One of the problems that the late Bill Strange and I discussed many years ago elsewhere in cyberspace where he posted as "Mr. Geodesist" was that of the probable error in replacing missing monuments using coordinates alone, such as would be the case with network RTK coordinates. Specifically, the problem was this lo those many years ago and hasn't fundamentally changed :
Suppose that:
1. On one date you determine the coordinates of some survey marker by network RTK or any other process that doesn't involve any tie to any other local reference point as conventional surveying typically does, and that process has uncertainties of, say, +/-0.02 ft. (standard error) in both the N and E values of the coordinates that you determine for the position of the marker. You determine the Northing and Easting in, say, your state plane coordinate system with uncertainties of +/-0.02 ft. in N and +/-0.02 ft. in E.
2. The marker is destroyed so completely that all that remains is the position that you earlier determined for it when it existed. You did a good job of determining the coordinates and that's all that's now left as evidence of where the marker at the corner was, +/-0.02 N and +/-0.02 E.
3. You are called back, say, a year later to remark the corner and use the same technology that can measure the N and E values of coordinates in nominally the same system with the same uncertainties of +/- 0.02 ft. (standard error) each. Say it's network RTK.
Here's the question:
What is the most probable error that you will make in remarking the corner? That is, what is the most likely distance that the new marker you set with, say, network RTK that can measure coordinates with standard errors of, say, +/-0.02 ft. will be from the original position of the marker (of which no trace remains other than the previously determined coordinates)?
Hint: If you said the most probable error is zero, that's wrong. Think again. If you said 0.04 ft. you're getting warmer, but think again.
with little thought about it at all, my first inclination is to use propagation of variances for an answer of -/+0.028ft in each E and N from the true position.
close?
Roun heah in Arkansause, the original 0.02' would be suspect. Then, the second one would be a pipe dream, and if it wound up within 0.20' well, most folks cannot build fence that good.
Time to go home. Just a geographical thing!
🙂
N
Repeatability Is Not Precision Or Accuracy
RTK has rather good repeatability, since whatever is wrong at the base is highly likey to be wrong at the rover.
However, precision and accuracy flow from multiple observations.
BTW, in order to prove an RTK survey is within ALTA specs it must be checked by a higher level of observation. Static GPS and a precise traverse would fill the bill. I don't see that RTK qualifies for that check.
Or you could just flat out lie about your precision/accuracy.
Paul in PA
wouldn't the most "probable" error run in the 0.01' range? That is 50% above it and 50% below...
you determine the coordinates of some survey marker by network RTK or any other process that doesn't involve any tie to any other local reference point as conventional surveying typically does
There's your problem right there.
Might as well use a rag tape if you're not going to use RTK properly.
:gammon:
Repeatability Is Not Precision Or Accuracy
Repeatability IS precision as far as I remember.
Our normal check to existing GPS points is 0.03'. However, you're looking for the stats, so if you're saying that the standard error is 0.02', then that's one sigma, so empirically, (0.02'x2)x2=0.08' for a 95% confidence.
We see much better than that. Like I said, it's a centimeter at 95% so 0.03' that we see is what the spec of the gear is.
Here Here and touche'. I guess that's how to spell too shea? I dunno but spell check didn't seem to mind. I don't believe this pertains to the intent or subject of the question which has to do with probability (or does it?) but suppose the coordinate was recorded incorrectly in the first place or a digit got transposed or punched in incorrectly when resetting the point. It would be great to have a reference point to check to ensure there wasn't any error.
Here we go again. Are you all really going to get suckered back into the mud???
I'm waiting for Sheldon Cooper to jump in and say Bazinga. This argument reminds me of some of the funny exchanges on Big Bang Theory.
> Here we go again. Are you all really going to get suckered back into the mud???
So, how many RTK units can you place on the head of a pin? 😀
Gavin
Evidently, you've never met Kent McMillan until recently. 🙂
He's just settling in dude.
Kris
Gavin - I think that is just good old East Texas mud/swamp.
:good: :good:
Gavin
No, Matthew is correct. It's a slough on near the Sabine River. That stuff that is in there, I can't identify, other than to say, it burns your skin.
Horrible job, great memories though. 🙂
Kris
:good:
Just to clarify the problem, the situation is that on one day, using some positioning technology that gives coordinates with standard errors of 0.02 ft. (say) in N and in E values, the system used displays the coordinates for a boundary marker that you find (or originally set). Then, on some later day after marker and all traces of it have been destroyed, you set a new marker at a position that the same positioning system says has the identical coordinates, values that also have standard errors of 0.02 ft. in N and in E.
So, just using the coordinates displayed by the positioning system, you would think that the replaced marker is exactly where the marker originally was, right? Or you recognize that there is some random error in the replacement, but still the most probable position of the replaced marker is exactly where the marker originally was.
The mathematic situation is this:
1. Call the original markers (1) and the replaced marker (2). The coordinates displayed for (1) are N(1), E(1), but since both contain some unknown errors n(1) and e(1), the actual position of the original marker is N(1)+ n(1), E(1)+ e(1).
2. Call the replaced marker (2). The coordinates displayed for (2) when it was set with the utmost care are exactly the same as those of (1): N(1), E(1). However those coordinates also contain unkonwn errors n(2) and e(2). So the actual position of the replaced marker is N(1)+ n(2), E(1)+ e(2).
3. The North and East components of the difference in the actual positions of original and replaced markers is n(1)- n(2) for Northing and e(1)- e(2) for Easting.
4. Since n(1) and n(2) both have standard errors of +/-0.02 ft., Assuming that they are random and are normally distributed that means that the quantity n(1)- n(2) is also normally distributed, but with a standard error of +/- SQRT(2) x 0.02 = +/-0.028 ft.
5. Likewise for the quantity e(1)- e(2). It is normally distributed with a standard error of +/-0.028 ft.
6. If the error in the actual replaced position of (2) is D, the distance from the actual position of the replaced marker to the actual position of the original marker, then D = SQRT{[ n(1)- n(2)]^2 + [ e(1)+ e(2) ]^2 }
7. The actual values of the random errors are not known, but as derived above, the standard errors of the n and e differences are +/-0.028 ft.
8. However, D, the error in the actual replaced position of (2) propagated from the random errors in the n and e differences, is not normally distributed. That is where the answer to the question lies. Intuition that said the most likely error was zero has failed. Zero is actually a very, very unlikely error. Interestingly, there is a larger number that is the error most likely to occur.
> Our normal check to existing GPS points is 0.03'. However, you're looking for the stats, so if you're saying that the standard error is 0.02', then that's one sigma, so empirically, (0.02'x2)x2=0.08' for a 95% confidence.
Kris, the question is somewhat different. There actually is an error in this situation that is the most probable error and it won't be zero. The implications are that if a surveyor proceeds as described he or she is saying that they definitely expect to miss the original corner by a certain amount and consider it to be quite unlikely that they will actually hit the corner with the replaced marker. This would be an inherent characteristic of network RTK, for example, if used as described in this problem.
Kent
You should google the "Delphi Method" or analyzing data. It seems you're missing a critical component for this method.
🙂