I'm preparing further refinement of a traverse I've done and put into Starnet. I'm going to take uber care to minimize centering errors etc, and shoot many repeated angles (turn and hold, turn and hold, etc.). I read somewhere (here I think), that "with a 10" instrument, shooting multiple repeated angles, left and right, you can achieve much greater accuracy". I think they said something like 2" or so...cant find the post.
Anyway, is this true? If so, it must be a statistical thing. I have a 20" instrument. If I turn the same angle a dozen times, left and right, can I put all 24 readings into Starnet to reduce them, using least squares? Would that be a way of measuring the standard deviation of the shots, and deriving a "most probable" angle? Is there another way to do this?
You can "hold and turn" from now until Christmas and you won't improve your angle much with a modern electronic instrument. The main sources of error in an electronic instrument are horizontal collimation and vertical indexing, and the way to cancel them out is by turning the angle in both instrument faces (direct and reverse).
With transits and theodolites that had upper and lower motions, the purpose behind the "hold and turn" was to ensure that the angle was turned on each part of the circle; this averaged out error caused by circle eccentricity. When you hold an angle electronically and turn back to the backsight you're still turning on the same portion of the circle; you'd have to physically turn the entire instrument. And in any case, error from circle eccentricity has probably been nearly eliminated by modern manufacturing processes.
When a manufacturer rates an instrument's angular accuracy, what they are saying is that the standard deviation of angles turned in F1/F2 is however many arc seconds. I'll leave it to someone who knows statistics to speculate on how tight of an angle you can turn with a 10" gun through repetition.
I think I recall that to get the instrument spec you have to do 2D2R. I have never understood why it was defined that way.
If you average N times that many measurements, with a rotation so you are using a different part of the angle scale each time, you can ideally divide your expected error by sqrt(N). This statement applies to brass transits and to older total stations with glass circle angle scales, and perhaps (but I'm not absolutely sure) the latest generation of electronic instruments.
One way to put it into Star*Net is to enter the average and specify the standard error as the tighter number obtained by averaging. Another is to put in each 2D2R set with a standard error of the instrument spec. I suppose you could also find other combinations.
One thing to keep in mind is that Star*Net assumes all errors are random and uncorrelated. If you enter a bunch of angles with one setup, the centering errors are identical, instead of being random, and the statistics won't be right. Rotating and re-centering the tribrachs would provide some randomization and a check on reality of centering.
Notice that 10 seconds at 384 feet (your longest sight) is only 0.02 ft sideways error. To gain any advantage from better angles, your centering needs to be better than that. And for shorter sights, centering error will dominate even for cruder angles.
Before starting a campaign for ultimate accuracy, I'd very carefully check my tribrach adjustments were as good as I could get, and figure out how well I could center them (that laser isn't quite ready).
I was thinking something like this:
I used "From-At-To", Centering errors: .02, and Accuracy settings: 10"
I'm not sure this is isolating what I'm trying to determine (how close to the ultimate capability of the instrument I can get).
I was taught to wrap an angle 6 times at each PI for route surveying and mean the angle.
I'm curious what make and model instrument you are using that has a 20" least count? I've never heard of one in modern surveying equipment.
I used to have a report on the accuracy of a Kern DKM-3 theodolite determined by the Italian IGM. One technician spent SIX MONTHS turning angles in an optical lab and then did a Fourier Analysis of the circle graduations and micrometer error. The conclusion was that it was a very good theodolite. Sometime in the past 30-40 years, one of my Graduate Students never returned it to me.
> I'm curious what make and model instrument you are using that has a 20" least count? I've never heard of one in modern surveying equipment.
Depends on what your definition of "modern" is. The GTS 203 was built around 1994. It's either a 10" or 20" instrument. Someone here suggested that if the "minimum reading" choice is 10" or 20" then it's a 20" instrument. I'm really not sure. My current challenge is to just be able to use it to it's capability, if for no other reason than to claim that if my traverses aren't closing it's the instrument's fault.
I Probably should have held out for a better machine...Paul of PA suggested a 215 or 225, which are 5" instruments. If anyone here has one kicking around they want to sell, I would consider selling this thing on ebay and moving up...Heck, I started with a 30 year old Topcon optical theodolite. I really do think I'm getting close to what this thing can do.
> I think I recall that to get the instrument spec you have to do 2D2R. I have never understood why it was defined that way.
The instrument spec is for a pointing and each angle is composed of 2 pointings. So for an angle you have the instruments spec error in the backsight pointing PLUS the instrument spec error in the foresight pointing for each angle. That is, there error in an angle that is composed of single pointings to the BS and FS is twice the instrument spec.
The error in the mean of a large number of pointings will approach zero, and this is true for both FS and BS. So to reduce your pointing error - and therfore the angle error - make more pointings. Turns out that the sweet spot in the math is 2D/2R to achieve your instrument spec for pointings in an angle.
This is detailed in Charles Ghilani's book Adjustment Computations.
"The conclusion was that it was a very good theodolite."
Too funny.
There are plenty of 10" "construction grade" instruments out there that will display to 1". There are very few true 1" instruments out there.
> There are plenty of 10" "construction grade" instruments out there that will display to 1". There are very few true 1" instruments out there.
