Determining Total Station Distance Standard Errors, Part II

> 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?

What, calculate the apparent scatter of 100 measurements to the same prism remaining on the same point from the same instrument station? Sure, you could do it, but it wouldn't give any very useful answer.

>Would that give me 1-Sigma value I could use in Starnet for the uncertainty of distance measurements?

No, it wouldn't. Most EDMs produce range measurements with errors that are non-linear and dependent upon a variety of factors, including the distance measured.

A much more valuable test would be to get a good quality graduated steel tape, stretch about 10m of it under standard tension and known temperature, uniformly supported on a smooth horizontal surface, and move a prism in tribrach along it, taking range measurements at exact regular increments of, say, 0.5m. Any non-linear cyclic errors should show up when the results are examined.

What I said was "Standard errors are 1-sigma, not 95% confidence." I had interpreted a previous comment to say that you intended to put a 95% number into Star*Net. I meant that the standard error number you put into Star*Net is 1-sigma.

The phrase I was responding to was "the Standard error which I'd derive in Starnet, using the 95% Chi squared results."

I didn't intend it to be a comment on the manufacturer's specs, as I'm not sure if they all specify it one way or the other.

> What, calculate the apparent scatter of 100 measurements to the same prism remaining on the same point from the same instrument station? Sure, you could do it, but it wouldn't give any very useful answer.

But wouldn't it isolate the errors due strictly to the EDM electronics in the instrument (even if for only that one distance)? And wouldn't it tell me how wide the scatter is? Isn't that what Standard Deviation (for a single part of the whole process) is all about?
>
> >Would that give me 1-Sigma value I could use in Starnet for the uncertainty of distance measurements?
>
> No, it wouldn't. Most EDMs produce range measurements with errors that are non-linear and dependent upon a variety of factors, including the distance measured.
>
> A much more valuable test would be to get a good quality graduated steel tape, stretch about 10m of it under standard tension and known temperature, uniformly supported on a smooth horizontal surface, and move a prism in tribrach along it, taking range measurements at exact regular increments of, say, 0.5m. Any non-linear cyclic errors should show up when the results are examined.

That seems more an attempt to determine the accuracy (as opposed to the precision) of the EDM, wouldn't it? I plan on taking the unit to an NGS range in the spring for that.

Once I can confirm the systematic errors (including the instrument constant), and correct for that if needed, wouldn't I then be able to apply the +/- xx mm + xx ppm learned from the proposed test above?

Do most folks just use the published numbers for their instrument in Starnet, and be done with it?

> > What, calculate the apparent scatter of 100 measurements to the same prism remaining on the same point from the same instrument station? Sure, you could do it, but it wouldn't give any very useful answer.
>
> But wouldn't it isolate the errors due strictly to the EDM electronics in the instrument (even if for only that one distance)? And wouldn't it tell me how wide the scatter is? Isn't that what Standard Deviation (for a single part of the whole process) is all about?

No. The standard error of a range measurement should be a measure of the errors (measured - actual) across the whole spectrum of performance. I'd order a copy of J.M. Rueger's "Electronic Distance Measurement" if you want to learn something about EDM errors.

> > A much more valuable test would be to get a good quality graduated steel tape, stretch about 10m of it under standard tension and known temperature, uniformly supported on a smooth horizontal surface, and move a prism in tribrach along it, taking range measurements at exact regular increments of, say, 0.5m. Any non-linear cyclic errors should show up when the results are examined.
>
> That seems more an attempt to determine the accuracy (as opposed to the precision) of the EDM, wouldn't it? I plan on taking the unit to an NGS range in the spring for that.

Well, to be a meaningful number, the standard error of a range measurment should be not a measure of internal precision, but of external accuracy.

A person with a minimal interest in learning about EDM errors should probably just use the manufacturer's statement of accuracy and just devise a test method to make sure that the standard error values based upon that are not too small.

> A much more valuable test would be to get a good quality graduated steel tape, stretch about 10m of it under standard tension and known temperature, uniformly supported on a smooth horizontal surface, and move a prism in tribrach along it, taking range measurements at exact regular increments of, say, 0.5m. Any non-linear cyclic errors should show up when the results are examined.

Like this test? This seems pretty easy to do, so I'll get on it.

> just devise a test method to make sure that the standard error values based upon that are not too small.

