This is another minor part of the project that I'm working on. The next phase of the work is to run conventional traverse from CP No. 87 to CP No.108, along a run of about 1789 ft., through what will be nine stations. So, the traverse legs will average about 200 ft. and there really is no feasible way to extend them.
The traverse route is shown schematically in red. The GPS vectors are the thin blue lines.
So far, CP Nos. 86, 87, 108 and 109 have been positioned by GPS methods that give the following uncertainties in their NAD83 positions.
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Error Propagation
=================
Station Coordinate Standard Deviations (FeetUS)
Station N E Elev
86 0.008998 0.007779 0.037761
87 0.012242 0.011079 0.045470
108 0.012809 0.011464 0.048869
109 0.013933 0.012767 0.045284
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What the standard deviation values mean is that there is a 68% chance that the errors in the N and E components of the coordinates computed from the GPS vectors are not in error by more than the values listed. They look pretty good, right?
The idea is to run the traverse from CP No. 87 to CP No. 108 (through the intermediate stations 101 through 107, not shown), using 86-87 as the starting azimuth and 108-109 as the closing azimuth. In other words, this will be a closed traverse, not an open traverse.
But while the standard errors of CP Nos. 86 and 87 and of 108 and 109 are quite small (and probably much better than the typical RTK use or OPUS-RS solution would ever approach), the azimuth uncertainties of the lines between the pairs are not negligible:
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Adjusted Azimuths (DMS) and Horizontal Distances (FeetUS)
=========================================================
(Relative Confidence of Azimuth is in Seconds)
From To Grid Azimuth Grid Dist 95% RelConfidence
Grnd Dist Azi Dist PPM
86 87 187-16-57.24 249.5169 21.56 0.0293 117.5397
249.5449
108 109 62-58-13.25 254.0454 27.21 0.0330 130.0604
254.0735
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The azimuth uncertainty of 86-87 is about 0°00'22" (at 95% confidence) and that of 108-109 is about 0°00'27" (also at 95% confidence). So, is that much better than any surveyor could possibly expect or is there an easy way to improve the positional uncertainties of the control points along the traverse?
A very important question, in mind, is the azimuth uncertainty from 86 to 109.
GPS does not tend to make short pairs useful, in my experience. The accuracy, over long distances makes widely separated pairs very useful.
In the end, one can only have a CEP of perhaps .05'. (Humor me.) Between two pairs 200' apart a combined 0.10' could easily create an unacceptable azimuth uncertainty.
But, over 2000', many surveyors would be quite happy with an azimuth uncertainty equal to a tenth.
Using a pair of receivers on a pair, while also using one or two on a base can create baselines and vectors that could make a short pair more useful. Personally, I have found that to be the case. Yet, I cannot recommend a pair. Triplets or greater are needed, in my opinion.
So the answer is always more quality measurements, with well planned baselines and stations.
Why don't you run your proposed traverse in planning mode? If the resulting uncertainties are not within acceptable limits, you can pre-plan what additional measurements you can add. How about tying some points along the way from 2 different stations? They don't even have to be related to the boundary or anything, you would just be adding figures. It will all come down to your coordinate uncertainties, anyway, right? Uncertainties in azimuth can be huge for points right next to each other and the positional uncertainty will still be good I think. I' m just asking because I'm sure you already know and are using your example as an opportunity to teach.
Traverse Between GPS Azimuth Pairs
requires long observations to expect precision from the get-go.
The traditional traverse from monument pair to monument pair starts with precise monuments. Typical GPS does not meet that criteria.
GPS triples provide better opportunity to get satisfaction on the first go around with less drastic adjustments.
Paul in PA
Would it be better, if you had 4 receivers available, to set up the 4 receivers, 2 on each end, and let them collect data at the same time? I would think that would help tighten up the two azimuth pairs.
This type of situation is why I have 4 static receivers.
I am watching this thread with great interest. I am always wanting to improve my methods.
> A very important question, in mind, is the azimuth uncertainty from 86 to 109.
But considering that 86 and 109 aren't intervisible, how can you use them to check the traverse for blunders? You have the coordinates of the endpoint and their uncertainties, but without the azimuth conditions of 86-87 and 108-109, what do you have?
> GPS does not tend to make short pairs useful, in my experience. The accuracy, over long distances makes widely separated pairs very useful.
Note that the uncertainties in the azimuths of 86-87 and 108-109 are only as good as they were because they were positioned via static GPS methods. Centimeter or worse RTK would have given azimuth uncertainties more than twice as large as those in the example, as would OPUS-RS most likely.
> So the answer is always more quality measurements, with well planned baselines and stations.
Actually, the answer in this case will almost certainly be to simply add two more GPS-derived positions along the traverse.
