[Therion] standard deviation and survey grade

Wed Oct 29 17:43:01 CET 2008

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) 
gives the explanation of this discrepancy:
 > 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.

Bruce Mutton a écrit :
>
> 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
>
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