Is this suggesting a different test, or the one described above?

ps: thanks for the J.M. Reuger reference. Very cool, but probably the densest stuff I've read since studying hyperbolic navigation principles of Loran C (a long, long time ago:-D )

Off on a tangent....

We checked three instruments on a CBL last year;

A Leica TCRA1101+ (manufacturer spec 2mm, +/- 2ppm) tested at 0.0006m, +/-0.0003m and 1.2ppm, +/- 0.6ppm.
A Leica 1201 (manufacturer spec 1mm, +/-1.5ppm) tested at 0.0004m, +/-0.0003m and 0.1ppm, +/-0.5ppm.
A Leica 1201 (manufacturer spec 1mm, +/-1.5ppm) tested at -0.0004m, +/-0.0003m and 0.8ppm, +/-0.5ppm.
The CBL test utilized a Leica NL (1:200,000) to center and GPH1P prisms on GZR3 carriers, GDF321 tribrachs and GST-20 tripods.

We were quite happy with the results.
And we like the Swiss.

> Like this test? This seems pretty easy to do, so I'll get on it.
>
>
>

Yes, that is from Rueger's early paper. There are more sophisticated ways to test cyclic error, but that is probably the easiest one I know of.

> > just devise a test method to make sure that the standard error values based upon that are not too small.
>
> Is this suggesting a different test, or the one described above?

A way to test whether the manufacturer's standard error values are too small would be to lay out a line of control points over the maximum distance you expect to use your EDM so that the total maximum distance is subdivided into parts of different lengths. Then you successively occupy each point and measure the distances to the other points and adjust the whole works by least squares. The ranges should be distributed so that they are not all even multiples of 10m, have units in the ones place that vary, i.e. 1, 2, 3, ... 0, and withmore or less the same numbers of each.

You can test the instrument constant by successively adding or subtracting a small constant from all the ranges and readjusting them. If the instrument constant is correct, the increased or decreased ranges should give a result with a larger error factor in the adjustment.

What I should have mentioned, though, is that the cyclic error test gets much simpler depending upon the fine modulation frequency of the instrument. An instrument with a fine modulation frequency of 14.98 MHz should have a basic measuring length of 10m and any cyclic error should repeat over intervals of 10m.

If your instrument uses a higher fine modulation frequency, then the basic measuring length will be expected to shorten in inverse proportion to the above, i.e. a frequency of 149.8 MHz should have a basic measuring length of 1m with any cyclic error repeating over that distance. That is much easier to test.

> What I should have mentioned, though, is that the cyclic error test gets much simpler depending upon the fine modulation frequency of the instrument. An instrument with a fine modulation frequency of 14.98 MHz should have a basic measuring length of 10m and any cyclic error should repeat over intervals of 10m.
>
> If your instrument uses a higher fine modulation frequency, then the basic measuring length will be expected to shorten in inverse proportion to the above, i.e. a frequency of 149.8 MHz should have a basic measuring length of 1m with any cyclic error repeating over that distance. That is much easier to test.

Good Lord, Kent! I was well on my way to planning both of the tests above...building my "linear sliding" tripod/tribrach/prism setup, etc. and now you want me to figure out what the EDM frequency of my instrument is??? Help me out here!

Is what you're referring to the "unit length of the instrument", mentioned by Rueger?
He called out using 1m, .5m, .25m...I was going to do 1 ft increments, because that's how my steel tape is marked, and measure x number of feet, but I don't know yet what the "unit length" is. I was just about to ask that when you posted.

As for the second test you suggest...that IS a second and separate test, correct?
Thank you for all the help (and the head aches).

> Is what you're referring to the "unit length of the instrument", mentioned by Rueger?
> He called out using 1m, .5m, .25m...I was going to do 1 ft increments, because that's how my steel tape is marked, and measure x number of feet, but I don't know yet what the "unit length" is. I was just about to ask that when you posted.

Well, the unit length is a function of the EDM design, meaning: whether it operates on the principle of phase comparison, what the wavelength of the carrier is, and what the fine modulation frequency is. The basic measuring length is a function of those and they vary by model and manufacturer. Somewhere there should be that basic information available.