> Why don't you run your proposed traverse in planning mode? If the resulting uncertainties are not within acceptable limits, you can pre-plan what additional measurements you can add.
Yes, it would be possible to do that, but in this example, the features of the problem are fairly obvious by inspection, i.e. the azimuth pairs at the ends of the closed traverse are relatively large.
> Would it be better, if you had 4 receivers available, to set up the 4 receivers, 2 on each end, and let them collect data at the same time? I would think that would help tighten up the two azimuth pairs.
Well, one could, I'm sure, do all sorts of things to decrease the uncertainties of the azimuths between 86-87 and 108-109 (including make solar observations), but isn't the best solution the one that gets the same or better results for the least effort? In this case there are at least two GPSable points along the traverse, 106 and one more. When those GPS derived positions are added to the adjustment (taking their uncertainties into account), the results are much improved in various ways.
Add a solar observation.
> Add a solar observation.
Except you'd really need two solar observations, one at each endpoint, to accomplish anything significant and that would add about an hour total to the field time: 20 minutes to do three sets on the Sun and at least 10 minutes setup at each end.
In an hour, you could get GPS-derived coordinates for at least two control points along the traverse route.
> ... is there an easy way to improve the positional uncertainties of the control points along the traverse?
Setting your base up on any point other than 86 and retying the others a second time would certainly tighten down your uncertainties. I know you like to do rapid-static but I'd be perfectly comfortable with RTK vectors. Set up the base and hit 5 control points should be an hour of work.
> Add a solar observation.
My experience with solar - which is admittedly limited - is that accuracies achieved in practice are comparable to those that Kent is sitting on now. I suppose that with practice one could do much better. How much practice have you had doing solars lately?
> > ... is there an easy way to improve the positional uncertainties of the control points along the traverse?
> Setting your base up on any point other than 86 and retying the others a second time would certainly tighten down your uncertainties. I know you like to do rapid-static but I'd be perfectly comfortable with RTK vectors.
I don't think that there is all that much room for improvement of the uncertainties of the azimuth pairs by GPS. At a nominal separation distance of 250 ft., an azimuth uncertainty of +/-10" (standard error, not 95% confidence, amounts to a net uncertainty component of only +/-0.012 ft. perpendicular to line.
> My experience with solar - which is admittedly limited - is that accuracies achieved in practice are comparable to those that Kent is sitting on now. I suppose that with practice one could do much better. How much practice have you had doing solars lately?
I'm willing to specify that a surveyor who had the proper equipment could determine the azimuth between two control points about 250 ft. apart with a standard error of better than +/-3" by solar observations. However, there is a relatively narrow window of time when that would be feasible (Sun's altitude below about 30degrees) and the sky conditions would be limiting (Sun casting sharp shadows and no intermittent cloud cover). To realize the full accuracy of the azimuth observation, the observation would have to be made and the traverse continued from the same tribrachs so that no centering errors would degrade the results.
All of that is just inconvenient compared to other options.
I think you'll see diminishing returns on any additional GPS pairs. You've got two pairs at each end and a point in the middle. Adjust with a pair on one end and one point at the other end, look at the results. Then add the pair point at the end pair and compare. Then add the midpoint and evaluate.
Adding additional points won't improve your results much, neither in the actual coordinates nor in the positional uncertainty of the points along the traverse.
>So the answer is always more quality measurements, with well planned baselines and stations.
>>Actually, the answer in this case will almost certainly be to simply add two more GPS-derived positions along the traverse.
I think we said the same thing there.
I agree with Shawn that a 3rd intermediate pair probably won't have a lot of direct return, given the short distances, but I'm wondering what a vector between 106 & say 103 or 104 might do.
Try it and see. I don't think the positional uncertainties of your intermediate points will be as bad as you expect.
Kent-
It looks like to me that with reasonably good procedures and equipment (which is certainly a given in your case), you might have around a 2 minute angular error just holding one pair as a reference azimuth and projecting the azimuth error and coordinate uncertainties. Holding the azimuth tie fixed at the end of your run would probably knock it down to 1 minute in the middle of your run. Why not drop in a third pair in the middle and mitigate the whole enchilada down to the precision specs you need (unless you need tighter azimuths across the whole project better than 30 seconds?). Also, do you need to carry ortho heights or is it a horizontal only deal?
Just 2 cents worth.....
Kent:
If this example is like your previous post about the traverse along the rock wall, the coordinate uncertainties you show are relative to the CORS sites that you used in the OPUS solutions, aren't they? As an old woods surveyor who in the day would be happy to see those low uncertainties in every course of a traverse, I find it amazing that the tiny uncertainties you show are relative to CORS sites many, many miles away.
Chris