Yea Lee, and most of them bounce around in a tool box in the back of the contractors truck. No doubt they are calibrated regularly... 😉
I used to turn multiple sets all day long in the '70's with my K & E, plumb bobs, then measure there and back with a steel tape. I retrace stuff all the time around here from guys who used the same gear. Pretty cool how good they were IMHO considering some of the terrain, but I'm not one to sweat over a tenth here and there. That was the guys monument and its 40 yrs old. Good stuff.
Pushing buttons and adjusting into outer space does not fix a problem. Just gives some folks warm & fuzzies. Nothing more, nothing less.
> one of my Graduate Students never returned it to me.
Most of us would say "one of my graduate students stole it."
The gist of your post is ok but is missing some details. An [msg=29064]old thread[/msg] tried to hash it out.
A "Pointing" in the specifications isn't just a simple reading on a target. It is defined as the average of 1 Direct and 1 Reverse at one target. That's what seems counter-intuitive to me and caused a lot of confusion in the old thread.
A 10" instrument will have 14" rms error when you take the direct reading on the target, relative to some internal reference point, averaged over all possible rotation positions the angle scale may happen to be in. The reversed reading has 14" rms error. Averaging them gets 10" rms, the specification.
Assuming independent errors, the variances add 14^2+14^2, you divide the sum by two to get an average, and take the square root to get standard deviation.
Then the foresight averaged direct and reversed also has 10" rms error, so the angle has 14" error. Doing 2D+2R brings us back to an average of 10" for the angle.
+/- the rms value = standard deviation = standard error = 68% confidence region. To get 95% or 99% confidence you have to allow it to be larger by another factor.
Total Station Accuracy Question - Testing Needed
> A 10" instrument will have 14" rms error when you take the direct reading on the target, relative to some internal reference point, averaged over all possible rotation positions the angle scale may happen to be in.
Actually, that wouldn't be necessarily true. If the specfication is that the smallest increment of the display is 10", then its entirely possible that the standard error of a direction taken as the mean of two faces could be as small as about +/-4". Some manufacturers use the same circle in a whole line of instruments and while advertising it as a ___" instrument based upon the least increment of the display are actually selling instruments that measure significantly better than the least count. Assuming just round-off error as the main source of uncertainty in a 10" instrument with a good circle, the standard error from rounding would be in the range of 3.5" to 4.0".
I would think that testing the angular accuracy would be the most straight forward way to determine what the instrument is capable of doing.
Correction: Change the word "Pointing" to "Direction" in my post.
Kent is right, of course, that least count and actual accuracy may not be the same.
> Kent is right, of course, that least count and actual accuracy may not be the same.
It seems unlikely in the case of any instrument that Topcon ever made, but if the main source of uncertainty is just that the display reads in 10" steps, and the maximum round-off error is, say, 5" or 6", then 68% of the true values would fall within 0.68 x 5" = 3.5" or 0.68 x 6" = 4.0". The standard error due to round-off in a direction taken as the mean of two faces would be about 3", which is perfectly acceptable for many purposes.
One very easy test would be to measure angles to the divisions on a high-quality engineer's scale or other divided rule.
Obviously, this assumes that a direction will be taken as the mean of two faces to cancel circle eccentricity and trunnion axis errors, and that the telescope is not grossly inferior. Since this is an El Cheapo contractor-grade instrument, presumably there is only one circle scanner in the instrument. So, for best results, all angles would need to be measured on two faces to cancel the errors due to that fact, among other reasons.
10" Total Station
Reporting to 10" cannot get more accurate due to the 10" rounding.
Now if you had a transit, multiple observations accumulated on the plates cn give much better accuracy.
You have the wrong instrument for accuracy.
A 10" instrument reporting to 1, 2 or 5 seconds can get better accuracy from multiple shots.
Paul in PA
10" Total Station
> Reporting to 10" cannot get more accurate due to the 10" rounding.
>
> Now if you had a transit, multiple observations accumulated on the plates cn give much better accuracy.
>
> You have the wrong instrument for accuracy.
>
> A 10" instrument reporting to 1, 2 or 5 seconds can get better accuracy from multiple shots.
>
> Paul in PA
As a test, in my Starnet triangle example, I kept adding additional readings of 60-00-00. Every time I added one, the Error Factor dropped. Depending on where I had my centering errors and instrument angle accuracy set, it would drop below the Chi-Square upper limit. I thought that would imply that more readings are better than fewer.
But the gist of what I'm reading here is that plunging and taking two or three readings with each face to eliminate mechanical errors might be fine, but don't spend a half an hour or more measuring an angle 50 times. Is that about the bottom line?
Still need advice on where to set the "Angle", "Direction", and "Azimuth/Bearing" settings for the instrument in Starnet. They're currently at 10".
Maybe not a 10" Total Station
> Still need advice on where to set the "Angle", "Direction", and "Azimuth/Bearing" settings for the instrument in Starnet. They're currently at 10".
What one really should do is test the instrument to see what the actual uncertainty of a direction taken as the mean of two faces really is. It is very simple to do and may well be considerably better than a standard error of +/-10". Just because the display rounds to the nearest 10" doesn't mean that 10" is the uncertainty of a direction.
For example, a direction to a target Face Lt that is displayed as 20°25'40" may be in the range of 20°25'35" to 20°25'45" if the rounding is good. That is a range of +/-5" from the value displayed and there would be a 68% chance that the value displayed was within 0.68 x 5" = 3.5", considering rounding error alone.
