On the subject of relative uncertainty of position between any two points positioned by a survey, consider this example.
Point 1 is the station where the project was connected to NAD83(2011)Epoch 2010.0 via OPUS. From that station, control was extended across the project by GPS vectors, many of them also connected by conventional measurements. The 95%-confidence error ellipse of Point 1 was derived from the covariance matrix that the OPUS Extended Output report returned. It represents what is called the Network Uncertainty of Point 1, the uncertainty of its position with respect to NAD83 as realized by the CORS network, measured by the semi-major axis of the same 95%-confidence error ellipse, which is, of course, 0.04 ft.
Points 135, 136, 137, and 138 are boundary markers. Their network uncertainties are greater than that of Point 1 because of the small errors in the survey measurements by which their positions were derived, either directly or indirectly, from Point 1 that were added in.
[pre]
Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%
Station Semi-Major Semi-Minor Azimuth of Elev
Axis Axis Major Axis
1 0.040151 0.016824 171-50 0.082295
135 0.054453 0.029016 170-42 0.120758
136 0.053898 0.029342 163-24 0.107214
137 0.048239 0.028750 172-24 0.099874
138 0.046755 0.027118 173-07 0.099195
[/pre]
Here's a diagram of the situation.
The above 95%-confidence error ellipses are with respect to the local realization of datum, i.e. the CORS Network.
But suppose what I really want to know is what the uncertainties of the ties between the boundary markers are, not the uncertainties with respect to the local segment of the CORS network? Well, if I'm using least squares survey adjusment software, like say, Star*Net - which as it turns out I am - I can get that answer quite easily, practically as an incidental result :
It comes in two forms. One is as the uncertainty in distances and direction at 95% confidence as listed in this table:
[pre]
Adjusted Bearings (DMS) and Horizontal Distances (FeetUS)
=========================================================
(Relative Confidence of Bearing is in Seconds)
From To Grid Bearing Grid Dist 95% RelConfidence
Grnd Dist Brg Dist PPM
135 138 N76-08-22.55E 594.1877 13.24 0.0260 43.6898
594.2695
136 137 S79-57-30.79W 384.7433 19.53 0.0172 44.7238
384.7965
137 138 S13-50-43.05E 100.0342 38.59 0.0154 153.8237
100.0481
[/pre]
The other is as the 95%-confidence relative error ellipses between the same points:
[pre]
Relative Error Ellipses (FeetUS)
Confidence Region = 95%
Stations Semi-Major Semi-Minor Azimuth of Vertical
From To Axis Axis Major Axis
135 138 0.038220 0.025838 171-15 0.089795
136 137 0.036444 0.017177 168-08 0.046997
137 138 0.018895 0.015168 89-27 0.016432
[/pre]
For crying out loud, Kent.
Just go paint a picture.
Well, O.K., I can understand obsession, although my obsessions tend to run towards counting utility poles and lining up my colored markers and discussing Lewis and Clark whenever we have salmon for dinner, I can appreciate your obsessions....really.
It just gets tiresome, you know?
Ah, heck, what do I know. You're probably right. The future of Land Surveying undoubtedly hangs on an understanding of error ellipses.
Don
In the adjustment as run above, I had Star*Net compute the Network Accuracy of all points positioned by the survey, the uncertainty of every point with respect to the local segment of the CORS Network.
For the purposes of inspection of the Local Accuracy of the boundary points, I could have "told" Star*Net to hold the position of Point 1 as absolutely correct and then calculated the uncertainties of all the other boundary points in relation to it.
Here's what those results looks like. The error ellipse axes of length 0.0000 at Point 1 means that there is no uncertainty assigned to the OPUS-derived coordinates. This isn't, of course, correct with respect to NAD83. It just says that the uncertainty in the OPUS position won't be added into the uncertainties of the rest of the network points.
[pre]
Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%
Station Semi-Major Semi-Minor Azimuth of Elev
Axis Axis Major Axis
1 0.000000 0.000000 0-00 0.000000
135 0.036803 0.023611 168-49 0.088374
136 0.036973 0.022446 150-08 0.068719
137 0.026760 0.023288 176-45 0.056589
138 0.024113 0.021093 5-59 0.055381
[/pre]
Here are the relative uncertainties between the same pairs of boundary points. Note that they haven't changed.
