Determining Total Station Distance Standard Errors

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> Is there a way to do this without a test range? There's one such NGS range some 40 miles from me that can be used with advanced warning and permission (it's on an airfield) ...

There are two separate matters here. What you first asked was how to determine the standard error of a distance given by your total station. The second is how to verify that the ranges aren't systematically in error.

As for the determination of standard error, that depends upon the range of distances you'll be measuring. If you'll hardly ever measure a distance greater than 600 ft., then setting up a test line with a maximum interval of 600 ft. and intermedicate points along it to make a series of shorter invervals (which aren't all even 10m multiples) will serve the purpose.

You'll still have to check the scale of the EDM against a known length standard such as a calibration baseline, but that's somewhat different since the typical calibration baseline design in the US has even 10m intervals which will tend to hide some types of EDM errors. If the reference frequency of the EDM has been checked in the shop recently and found to be within specification, I'd probably not stay up late at night worrying that the EDM itself was giving distances with significant scale errors and would focus on the errors that show up in short-range measurements from other causes.

Distance error consists of several parts. You can check for offset error with the AB+BC-AC method. You can't check scale factor without a (fairly long) calibrated distance to work against.

There is cyclic error in an EDM, typically repeating every 10 meters (or 5 or 20 depending on the design). There was a [msg=20155]discussion several years[/msg] ago where Kent explained how to test that, after some initial confusion from me.

Then there is the repeatability at any given distance, which you can estimate by measuring it multiple times, including fresh setup errors if that is part of what you are interested in.

I'd consider setting up some marks in a straight and level line of long length X, with distances in meters of approximately 0, 2.5, 5, 7.5, 10, X/2, and X. Then measure all combinations as many times as you wish and do a least squares to examine the errors of fit.

Edit: I should learn to refresh the thread before posting. Kent usually beats me to it.

> Distance error consists of several parts. You can check for offset error with the AB+BC-AC method. You can't check scale factor without a (fairly long) calibrated distance to work against.
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> There is cyclic error in an EDM, typically repeating every 10 meters (or 5 or 20 depending on the design). There was a [msg=20155]discussion several years[/msg] ago where Kent explained how to test that, after some initial confusion from me.
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> I'd consider setting up some marks in a straight and level line of long length X, with distances in meters of approximately 0, 2.5, 5, 7.5, 10, X/2, and X. Then measure all combinations as many times as you wish and do a least squares to examine the errors of fit.
>

Thank you both.

Cliff notes recap, to see if I got it right:

1. Offset error, or the "repeatability" factor is the Standard error which I'd derive in Starnet, using the 95% Chi squared results from the above test. I can't do them all at once (only have three tripods), but could do them sequentially with lots of redundancy (after 2' or so of snow melts, and I can see the dirt again). I'll then carry those numbers in LSA as the distance standard error.

2. Don't worry about the cyclic error. 99% of my measurements are under 600'.

3. Take two Advil before reading a thread such as the one you linked.o.O

> 1. Offset error, or the "repeatability" factor is the Standard error which I'd derive in Starnet, using the 95% Chi squared results from the above test. I can't do them all at once (only have three tripods), but could do them sequentially with lots of redundancy (after 2' or so of snow melts, and I can see the dirt again). I'll then carry those numbers in LSA as the distance standard error.
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> 2. Don't worry about the cyclic error. 99% of my measurements are under 600'.

No, I don't think you quite got it. Over short distances of 600 ft. or less, the cyclic error may be one of the major components of the standard error and should not be overlooked in testing. The cyclic error and other EDM errors are typically small, but can make a significant contribution to the standard errors of distances measured with the EDM.

The instrument offset correction, if wrongly chosen, will produce a systematic error which should be corrected, not treated as a random error.

> No, I don't think you quite got it. Over short distances of 600 ft. or less, the cyclic error may be one of the major components of the standard error and should not be overlooked in testing. The cyclic error and other EDM errors are typically small, but can make a significant contribution to the standard errors of distances measured with the EDM.
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> The instrument offset correction, if wrongly chosen, will produce a systematic error which should be corrected, not treated as a random error.

Yes, but given that those errors are "in there" already, they'd be accounted for. I don't think I need to separate them out...there's no place in Starnet to do so that I know of anyway.

