[Therion] standard deviation and survey grade

[Bruce Mutton]

Time has come to assign my least accurate survey data a lower accuracy!

I'm curious as to how Therion deals with the std deviations. Had a look,
but can not find much more than is in the Therion book.



First, what are the default values adopted by Therion? Currently I have
only one survey in a large(ish) dataset that has been allocated sd's. From
a casual look at the distortions it clearly works - in that a nice result is
obtained with more distortion in the lower accuracy area. I guess that if
the default values are zero, then all the distortion would be forced to an
area given non-zero sd's; Is this how it works?



In this case it would seem that if one survey parameter has a sd setting,
all the surveys should all have their respective settings allocated for this
parameter to more accurately model a realistic distribution of corrections.



Second, has anyone made any attempt to associate sd values with recognised
cave survey grades (bcra grades for example).



Here is my off the cuff assessment of what in NZ some people call bcra5 but
is really well short.



grade NZBCRA4 # Bruces assessment of the BEST typical NZ surveying
practice MIGHT achieve

tape length 0.1 meter # ie -0.2m to +0.2m for measurement to chest to
0.1m

compass bearing 1 deg # ie -2 deg to +2 deg for sighting to light of
person on station to 1 deg

gradient clino 1 deg # ie -2 deg to +2 deg for sighting to light of
person on station and sometimes accounting for 'eye to light' offset to 1
deg

endgrade



I suspect the sd's may often be larger than this. The actual sd for polar
measurements probably depends a lot on the average length of the legs I
expect



Thanks

Bruce

[Xavier Pennec]

Hi Bruce,

I also tried to customize the quality of the measurements a while ago to
be able to take into account important external loops that are less
accurate than other, and more importantly to weight correctly different
GPS and cartographic reference points.

The underlying idea is to assume that the measurements follow a Gaussian
law with standard deviation sigma. In the statistical setting, you can
show that in this case, you have to replace least-square estimations in
the loop closure correction by weighted least-squares, where the weights
are actually the (square of the) inverse of the the standard deviation.
Although this is not documented in the Therion-book, this is described
shortly in the survex manual (see below) and in different books on cave
survey (A reference book in French is Speleographie by Faucher and
Mautref, but I think this is also detailed in On station and other
English survey book, although I am less familiar with them).

In practice, the 3-sigma rule says that 99.7% of your measurements are
within the bounds [exact value -3*sigma ; exact value + 3* sigma]. This
is why a tape measure which is assumed to be within ±0.1 meter should
have a std dev of 0.033m. One can also use the fact that about 95% of
the values are within two standard deviations. The default definition of
the grades BCRA3 and BCRA5 are in the file therion/lib/grades.th. These
measures closely follow survex' ones.

The value retained by survex and therion correspond to 3*sigma (i.e.
99.7%) although it is said to be 95% in the comments. They do correspond
to the BCRA definition of these grades
(http://bcra.org.uk/surveying/index.html) except for the angular
measures in grade 3 which is 10 degrees instead of 2.5 degrees:
* Grade 3: A rough magnetic survey. Horizontal & vertical angles
measured to ±2.5º; distances measured to ±50 cm; station position error
less than 50cm.
* Grade 5: A Magnetic survey. Horizontal and vertical angles measured to
±1º; distances should be observed and recorded to the nearest centimetre
and station positions identified to less than 10cm.

Compass Point #14 (http://www.chaos.org.uk/survex/cp/CP14/CPoint14.htm)

How does the Survex file get from +/- 2.5 degrees to a standard

deviation of 3.33 degrees?

[Wookey replies: ah, yes, well spotted. That's a mistake, caused by

me forgetting to check the spec!. It should indeed read > 0.83 degrees
for compass & clino SD, and 0.17 for tape and position SD.

Anyone using this feature in Survex v 0.70 should amend their

BCRA3.SVX file.]

Thus it seem that Therion's grade 3 definition should be updated (and
95% changed to 99.7% in the comments). In practice, however, I found
that using this definition of grade 3 for unreliable surveys is quite
good as the tape reading is usually very easy (it is resonnable to
assume that it is within +/- 0.5m) while compass and clino measurements
can be easliy wrong by 5 to 10 degrees for untrained people. Thus, I use
in practice:
* grade 3 for unreliable surveys,
* grade 5 for relieable ones,
* sd of 1 1 5 meters of SD for fixed points which coordinates are
determined from digital geo-referenced maps,
* sd of 10 10 30 to 30 30 100 meters for GPS points with my old Garmin
12 (sd of 2 times the FOM in X and Y and 3 times larger in Z because of
the triangulation errors). For even older GPS measurements, I used 3
times the FOM in X and Y and 9 times in Z).

