Loop Closures

[Wookey]

+++ Peter Smart [2014-11-04 17:12 -0500]:
> 
>  
> Hi,
> 
 
> Can someone give me alink to somewhere that survey loop closures as
> in Survex are carried out and documented?

The very first issue of compass points had an article about the method here:
http://www.chaos.org.uk/survex/cp/CP01/CPoint01.htm#Art4

> Im OK with the general principle but don’t really understand the
> stats and listing in Survex. I understand that the loop is broken
> down to an out and back lines defined by nodes which link to other
> points in the survey.BUT:

Do you mean the output in the .err file?

> 1) Is it moved a horizontal or sloping distance ie does it take
> account of both plan and elevation loop closure? How much of
> the error is then vertical versus horizontal?

The least squares anaylsis in done in 3D. The err file splits out
vertical and horizontal misclosures:

so
161.twintubs.7 - 161.twintubs.3
Original length   5.10m (  1 legs), moved   0.11m ( 0.11m/leg). Error   2.19%
1.237954
H: 0.233058 V: 2.007189

means that the segment (1 leg) between 161.twintubs.7 and
161.twintubs.3 has just over 2% error which is largely a vertical
offset. I can't actually remember what units those numbers are in:
Standard deviations, percent or metres. Neither of the last two seem
right.

Ol?

This stuff could be much better docunmented in the manual. Anyone keen
to do that?

> 2) There are 3 numbers listed after the original length distance
  moved etc line in the output. The first is on a line alone with no
  designation the other two arelisted as H: nnn and V: nnn. Is this
  information about the vertical and plan misclosureverall? 

Yes. The first number is the overall misclosure and the next line are
the horizontal and vertical components of that. The units are a mystery although I'm sure this question has been answered before. 

> is the
> loop closure routine progressive starting from small and working up
> to large loops or is it an error minimisatiion optimisation type
> scheme?

It is a least squares analysis, one for each segmentable section of
the data. The network can be chopped into sections at 'articulation
points', which is points where there is only one edge (series of legs)
between two more complex bits of network. Each of those can be solved
eaparatly to reduce the memory usage and make things faster. 

> 4) Some of the legs involved in a loop end up with zero movement
  despite the tie line moving substantially. This gives zero errorson
  the out part of the loop and significant ones on the return
  section. Is this simply a matter of geometry eg the error may be in
  easting only so legs that have only a northing component aren’t
  corrected?

This could happen due to the geometry as you suggest. You would get
zero adjustment in one direction if the error is entirely
perpendicular to that, but for a survey segment of more than one leg
that would never actually hapen as surveys always zig-zag a bit.

More likely you have an extra constraint in the data such a *fix
points with very low SDs attached so they constrain the segment
between them.

> Survex is capable of including different standard deviations for
> individual survey lines or legs. Does the loop closure routine take
> this into account eg by forcing more movement on a BCA grade 3 line
> compared to BCRAGrade 5? 

Yes. Every leg/segment gets SDs assigned, either defaults due to the
data type or BCRA grade info (just a set of SDs for readings). Errors
are distributed according to the SDs. This is just a feature of the
least squares algorithm

> Issue is if you have a reliable survey how
> do you force this to have more say in the final positions after loop
> closure compared to the lower grade survey without simply fixing a
> point at the end of the ‘good’ survey?

You use the *SD command to allocate relatively low standard deviations
to the data that is more accurate, and/or higher SDs to the data that is worse. 

Olly can proably give better answers on some of these points, but I
hope that helped.

Wookey
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