In a thread below about that description of a 90.00 acre tract of land that included the geodetic grid coordinates of various points positioned by the survey, there was some discussion about the accuracy of coordinates. Here's the situation: the connection was made to NAD83 (CORS96) Epoch 2002.0 via OPUS solutions on three days.
Detail showing three OPUS solutions on Control Point No.1 and estimated actual position
Pt. 1 in the diagram represents the best estimate of the control point obtained by least squares (an adjustment of the three days' positions in Star*Net using the covariance matrices for each that OPUS reports). The residuals were:
1Day313-1 = 0.028'
1Day278-1 = 0.026'
1Day279-1 = 0.042'
The least squares estimate of Pt. 1 had standard errors of 0.013 ft. in its N and E components, meaning there was about a 68% chance that the estimate was in error by less than that amount.
Then, NAD83 was transferred from that control point via GPS vectors,
Overall Survey Network Tied to Control Point No.1
All of the vectors were short (well under 10km) and the static L1 solutions were generally quite good. For example, the relative uncertainty of Rod and Cap No. 174 in relation to CP 1 was under 0.01 ft. at 95% confidence. That was one of the best transfers.
There were other points, Nos. 177 and 176 roughly 400 ft. away from 174 that were positioned from CP 1 and then the angle 177-174-176 and the distances 174-177, 177-174, 174-176, and 176-174 were measured conventionally.
Detail Showing Connections from No.174 to other GPS Points
Finally, with the instrument set up on No. 174, reference markers about 20 ft. away on each of the proposed boundaries leading to No. 174 were set out with the total station and the distances measured to them directly from No.174.
Details of Markers Set for Reference about 20 ft. away from No.174
So, the relative uncertainties of the reference markers Nos. 186, 187, and 188 in relation to No. 174 were very small, under 0.01 ft. However, the uncertainties of the same markers in relation to NAD83(CORS96)Epoch 2002.0 as delivered via OPUS were greater than theirs to each other. Their NAD uncertainties at 95% confidence level were about 0.035 ft. in N and E and about 0.014 at 68% confidence.
So does that mean that a surveyor ought to round all coordinates off to the nearest 0.03 ft.? If he did, he'd lose the fact that those four markers, Nos. 174, 186, 187, and 188, were much more accurately positioned in relation to each other.
This is why I think it's reasonable to quote coordinates in feet to three decimal places, but note that their absolute uncertaintes in relation to NAD83 are whatever value they are, but which is most likely larger than 0.01 ft. The additional decimal place preserves the local relative accuracy of survey markers (assuming that it's there) that would be lost by coordinate rounding.
From a bearing prospective, I agree. Many times, without taking the coordinates out to three, sometimes 4 decimals will result in different bearings (seconds) along a line.
Not taking the accuracy standpoint, but I don't want my description to argue with myself in the body of the description.
> From a bearing prospective, I agree. Many times, without taking the coordinates out to three, sometimes 4 decimals will result in different bearings (seconds) along a line.
>
> Not taking the accuracy standpoint, but I don't want my description to argue with myself in the body of the description.
Yes, exactly. That's why it's better to make some statements about coordinate accuracy and not try to do it via the precision of expression. I only make a statement about accuracy with respect to NAD83 since that seems the most useful uncertainty to me.
That is, if the next surveyor through is also tied to NAD83(CORS96)Epoch 2002.0, he or she would be able to confirm that his or her own determinations of coordinates of the same points are either consistent or not with those I reported.
> In a thread below about that description of a 90.00 acre tract of land that included the geodetic grid coordinates of various points positioned by the survey, there was some discussion about the accuracy of coordinates. Here's the situation: the connection was made to NAD83 (CORS96) Epoch 2002.0 via OPUS solutions on three days.
>
> Detail showing three OPUS solutions on Control Point No.1 and estimated actual position
>
>
> Pt. 1 in the diagram represents the best estimate of the control point obtained by least squares (an adjustment of the three days' positions in Star*Net using the covariance matrices for each that OPUS reports). The residuals were:
>
> 1Day313-1 = 0.028'
> 1Day278-1 = 0.026'
> 1Day279-1 = 0.042'
>
> The least squares estimate of Pt. 1 had standard errors of 0.013 ft. in its N and E components, meaning there was about a 68% chance that the estimate was in error by less than that amount.
>
> Then, NAD83 was transferred from that control point via GPS vectors,
>
> Overall Survey Network Tied to Control Point No.1
>
>
> All of the vectors were short (well under 10km) and the static L1 solutions were generally quite good. For example, the relative uncertainty of Rod and Cap No. 174 in relation to CP 1 was under 0.01 ft. at 95% confidence. That was one of the best transfers.
>
> There were other points, Nos. 177 and 176 roughly 400 ft. away from 174 that were positioned from CP 1 and then the angle 177-174-176 and the distances 174-177, 177-174, 174-176, and 176-174 were measured conventionally.
>
> Detail Showing Connections from No.174 to other GPS Points
>
>
> Finally, with the instrument set up on No. 174, reference markers about 20 ft. away on each of the proposed boundaries leading to No. 174 were set out with the total station and the distances measured to them directly from No.174.
>
>
> Details of Markers Set for Reference about 20 ft. away from No.174
>
>
> So, the relative uncertainties of the reference markers Nos. 186, 187, and 188 in relation to No. 174 were very small, under 0.01 ft. However, the uncertainties of the same markers in relation to NAD83(CORS96)Epoch 2002.0 as delivered via OPUS were greater than theirs to each other. Their NAD uncertainties at 95% confidence level were about 0.035 ft. in N and E and about 0.014 at 68% confidence.
>
> So does that mean that a surveyor ought to round all coordinates off to the nearest 0.03 ft.? If he did, he'd lose the fact that those four markers, Nos. 174, 186, 187, and 188, were much more accurately positioned in relation to each other.
>
> This is why I think it's reasonable to quote coordinates in feet to three decimal places, but note that their absolute uncertaintes in relation to NAD83 are whatever value they are, but which is most likely larger than 0.01 ft. The additional decimal place preserves the local relative accuracy of survey markers (assuming that it's there) that would be lost by coordinate rounding.
I noticed in your previous thread and here that you did no denote the geiod used on your x.y heading
> I noticed in your previous thread and here that you did no denote the geiod used on your x.y heading
I'll bite. Why would I need to include that information when what I'm providing are the horizontal components of coordinates that are projected from NAD83, not their GPS-derived elevations?
just a detail...
> just a detail...
Well, Grover Cleveland's birthday would be a detail, also, but I left it out as well and for the same reason. :>
🙂