Hope this helps.

Xavier



Survex manual explanation of std dev:
--------------------------------------
Syntax: *sd <quantity list> <standard deviation>
Example: *sd tape 0.15 metres
Description: *sd sets the standard deviation of a measurement.
<quantity> is one of TAPE|COMPASS|CLINO|COUNTER|DEPTH|DECLINATION|DX|DY|DZ
<standard deviation> must include units and thus is typically "0.05
metres", or "0.02 degrees". See *units below for full list of valid units.
To utilise this command fully you need to understand what a standard
deviation is. It gives a value to the 'spread' of the errors in a
measurement. Assuming that these are normally distributed we can say
that 95.44% of the actual lengths will fall within two standard
deviations of the measured length. i.e. a tape SD of 0.25 metres means
that the actual length of a tape measurement is within + or - 0.5 metres
of the recorded value 95.44% of the time. So if the measurement is 7.34m
then the actual length is very likely to be between 6.84m and 7.84m.
This example corresponds to BCRA grade 3. Note that this is just one
interpretation of the BCRA standard, taking the permitted error values
as 2SD 95.44% confidence limits. If you want to take the readings as
being some other limit (e.g. 1SD = 68.26%) then you will need to change
the BCRA3 and BCRA5 files accordingly. This issue is explored in more
detail in various surveying articles.

Time has come to assign my least accurate survey data a lower accuracy!
I’m curious as to how Therion deals with the std deviations. Had a
look, but can not find much more than is in the Therion book.
First, what are the default values adopted by Therion? Currently I
have only one survey in a large(ish) dataset that has been allocated

[Olly Betts]

Post by Xavier Pennec
The value retained by survex and therion correspond to 3*sigma (i.e.
99.7%) although it is said to be 95% in the comments.

At least for Survex, that was fixed over 6 years ago:

http://trac.survex.com/changeset/1931

So either you're looking at a rather old release, or I missed some
places with that fix (if so, please point out where!)

Post by Xavier Pennec
They do correspond
to the BCRA definition of these grades
(http://bcra.org.uk/surveying/index.html) except for the angular

That was also corrected by the change above.

Post by Xavier Pennec
Thus it seem that Therion's grade 3 definition should be updated (and
95% changed to 99.7% in the comments). In practice, however, I found
that using this definition of grade 3 for unreliable surveys is quite
good as the tape reading is usually very easy (it is resonnable to
assume that it is within +/- 0.5m) while compass and clino measurements
can be easliy wrong by 5 to 10 degrees for untrained people. Thus, I use

The BCRA grades generally seem harder of compass readers than tape
readers, but I think it's confusing to keep a "bcra3" grade which
doesn't actually match BCRA grade 3.

That said, it would be interesting to come up with some sets of expected
SDs for "real world" measurements for various instrument types.

As you say, reading the tape to BCRA accuracy is much easier than the
angular requirements. The required station position accuracy is fairly
easy to achieve too, at least if you choose stations with it in mind
(i.e. make sure you can get your reading eye next to them, or offset
from both stations to compensate).

Clino and compass being the same is a little dubious too since magnetic
effects (from equipment, minerals, and fluctuations in the Earth's
field) affect only the compass, and also the force on the card is much
weaker than gravity, so the reading settles less decisively on the
compass than the clino.

Cheers,
Olly

[Stacho Mudrak]

Post by Olly Betts
http://trac.survex.com/changeset/1931
So either you're looking at a rather old release, or I missed some
places with that fix (if so, please point out where!)

It was problem in therion default BCRA grades. I have fixed it, like
they are in survex. Thanks for pointing out.

S.

[Bruce Mutton]

Just want to check on the recommended way to manage survey accuracy within
Therion.



