If you wonder about things like grid-ground and you aren't sure why you might be seeing differences between your GPS measurements and your total station measurements, here is a little exercise you can run through to firm up your understanding and increase your confidence in your approach to combining these 2 measurement technologies in your daily surveying practice.
Try going to your local EDM CBL nearest to your town to measure it with your GPS. Note that the published lengths are NOT projected to the state plane grid or computed as ellipsoid distances. They are purely slope distances measured by NGS using high precision instruments on 2 separate days. They reduced their slope measurements to the mark to mark published lengths and the horizontal lengths. Note the accuracy is published at tenths of millimeters.
See here for an example -
Texas EDM CBLs
https://www.ngs.noaa.gov/CBLINES/BASELINES/tx
Example - BASE LINE DESIGNATION: MIDLAND CBL TEXAS
You can compare your EDM slope measurements with the published mark to mark lengths to make sure your instrument is working properly. In some states, in order to qualify to perform work for the DOT or other agencies, you are required to measure an NGS EDM CBL using your GPS to verify your equipment, methods and procedures are all working properly.
Using 2, 3, or 4 GNSS receivers, log data occupying all the marks to obtain simultaneous data sets between each pair of marks. Then post-process all the baselines between all the marks. Note, you do NOT have to select a grid coordinate system to process that raw GPS data. That is because the raw GPS data is NOT referenced to the state plane coordinate system OR the ellipsoid as some may assume.?ÿ
So, all you need to do is open a new project to start a post processing session and select US Survey Feet as the units. Then, process the raw data to solve all the baselines which will be displayed as delta X, Y, and Z between all the points and the vector lengths will match the published EDM CBL mark to mark lengths AND your EDM slope measurements. EDM slope length = GNSS vector length. [ SQRT(dX^2 + dY^2 + dZ^2)= straight vector between the 2 points) ]?ÿ
And by the way, you can do the the same thing using RTK instead of post-processing. Just place your Base receiver on a mark and observe all the other marks with your Rover. For a full data set on that EDM CBL, move your Base to each mark and repeat the whole process. RTN and VRS are not well suited to make this direct comparison between GNSS vectors and EDM slope distances.
In this old article linked below, originally printed as a series of 3 installments for Professional Surveyor magazine, I purposely chose to use an example located near sea level in order to make an important point about scale factors. The EDM CBL comparison with GNSS vectors example is in this paper too. Go out and try it for yourself. Any uncertainty you had about grid-ground will disappear after you enjoy a day at your local EDM CBL performing this exercise. Why bother understanding any of this? Stay tuned for the next step, combining GNSS vectors and total station measurements in a least squares adjustment.?ÿ
GPS & EDM Measurements ?? Why Don??t They Match?
http://www.sawj.org/files/drupal4/GPS_Vs_EDM.pdf
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EDMI Calibration Base Line Program
https://www.ngs.noaa.gov/CBLINES/calibration.shtml
The (grotesquely) inaccurate statements made by salesmen, repeated by surveyors and believed by the public have obscured the basics of measurement science. If you properly project any two of those positions then compute the adjusted to ground vector you will get a third copy of essentially the same answer. Nearly all of the varistion will be in the observations.
CBLs are also a good playground for calculating distances, although the one in Midland won't work because its points don't have data sheets. The CBL in Limon, CO does have data sheets for three of its points and its elevation is more than 1600 meters, so it's a good one to use for demonstrations. Its description is here:?ÿ
https://www.ngs.noaa.gov/CBLINES/BASELINES/co
The PIDs are KJ0588, KJ0594, and KJ0593, the 0, 1400, and 400 meter marks, respectively.
The Colorado State Plane grid distance between the 0 and 1400 marks is 1399.8316 meters. The average of the combined factors for the two points is 0.99968732. Dividing the grid distance by the average combined factor gives 1400.2694 meters, 2.5 mm shorter than the published horizontal distance of 1400.2719 meters.
The calculated mark-to-mark distance is 1400.2935 meters, 1.3 mm shorter than the published distance of 1400.2948 meters.
The first calculation demonstrates the difference between grid distance and horizontal distance and how one can be transformed into the other. The second calculation demonstrates the nature of a slope distance and its relationship to a 3d coordinate system.
Perhaps the most important lesson is that State Planes and xyz-coordinate systems are models;very good ones, but models nonetheless. Expecting the calculated distances to match measured distances is way too much to hope for, but when they're close, we can be confident that we're not horribly sigodlin.
Please forgive me for introducing calculations into the discussion. I can't measure, but I can cipher.
It might be interesting to break the 1400+ meters into smaller arbitrarily chosen pieces and use the combined factor for each piece, to see if the total came out even closer. The CF isn't a perfectly linear function even over that distance.
Right. While the elevation factors create a sloped straight line, the scale factor is a periodic function in a Lambert projection. Over short distances near the central parallel, it's nearly straight, but it curves sharply upward outside the limits of the projection. The difference between the combined factor for Limon CBL 0 and that for CBL 400 is 0.00000008, so the average for the two differs from either one by 0.00000004. In other words, either could be substituted for the mean with little loss in accuracy.
There's a really great CBL for learning purposes in Whiteville, NC, near the coast. It's the last one in the list here:?ÿ https://www.ngs.noaa.gov/CBLINES/BASELINES/nc
The elevation changes from 26.5 meters at CBL 0 to 21.0 meters at CBL 1030. Doing no math, but just comparing the difference between the horizontal distances and the mark-to-mark distances as you proceed down the line clearly demonstrates that mark-to-mark is a slope distance. Going just a bit into math, the horizontal distance from 0 to 1030 is 1030.0282 meters and the elevation change is 5.028 meters. The Pythagorean Theorem then says that the slope distance between the two is sqrt(1030.0282^2 + 5.028^2) = 1030.0405 meters. The published mark-to-mark distance is 1030.0428 meters, a difference of 2.3 mm.
When you're considering grid, ground, slope, and horizontal distances, CBLs are a tremendous learning tool. They're better when they have data sheets for the points, but there are relationships that can be explored without them.
@thebionicman, Agreed 100%. I would edit my post above to replace "match" with, "may be compared to". As for projections, etc., I was only attempting to offer those bewildered by this so called grid-ground issue a way of "seeing" or discovering something they most likely are not aware of. A visit to the EDM CBL to perform this exercise will give them an experience that will solve the problem swiftly.
@mathteacher, I thought about mentioning that some marks on some CBLs are in the NGS database, but then I decided to leave that part out initially considering the folks this little drill is intended to help. But, I love your replies and I totally agree with you that these CBLs are fantastic play grounds, or, labs, where you can test lots of things with assurance you are getting the "right" answers, ie, you can be confident are "doing it right".
Lab is probably a better term than playground; to me, they're both. One aha moment for me came when I saw the difference between a CBL's State Plane grid azimuth from end to end and its geodetic azimuth over the same distance. Aha! The curved surface is not represented exactly by the plane surface! The source CBL was the Asheville, NC CBL.
Of course, your published work is also invaluable. Thanks for sharing so much.
Another resource is the Technical Memorandum: https://geodesy.noaa.gov/library/pdfs/NOAA_TM_NOS_NGS_0010.pdf
Images from Appendix I are shown below: ?ÿ
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