By the way, this is something that has been discussed before, but here is an easy test procedure for determining fairly realistic values of the centering uncertainties of a total station outdoors in normal field conditions.
The method consists of setting a ground mark that is typical of the sort of traverse point you use, i.e. 60d nail, tacked hub, or (as in my case) a punchmark on the head of a 3/8 in. x 8 in. spike.
Then set marks about 7 ft. away from that ground mark, approximately North, South, East, and West of it. The idea is to set marks that are very distinct in the telescope of the total station and that the instrument can be pointed at as nearly exactly as possible. I find that a punchmark on the head of a spike works very well.
Measure the distances from the central ground mark to the four marks N, S, E, and West. Tape or EDM should work perfectly well. No exceptional accuracy is necessary. +/-0.02 ft. is perfect.
The test, such as it is, then consists of setting up the total staion over the central ground mark using whatever plummet, optical or laser, it has, and measuring a round of directions to the four marks N, S, E, and W.
Shift the total station's tribrach off center, rotate it, say, about thirty degrees, and center it on the central ground mark again. Measure a round of directions to the four marks N, S, E, and W.
Do this for, say, ten times in all. Twenty if you're energetic.
What you'll end up with from the first set is a set of measurements from which, assuming a direction to one ground mark, you can compute the coordinates of the N,S,E, and W marks.
Then, the next sets are in effect redundant resections by directions only, from which the coordinates of the instrument may be computed in relation to that of the position occupied in the first set.
This is a snap to compute in Star*Net and most likely in other least squares survey adjustment software as well.
You'll almost certainly end up with ten different sets of coordinates for the instrument station. The plot below is a detail showing the ten different positions from a test and indicating the 95% confidence error ellipses of each different instrument position solved.
Here are the adjusted coordinates of those same instrument setups computed from actual measurements made with a Zeiss Elta 50 with a rotatable optical plummet. From the scatter of the N and E components, the uncertainties can be estimated in the form of standard errors (which I'll leave the reader to work out).
[pre]
Adjusted Coordinates (FeetUS)
=============================
Station N E
1 0.0000 0.0000
2 -0.0012 0.0013
3 -0.0007 0.0007
4 -0.0002 0.0013
5 -0.0007 0.0021
6 -0.0012 0.0024
7 -0.0014 0.0002
8 0.0005 0.0019
9 0.0004 0.0021
10 -0.0015 0.0008
[/pre]
Great Stuff Kent,
You had some other procedures you had developed for 'A priori" estimates back in the day. Too bad I can't seem to find them.
How does this method not include the angular measurement error to each point?
> You had some other procedures you had developed for 'A priori" estimates back in the day. Too bad I can't seem to find them.
Yes, that would be next. Centering errors are a logical place to start since they are easiest to characterize and most overlooked.
> How does this method not include the angular measurement error to each point?
It does. When the resections are solved by least squares (in Star*Net in this example) to get the coordinates of each setup relative to the first setup, the directions are weighted by their standard errors. In this case, the standard error of a direction was assumed to be 3". That is reflected in the sizes of the error ellipses for the solutions of the different setup coordinates. An error of 3" in a direction angle at a distance of about 7 ft. contributes a very small uncertainty. It isn't a critical value for the purpose of evaluating centering errors.
It does include the angular error, but the points being sighted are so close that any angular error would be negligible.
The sighting would have to be off by 30" to 1' to approach the same order of magnitude of the centering errors that Kent has listed.
Okay, I'll go ahead and work the statistics for the above coordinates of different setups over the identical ground mark.
[pre]
Adjusted Coordinates (FeetUS)
=============================
Station N E
1 0.0000 0.0000
2 -0.0012 0.0013
3 -0.0007 0.0007
4 -0.0002 0.0013
5 -0.0007 0.0021
6 -0.0012 0.0024
7 -0.0014 0.0002
8 0.0005 0.0019
9 0.0004 0.0021
10 -0.0015 0.0008
--------- ---------
s.e. +/-0.0007 +/-0.0008
[/pre]
So, the pooled estimate from the scatter of the N and E components would be:
[pre]
SQRT [ (0.0007² + 0.0008²)/2 ] = 0.00075 ft. = 0.24mm
[/pre]
That value, 0.24mm, would be the estimated standard error of centering for that instrument using that style of ground mark.
> ... here is an easy test procedure for determining fairly realistic values of the centering uncertainties of a total station outdoors in normal field conditions...
If this test was done indoors, and your instrument is reflectorless capable, your targets could be pencil marks on the walls.
I also suggest that a part of the test be to run through several sets of measurements without resetting the tribrach, to test what the effect of distance measurement error might be.
Your results show that your tribrach is in excellent adjustment. It may also be illuminating to run the test with a tribrach that has been in service some time since its last adjustment.
> I also suggest that a part of the test be to run through several sets of measurements without resetting the tribrach, to test what the effect of distance measurement error might be.
Note that you can analyze the effect of distance measurement errors by simply altering the values used in the adjustment. As long as the N and S pair and E and W pair are approximately collinear with the instrument station, the effect of distance measurement errors is quite small.
The test procedure is determining the relative coordinates of all subsequent setups to the first from which the coordinates of the N,S,E,W points were computed, which is a different exercise than computing their absolute coordinates in relation to the N,S,E,W points.