I have a hierarchal dataset with a three cave system, set up with index and
configuration files so that I can compile any individual or combination of
the caves. I'm about to expand the dataset to accommodate perhaps a dozen
caves, and many more minor holes / karst features. Likewise they will need
to be compiled individually or in sets. To date I have not included 'grade'
or 'sd' statements in my survey.th files, except for 'sd' statements where I
know the survey quality is really poor.



Recently I have put together a single top level grades.th file, and
referenced this in my top level index files only.



I assume that the 'correct' way is to apply a grade statement(and infer
plumbs on/off) in each and every low level survey-endsurvey block.



Instead, I have cheated perhaps, by adding a grade statement (and infer
plumbs on) to AllThreeCavesSystemINDEX.th. If I then add a grade statement
in one of the sub-surveys, am I potentially changing the grade applied by
Therion to the whole cave system?



I'm not sure, but I seem to be getting odd results, in that the corrections
applied to different parts of loops do not seem to respond to changes as I
expect. I'm not sure of the scope implied by the last sentence in this
extract from the Therion Book.



"

grade <grade list> . Sets standard deviations according to the survey grade
specification (see grade command). All previously specified standard
deviations or grades are lost. If you want to change an SD, use the sd
option after this command. If multiple grades are specified, only the last
one applies.

"



Any suggestions on where I should be putting grade statements?

Bruce

[Bruce Mutton]

This post might be inappropriate. Click to display it.

[Stacho Mudrak]

Post by Bruce Mutton
I'm still looking for a 'best practice' on where to put grade statements and
how to control their scope/visibility. Perhaps someone could write a brief
note for the Wiki or the Therion Book?

It looks, using survey grades will change in therion in the near
future. The reason is, that in current configuration, it is not very
clear, how to use it. We have studied the problem a little bit and it
looks, that there are more or less same survey grades used around the
world. So our suggestion is to use just simple

grade N

option in centerline, where N will be survey grade from 0 - 7, where
1-6 = BCRA 1-6, 7 = BCRA X and 0 will be data without any quality
(e.g. position of cave nobody is able to locate now). This grade
should be specified in each centerline object. And such a
configuration will allow doing statistics on survey data from
different sources. Of course, it will still be possible to refine data
quality using "sd" option, but grades will remain the same for all
survey data in therion.

If you have any comments, please let us know.

Regards, S.

[Bruce Mutton]

Post by Stacho Mudrak
So our suggestion is to use just simple
grade N
option in centerline, where N will be survey grade from 0 - 7, where
1-6 = BCRA 1-6, 7 = BCRA X and 0 will be data without any quality
(e.g. position of cave nobody is able to locate now).

I quite like this idea. It will not affect me, but I imagine some people
will have quite a lot of data where they would like backwards compatibility
with the current (old) way of specifying grades??

Post by Stacho Mudrak
This grade
should be specified in each centerline object. And such a
configuration will allow doing statistics on survey data from
different sources.

This seems to be a sensible approach. Beyond very simple caves, the grade is
something that should be considered with every piece of survey, just like
the date and who did the surveying. Just need to decide on a default grade
that applies if no grade statement is present.

Post by Stacho Mudrak
Of course, it will still be possible to refine data
quality using "sd" option, but grades will remain the same for all
survey data in therion.
If you have any comments, please let us know.

What about 'position'? I don't think the BCRA grades have much to say about
these. (I'm sure we can make something sensible up)

Regards,
Bruce

[Martin Budaj]

Post by Bruce Mutton
What about 'position'? I don't think the BCRA grades have much to say about
these. (I'm sure we can make something sensible up)

First proposal could be:

GRADE; POSITION / HEIGHT error (95% confidence); comment

0 -- position unknown
1 1000 m -- rough estimate / memory
2 100 m -- GPS in bad conditions (canyons, foliage, SA), small-scale map
3 15 / 45 m -- GPS, large-scale map
4 5 / 15 m -- GPS longer observation, distinct features on a large-scale map
5 1 / 3 m -- GIS GPS
6 15 cm -- geodetic GPS, theodolite/total station, technical nivelation
7 5 cm -- geodetic GPS, precise theodolite/total station,
precise nivelation

Martin

[Bruce Mutton]

Seems OK as a start. Agree that the elevations are often less accurate than
the plan positions...
Just to clarify, are the values listed to be 2x sd (mean to 95% limit)
Or 4x sd (lower 95% limit to upper 95%)?
Bruce

