop.

I suspect the problem here is a loss of precision somewhere in the
calculations.  My initial prime suspect is where the coordinates are
coverted from real numbers to integer cms while writing the .3d file.

Cheers,
    Olly