> Your results show that your tribrach is in excellent adjustment. It may also be illuminating to run the test with a tribrach that has been in service some time since its last adjustment.
To be clear: the total station tested had an optical plummet in the alidade, not the tribrach. Standard centering procedure consists of checking centering using the plummet in different orientations of the instrument.
The point of rotating the tribrach in my test was actually in connection with another part of the test that measured directions to more distant targets to compute the standard error of a direction. That Elta 50R doesn't have a circle that can be separately rotated if you want to measure using different parts of the circle. So the tribrach has to be rotated to change the parts of the circle used for successive sets of directions.
If you were using either a laser plummet or optical plummet that was fixed in the tribrach, rotating the tribrach through about 360° in the series of setups should give a realistic estimate of centering errors for the state of tribrach adjustment. You're right that without knowing the state of tribrach adjustment, it's optimistic to use a standard error determined by testing a tribrach in good adjustment.
[sarcasm]How do I do this with RTK?[/sarcasm]
> [sarcasm]How do I do this with RTK?[/sarcasm]
Multiply the coordinates by a factor of 100. :>
> [pre]
>
> Adjusted Coordinates (FeetUS)
> =============================
>
> Station N E
> 1 0.0000 0.0000
> 2 -0.0012 0.0013
> 3 -0.0007 0.0007
> 4 -0.0002 0.0013
> 5 -0.0007 0.0021
> 6 -0.0012 0.0024
> 7 -0.0014 0.0002
> 8 0.0005 0.0019
> 9 0.0004 0.0021
> 10 -0.0015 0.0008
> --------- ---------
>
> s.e. +/-0.0007 +/-0.0008
> [/pre]
Just to demonstrate how insensitive the relative coordinate solutions are to errors in measurement of the distances from the instrument setup point to the N,S,E, and W marks, I added 0.5 ft. to all of the distances that I actually measured (distances of about 7 ft.) and recomputed the series of setup coordinates holding the coordinates of setup 1 fixed at 0,0.
As the following show when compared with the original values above, the RELATIVE coordinates recomputed using the grossly erroneous distances differed at most by 0.0002 ft. (0.06mm). The whole series was basically the same for the purpose of estimating the centering error.
[pre]
1 0.0000 0.0000
2 -0.0013 0.0014
3 -0.0007 0.0007
4 -0.0002 0.0014
5 -0.0007 0.0022
6 -0.0013 0.0026
7 -0.0015 0.0002
8 0.0005 0.0020
9 0.0004 0.0023
10 -0.0016 0.0008
[/pre]
Yes of course, but when we analyze error sources, we should do so as rigorously as possible. It would be at least worth determining angular error first or discussing how you conclude it is insignificant in the analysis, especially on a board where we have many different education/background levels.
> Yes of course, but when we analyze error sources, we should do so as rigorously as possible. It would be at least worth determining angular error first or discussing how you conclude it is insignificant in the analysis, especially on a board where we have many different education/background levels.
Well, that's the beauty of using least squares to solve the coordinates of the successive setups from redundant observations (three directions is sufficient, four are redundant). The realism of the standard errors assigned to the directions is tested in the adjustment when the chi square test is applied to the residuals.
Aside from that detail, the elegance of this method is that if you assign an incorrect standard error to the directions observed to the N,S,E, and W points from which the setup coordinates were computed, you still get the same answer.
For example, while 3" was a realistic value for the standard error of a direction observed with the Elta 50, I changed the standard error to 30" and reran the adjustment to compute the setup coordinates. The coordinates were the same since the weights on the directions remained equal. The only difference was that the test on the residuals showed that the standard error assigned to the directions was too large.
If the instrument has an optical plummet in the instrument, not tribrach, how likely is it for centering errors to exist?
I always assumed if it was on 'target' throughout it's full 360° then all Ok, or is that a myth?
Actually used this approach for fixed optical plummets in tribrach for a while now but without any fancy software.
But that was based on above assumption.
I have 4 points around the circle I measure to at close range with TS, and at eye height and then plumb the fixed optical plumb tribrach over the point. Then note the differences in measurements and adjust accordingly. At most it needs 2 trials and I'm there very quickly - in theory, which takes me back to original question.
I found it very quick and accurate (???)
I used other methods in past but one day decided this was way to go and kept it up.
> If the instrument has an optical plummet in the instrument, not tribrach, how likely is it for centering errors to exist?
> I always assumed if it was on 'target' throughout it's full 360° then all Ok, or is that a myth?
I'd say it's 100% certain that centering errors will exist in any setup of an instrument with an optical plummet over a ground mark. The question is what the likely limits of those largely random errors are. The standard error of +/-0.24mm found in the test described above is not very much.
For example, one basic limiting factor on an optical plummet is the magnification of the telescope in the plummet. If the telescope cannot resolve detail at ground level that is smaller than X millimeters, then "on target" just means that the centering errors may be that large.
The other element is the nature of the ground mark itself. If a surveyor is centering over a ground mark that is a relatively course thing, then one of the limits of the centering process would strike me as being the accuracy with which the center of that thing may be judged in the reticle of the optical plummet.
Probably the best answer is to test the centering by the method described (or some improvement upon it) to characterize the random errors of centering of successive setups over the same ground mark under nominally the same conditions.