-----Original Message-----

Post by Bruce Mutton
What about 'position'? I don't think the BCRA grades have much to say about
these. (I'm sure we can make something sensible up)

First proposal could be:

GRADE; POSITION / HEIGHT error (95% confidence); comment

0 -- position unknown
1 1000 m -- rough estimate / memory
2 100 m -- GPS in bad conditions (canyons, foliage, SA), small-scale
map
3 15 / 45 m -- GPS, large-scale map
4 5 / 15 m -- GPS longer observation, distinct features on a large-scale
map
5 1 / 3 m -- GIS GPS
6 15 cm -- geodetic GPS, theodolite/total station, technical
nivelation
7 5 cm -- geodetic GPS, precise theodolite/total station,
precise nivelation

Martin

[Duncan Collis]

Why not use something similar to the EPE (estimated position error)
that most GPS units display? I think the terminology (and probably
the exact meaning of the measurement) varies a bit from one
manufacturer to another, though.

Duncan

[Martin Budaj]

On Mon, Nov 24, 2008 at 8:25 PM, Bruce Mutton

Post by Bruce Mutton
Seems OK as a start. Agree that the elevations are often less accurate than
the plan positions...
Just to clarify, are the values listed to be 2x sd (mean to 95% limit)
Or 4x sd (lower 95% limit to upper 95%)?

It is meant to be 2 * SD.

Duncan: basically it is EPE with 95% confidence.

Martin

[Olly Betts]

Post by Martin Budaj
GRADE; POSITION / HEIGHT error (95% confidence); comment
0 -- position unknown
1 1000 m -- rough estimate / memory
2 100 m -- GPS in bad conditions (canyons, foliage, SA), small-scale map
3 15 / 45 m -- GPS, large-scale map
4 5 / 15 m -- GPS longer observation, distinct features on a large-scale map
5 1 / 3 m -- GIS GPS
6 15 cm -- geodetic GPS, theodolite/total station, technical nivelation
7 5 cm -- geodetic GPS, precise theodolite/total station,
precise nivelation

I don't think inventing numbered grades here is a good approach. For
centre-line survey data, a grade summarising how it was collected makes
sense as you're trying to summarise the accuracy of a lot of
measurements at once, and there's no direct indication of individual
errors for particular readings. It also gives people a benchmark to aim
for, which can be tested by analysing loop misclosures.

But for a GPS measurement, civilian units do give an indication of
errors per reading - e.g. EPE or FOM. While you can't directly use
these as standard deviations or anything so convenient, at least by
allowing them to be recorded, you allow software processing the data to
make use of them.

Even where an error indication isn't directly available (e.g. reading
from a map), I'd have to look up in the table above to know that my
"distinct feature on a large-scale map" qualifies me for "grade 4".
I might as well use the table to see it qualifies me for "5m horizontal,
15m vertical" position error.

Also, the suggested grades force particular pairings of horizontal and
vertical errors. Just because a "GIS GPS" might be 1m/3m, that doesn't
mean that every alternative technique for surveying to 1m horizontal
accuracy would give 3m vertical accuracy.

Cheers,
Olly

[Martin Budaj]

Post by Olly Betts
I don't think inventing numbered grades here is a good approach. For
centre-line survey data, a grade summarising how it was collected makes
sense as you're trying to summarise the accuracy of a lot of
measurements at once, and there's no direct indication of individual
errors for particular readings. It also gives people a benchmark to aim
for, which can be tested by analysing loop misclosures.

The reason why we started to think about position measurement grades
is that we are collecting data about hundreds of caves and other karst
features in our area. In the summary tables (export cave-list) we need
some indication of precision of entrance location (e.g. to select
entrances the position of which needs to be refined). So some
standardization seems to be necessary.

Naturally the SD setting would be available for measurements with
known error estimates.

Post by Olly Betts
Also, the suggested grades force particular pairings of horizontal and
vertical errors. Just because a "GIS GPS" might be 1m/3m, that doesn't
mean that every alternative technique for surveying to 1m horizontal
accuracy would give 3m vertical accuracy.

There is the same problem in centreline data (different combinations
of compass/clino/distance accuracies) with just one generic grade to
keep things simple. Perhaps the standard positioning grades need not
to distinguish between horizontal and vertical accuracies and user
should use SD setting for fine-tuning?

Martin