I found this source that appears to provide the information that the basic measuring length of the Topcon ES series is 2m. That for a GTS502 is 5m

http://www.dtpli.vic.gov.au/__data/assets/excel_doc/0020/218162/Topcon-Instrument-Parameters.xls

Many other total stations are described on this list from the same source:

http://www.dtpli.vic.gov.au/__data/assets/excel_doc/0006/218166/EDM-Instrument-Parameters.xls

In that case, you can perform the test that Rueger described, but using a 2m or 5m graduated tape, advancing the tribrach in prism by 1/10 of the basic unit length between measurements.

> A way to test whether the manufacturer's standard error values are too small would be to lay out a line of control points over the maximum distance you expect to use your EDM so that the total maximum distance is subdivided into parts of different lengths. Then you successively occupy each point and measure the distances to the other points and adjust the whole works by least squares. The ranges should be distributed so that they are not all even multiples of 10m, have units in the ones place that vary, i.e. 1, 2, 3, ... 0, and with more or less the same numbers of each.

I'm thinking of doing this in addition to the cyclic test that is ongoing.
Before I commit though, I want to be sure I have the equipment to do it properly.

Question One is: How many points, and must they all be set up at once? I only have 4 tripods, including one prism pole tripod. I have three prisms, two on tribrachs with optical plummets, one without (but I can do the setup with another that does and then swap the prism).

Is it worth even trying this if I have to move the equipment a bunch?

PS: I'm still thinking the "manufacturer's standard error values" might be too high, not too small. But this test would seem to confirm that one way or the other.

Determining Cyclic Errors of EDM Ranges

For those others who may be interested in determining the cyclic errors of the EDM in their total station, here's one way to do it with very little fuss. To do it, you need to know the basic measuring length of your total station. That is half the wavelength of the carrier at the fine modulation frequency. This example is for an instrument with a 10m basic measuring length.

This method is neat because it does not require exceptionally careful alignments or centering and does not require knowing any distance with great accuracy. The range consists of eight stations that can be something as crude as chalk marks made on a sidewalk at the following distances +/- a couple of centimeters. Chalk marks made the same distance in from the straight edge of a sidewalk are an easy way to lay this test range out.

Sta Dist (m)
A1 0.00
B1 2.50

C 16.25
D 18.75
E 21.25
F 23.75

B2 35.00
A2 37.50

On a fairly level lawn, just pulling a tape for alignment and setting nails at the distances +/- a couple of centimeters should work fine.

The test consists of setting up two prisms in tripods at the stations B1 and B2 and then successively occupying stations C, D, E, and F, all of which are on line with B1-B2 within a few centimeters.

At each setup in F Lt and F Rt, log slope ranges in meters to B1 and B2, zenith angles to B1 and B2 for each slope range, and the angle B1-Station-B2.

Occupy c, D, E, and F getting what in effect would be sufficient data to solve their positions by resection if the coordinates of B1 and B2 were known.

Then shift the prisms and tripods to A1 and A2 and occupy C, D, E, and F again, logging the same measurements as before at each.

The following ranges +/- a cm or two will have been measured:

Prisms @ B1 & B2 (32.50m total length)

13.75
18.75
16.25
16.25
13.75
18.75
11.25
21.25

Prisms @ A1 & A2 (37.50m total length)

16.25
21.25
18.75
18.75
21.25
16.25
23.75
13.75

From these measurements, the cyclic errors of EDM ranges at increments of 2.5m representing four points in the cyclical error pattern that repeats every 10m can be worked out from these ranges:

11.25m
13.75
16.25
18.75
21.25

The distances A1-A2 and B1-B2 corrected for cyclic error are taken as the arithmetic means of the sums of the distances measured A1-Station-A2 and B1-Station-B2, respectively. The actual ranges may contain some error in the instrument or prism constants. That doesn't matter for the purpose of this exercise, which is to describe the pattern of cyclic error.

Knowing the mean distances A1-A2 and B1-B2, the apparent errors at the stations where ranges 16.25 and 18.75 were measured to both prisms at the same station can be worked out as the correction that would have to be applied to each of the pairs of 16.25m or 18.75m ranges that would give the mean distance between the prisms.

The first assumption is that the cyclic errors in 11.25m and 21.25m are essentially the same for an instrument with a 10m basic measuring length. Likewise, the cyclic errors in 13.75m and 23.75m,

That gives the cyclic corrections for ranges _1.25m, _3.75m, _6.25m, and _8.75m.

To verify that these same corrections apply at longer ranges, the statins A1, B1, A2, & B2 can be moved away from C,D,E,& F by some integral multiple of the basic measuring length and the test repeated.