I think a valid consideration is that each time a human or a computer program performs an operation on a number, there is a potential to introduce a blunder. If the operation is copying and the operation is being performed by a computer, a simple copy is safer than a combination of copying and rounding, because the rounding software may be faulty or improperly applied. If the operation is being performed by a human, copying a large number of digits is blunder-prone, so there is more justification to copy & round.
As clarity and traceability is always my goal, I would do as Bill93 argues. Use the published coordinates then provide a disclaimer about the accuracy of the distance.
The old length-relative accuracy reporting indicators (e.g third-order) were used due to the limitations of technology. Modern accuracy reporting is more robust and meaningful.
It is hard to imagine a circumstance where I would ever use intersection stations to position something. With access to only a theodolite and needing to position something at a lower order of accuracy, I could resort to a three-or two-point fix. That is, if I could find a location with a sufficient number of intersection stations providing good geometry.
The accuracy of the fix is determined by comparison of solved lengths therefore length-relative accuracy.
It should not surprise anyone that many intersection stations (e.g. church spires, water tanks, stacks and radio towers or masts) have changed or been replaced since they were positioned. I recollect a call to a penitentiary office to check where their water tank had been replaced. They must have thought I was planning a break out or something equally nefarious.
With the reliance on outside parties to update station recoveries, I note the following evidence of someone not knowing what they are doing:
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I suspect that most of us do the same thing. However, @geeoddmike raised an interesting question. For his example points, Inverse returns 3114.7015 m. One point, the CORS station, has little positional error, but the other point, the courthouse spire, has unknown but perhaps significant positional error.
So it seems obvious that the computed distance can't be correct to tenths of a millimeter. The question is, is the computed distance correct even to tenths of a meter? Of course, even if it's off by a tenth of a meter, the measurement has accuracy of better than 1:30000.
Not all data sheets report positions with 5-decimal places in seconds. For those that do, we have to think that NGS believes 5 places to be justified by one rule or another.
Still, we're really discussing rules of thumb, which aren't supposed to be deadly accurate anyway.?ÿ?ÿ
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In every datasheet download the first line is a link to a file describing the contents of the datasheet. The file provides this information about how it reports horizontal geodetic coordinates:
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In another post on this thread I mention the use of intersection stations in the three-point fix problem. Truncating coordinates would prevent the use of this method.?ÿ
BTW, if anyone has issues with NGS datasheet contents or the way data is displayed they should contact their NGS regional advisor. He can address your concerns to the NGS datasheet committee which regularly meets to address such concerns.
At one time the policy was to only display the ??geoid height? to two-decimal places. This was to discourage users from assuming they were more accurate than the centimeter level. Now they are shown to the millimeter with a disclaimer on the datasheet and link to a tool providing an accuracy assessment of the uncertainty at that point.
Unfortunately, evidence shows not many read the text nor the references.?ÿ
@geeoddmike I bet there's a good, clear sky view from the top of that mast. ????
@mathteacher?ÿ MT, most people (almost all) just enter the numbers NGS gives and use what the computer spits out and never worry(or think)
about thinks like Uncertainty of the results. They should read books like "An Introduction to Error Analysis" by John R. Taylor, Observations and Least Squares by Edward M. Mikhail ,?ÿ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurements Results, Numerical Mathematical Analysis by James B. Scarborough. I could list at least 20 more but I know you will get the idea.
0.00001 seconds that NGS list on the majority of their Data Sheets equals 0.2 to 0.3 mm. There is no way NGS can survey to that accuracy but the?ÿcomputer can give those digits. (on special projects sub-millimeter has been reached).
Probability the most accurate surveyed sites (year 2020) are the ITRF co-location sites. VLBI, SLR GNSS and DORIS and I do not think they reach sub-millimeter.
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JOHN NOLTON
@john-nolton et al,
As I tried to say in previous posts, the NGS datasheets show five-decimal place seconds to insure that transformations to Cartesian XYZ agree at the millimeter level. I tried to illustrate that the significant digits shown are NOT a statement that they are accurate at the sub-millimeter level. Accuracy is reported separately.