In addition to the test described earlier, I was planning on running the standard AC+BC-AB test to check the instrument constant (which is currently shown on the sticker under the battery as 18.3 mm).

Wouldn't the combination of those two tests pick up all but purely systematic errors?

> Yes, but given that those errors are "in there" already, they'd be accounted for. I don't think I need to separate them out...there's no place in Starnet to do so that I know of anyway.
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> In addition to the test described earlier, I was planning on running the standard AC+BC-AB test to check the instrument constant (which is currently shown on the sticker under the battery as 18.3 mm).
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> Wouldn't the combination of those two tests pick up all but purely systematic errors?

I'll bet that someone can post a link that details the various errors inherent in EDM range measurements that will give you a better understanding of what the problem really amounts to.

In your case, the logical next step would to evaluate the standard errors of instrument and target centering unless you have a whole bunch of tripods and tribrachs to use in EDM testing. The EDM test pretty much depends upon the equipment you have available and what the expected centering errors are that you'll be dealing with.

Standard errors are 1-sigma, not 95% confidence.

Offsets are not a repeatability problem - it will be systematic in every measurement.

The AB+BC-AC test is for the combination of instrument offset and prism offset. Only a cal lab, calibrated prism, or special setup can determine instrument offset as separate from prism offset. I think usually instrument offset is just left alone, while setting the prism offset needed for your glass.

Cyclic error is part of the repeatability problem, since without careful calibration is appears almost random and I'd treat it as such unless I had done all the work to determine a correction function.

Yep, that old thread can give a guy a headache, particularly since it evolved slowly and didn't just present a tutorial.

You also asked the question how shops do their testing.
Our shop has a 10m calibrated base line inside our building. We measure both reflectorless and prism modes on each target. They should both be consistant with each other over the 10M shots.
We also have a couple of prisms outside for our longer 600' and 1000' shots to verify the longer ranges match our "gold standard" S8 1/2" instrument which has a calibrated EDM accuracy better than .1mm.
You can check the error but there is little you can do to adjust it. It requires service software and specialized testing tools and or alignment fixtures.
What you really want to verify is that your EDM is consistant over 10M by measuring each meter, then checking longer distances using the ABC methods described in the previous posts.
The good news is that most EDMs are very good and do not need to be adjusted very often. If you do happen to discover that your EDM is shooting long or short over all of the distances pretty much the same amount, you can change the prism constant by that amount of error as a temporary solution. Then take it to a service facility that has Level 3 certification, level 3 service is a term that some manufactures like Trimble uses to indicate a shop has the training and can do advanced adjustments like the EDMs or other indepth or advanced work on the instruments.
JSW

>In your case, the logical next step would to evaluate the standard errors of instrument and target centering unless you have a whole bunch of tripods and tribrachs to use in EDM testing. The EDM test pretty much depends upon the equipment you have available and what the expected centering errors are that you'll be dealing with.

Well, I screwed up my own thread by mistakenly posting the results of my observations in my other thread on steel tape assumptions.:-O

Rather than try to cut and paste it again here (I tried; the images don't work), here it is:

https://surveyorconnect.com/index.php?mode=thread&id=306652#p306763

One additional note: each observation of distance is actually the average of three that the instrument takes each time an observation is requested. They don't individually come up, so I entered the results as a single measuremnt (x 4) in Starnet.

> Standard errors are 1-sigma, not 95% confidence.
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> Offsets are not a repeatability problem - it will be systematic in every measurement.

I just discovered Math Teacher's "Digging out the Truth" thread from January:

https://surveyorconnect.com/index.php?mode=thread&id=299696

It talks about exactly what I'm trying to do (determine a good value to use in Starnet for the standard error of my instrument. Forget about Systematic errors for now...I know I cant address that without a proper test range.

But in that thread, it implies that the manufacturers' published numbers (2mm +/- 2ppm) are 2-Sigma, not 1-Sigma.

So here's the bottom line:
I think my Total Station is doing better than the published value. But how much better? I'd like to use a realistic value in Starnet.

So If I set up on my 100' "test range", and make 100 observations of distance, with a single prism in a tribrach (no set up changes), couldn't I just do the math (sqrt of the sum of the squares of the deviations), and put the result into Starnet? That would give me 1-Sigma, correct?