standard deviation and survey grade
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
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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grade BCRA3 -title "BCRA grade 3" # 95% of readings are within 0.5m tape 0.15 metres # 95% of readings are within 10 degrees compass 3.33 degrees # 95% of readings are within 10 degrees clino 3.33 degrees # 95% of positions are within 0.5m position 0.15 metres endgrade grade BCRA5 -title "BCRA grade 5" # 95% of readings are within 0.1m tape 0.033 metres # 95% of readings are within 1 degrees compass 0.33 degrees # 95% of readings are within 1 degrees clino 0.33 degrees # 95% of positions are within 0.1m position 0.033 metres endgrade
On Wed, Oct 29, 2008 at 05:43:01PM +0100, Xavier Pennec wrote:
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!)
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:
That was also corrected by the change above.
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:
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
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!)
It was problem in therion default BCRA grades. I have fixed it, like they are in survex. Thanks for pointing out. S.
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
Hi I'm still experimenting with grade and sd statements.. I can get some very extreme distortions with just a small relative difference in sd values. No problem, it's just a function of my mis-close, and the math. To my advantage it may help me to decipher the scope/visibility of grade statements if I can concentrate on the problem long enough. I finally took the hint in previous postings that BCRA grades 3 & 5 might be built into Therion. I tested it and indeed they are. Is this documented anywhere? Would have saved me quite a bit of experimentation (and embarrassment). 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? Bruce
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.
Stacho wrote:
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??
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.
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
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
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-----
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
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
On Mon, Nov 24, 2008 at 8:25 PM, Bruce Mutton <bruce.mutton@paradise.net.nz> wrote:
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
On Mon, Nov 24, 2008 at 05:18:14PM +0100, Martin Budaj wrote:
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
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
On Mon, Dec 15, 2008 at 1:45 AM, Olly Betts <olly@survex.com> wrote:
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.
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
participants (6)
-
Bruce Mutton -
Duncan Collis -
Martin Budaj -
Olly Betts -
Stacho Mudrak -
Xavier Pennec