As Mr Nolton mentions co-location surveys, I take the liberty of posting links to three papers describing how they are done and an overview of these surveys.
https://www.ngs.noaa.gov/CORS/Articles/ties-jog.pdf
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https://www.ngs.noaa.gov/corbin/iss/reports/NRL_Stafford_Report_2019.pdf
https://www.ngs.noaa.gov/corbin/iss/reports/FortDavisSiteSurvey.pdf
in addition to Mr Nolton??s call to read papers on error analysis and uncertainty, I would also suggest consideration of the importance of equipment, techniques and data reduction to the achievement of a standard. As can be seen in the survey reports above these surveys are rather exacting with lots of redundancy.
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BTW, I highly recommend visiting the McDonald Observatory. They offer (or offered) a nice tour. It is a beautiful part of the state. I usually stay at the Paisano in Marfa when in the area. Beautiful dark skies.
@geeoddmike?ÿ I think there is a lot more to the problem than NGS giving geodetic coordinates to 0.00001 places and?ÿ
transforming them to X,Y,Z coord.?ÿ The equations are simple (see Transformation of Rectangular Space Coordinates by Erwin Schmid, Tech. Bulletin No. 15, Dec. 1960 pg. 3) In each case you need to calculate N = a/ sqrt(1-e^2 Sin^2 [Lat.])
now "a" is a big number (6378137.0000?ÿ held fixed GRS80). You need to calculate e and then e^2 to more digits than (?)
[where the (? ) Is some number of digits to the right of the decimal point], then you need the sin then sin^2, then a subtraction, then a division. All this you loose decimal places. Once you have N you still have two more Trig. functions to find and then multiply
3 times to get your final answer for X or Y coord.
It was just last year that NGS learned how to calculate 1/f past 11 digits to the right of the decimal point.(see my post on NGS and SPC that Michael Dennis did.)
GeeOddMike I know YOU know this stuff but I put it in so others will read and try to understand something about?ÿsignificant digits. I would also recommend readers reading the first chapter of "Numerical Mathematical Analysis by
James B. Scarborough" also read the first chapter of?ÿ"Introduction to Numerical Analysis" by F,B. Hilderbrand.
I think that both of these are very good.
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JOHN NOLTON
Another problem is that one position is NAD83(1995) and the other is NAD83(2011), so there will likely be a shift between datum realizations.
I have been to the McDonald Observatory, but was unaware of these co-location surveys at the time. We did take the night time tour. We were staying at the Davis Mountains State Park for a family reunion. I was born in Alpine, so I have ties to the area. I agree, it is a beautiful part of the state. I have also observed the mysterious Marfa Lights between Marfa and Alpine.
The table seems to contradict the notion that the 5 decimal places don't represent a level of accuracy. Perhaps some folks who read text and references are not capable of interpreting what they've read.
The acceptance of hand held positions was an attempt to provide better positions for scaled benchmarks. They are consider sui generis types of positions.
I can see your issue. Having worked with this data so long, it is hard to recognize how some might find it less than clear.
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i should note that I approach my 12th year of retirement. My comments on policy and the like not authoritative.
Perhaps the whole episode would have been avoided had I not used the word "accuracy" in referring to the published coordinates of a point. On the other hand, a lot of good information came out of the discussion.
Sometimes we get pretty far away from the original question or comment. My goal was to "fact check' the xkcd chart. The NGS positions were real-world points represented by a large number of decimal places in seconds that could be compared to an equivalent number of decimal places in degrees. I never intended to question NGS publications, policies, or procedures.
I always learn from your posts and this discussion was no exception.
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Significant digits is a part of the math that we need to understand to the best of our ability.
Lat Long, versus measured distance, measured angle, curve data, et al. 1:10,000 at 100 units, or 1:10,000 at a million units are not the same, as WE know. But it??s the downstream users that need help most.?ÿ
The experience that I had at a mapping company was sad all too often. Like using 3.380833 to convert UTM meters to feet and vice versa. And the number of significant digits in decimal degrees versus digits in the seconds of DMS Lat Long. Or totally ignoring US ft versus Int. Ft. No idea of the impact of digits when converting coordinates in 3,000,000 meters range, in in-house software. And god forbid, a scanned map with 16 digits hanging on everything with no realization of the source data.?ÿ
a crappy PC units converter was spread around the office without a care or understanding of the low precision. Into and back out of CAD and it??s anybody??s guess.?ÿ
So it??s not just about Lat Long, it??s all data.?ÿ