[pre]
Relative Error Ellipses (FeetUS)
Confidence Region = 95%
Stations Semi-Major Semi-Minor Azimuth of Vertical
From To Axis Axis Major Axis
135 138 0.038220 0.025838 171-15 0.089795
136 137 0.036443 0.017176 168-08 0.046997
137 138 0.018895 0.015167 89-27 0.016432
[/pre]
> It just gets tiresome, you know?
Well, whenever you get tired of hearing about how to test the quality of a survey made by a combination of GPS and conventional methods and how to document compliance with the ALTA/ACSM Relative Positional Precision spec, be sure to mention it.
This example shows how to use a simple tool that I'm going to say probably 3/4 of message board readers are in the dark about.
> It just gets tiresome, you know?
> Don
There is always the option of not clicking on posts made by Kent. 😉
Even if you don't agree with him you have to admit that he does take a lot of his time to try to explain things and answer questions.
So thanks for post like this Kent!
Yes, Kent seems to be focused like a laser on this one particular issue, but he is absolutely right. Unless you are computing relative error ellipses between the monuments you tied in (not just between your control points, but between the points which define the boundaries of the surveyed property), you are not meeting the ALTA standards. My only beef with this method is that unless you have tied each corner from more than one setup (usually not practical), I think you are relying somewhat on the a-priori error estimates you have assigned your sideshot observations (help me out here, Kent). What I am trying to say is that if you somehow busted the setup over the corner you are tying in, and only located it from one setup, this method won't detect that. Having said that, the example Kent shows is exacly how I do it.
One item that lends credence to the analysis is the dramatic change in uncertainty for the length of the shortest line in your second table.
Do you look for such relationships to verify your output?
> My only beef with this method is that unless you have tied each corner from more than one setup (usually not practical), I think you are relying somewhat on the a-priori error estimates you have assigned your sideshot observations (help me out here, Kent). What I am trying to say is that if you somehow busted the setup over the corner you are tying in, and only located it from one setup, this method won't detect that.
In my experience, mixing conventional and GPS observations is very robust. For example, the magenta lines show the conventional ties from Point 16 that I made to three of the boundary markers. The thin blue lines to the same points are the GPS vectors to them.
Here are the residuals of those GPS vectors. The StdRes (Standardized Residual) column values are the test values. Values much larger than 2.0 are questionable. Values above 3.0 are considered to be outliers.
[pre]
Adjusted GPS Vector Observations (FeetUS)
From Component Adj Value Residual StdErr StdRes
To
(V40 Day308(1) 19:36 00026776.ssk)
13 Delta-N -57.7501 0.0169 0.0194 0.9
136 Delta-E 166.4172 0.0073 0.0148 0.5
Delta-U -0.7827 -0.0334 0.0737 0.5
Length 176.1544
(V41 Day308(1) 19:45 00026776.ssk)
13 Delta-N -122.0993 -0.0051 0.0211 0.2
137 Delta-E -212.9606 -0.0006 0.0160 0.0
Delta-U 3.6840 0.0506 0.0746 0.7
Length 245.5077
(V42 Day308(1) 19:52 00026776.ssk)
13 Delta-N -219.4112 0.0065 0.0148 0.4
138 Delta-E -189.7227 -0.0280 0.0131 2.1
Delta-U -0.7840 -0.0043 0.0559 0.1
Length 290.0631
[/pre]
Here are the residuals in the angles and distances to the same boundary markers after adjustment with the GPS vectors.
[pre]
Adjusted Observations and Residuals
===================================
Adjusted Measured Geodetic Angle Observations (DMS)
From At To Angle Residual StdErr StdRes
15 16 136 273-20-50.43 0-00-00.68 3.84 0.2
15 16 137 170-52-53.11 0-00-00.11 6.13 0.0
15 16 138 94-02-43.42 -0-00-02.08 11.85 0.2
[/pre]
[pre]
Adjusted Measured Distance Observations (FeetUS)
From To Distance Residual StdErr StdRes
16 136 350.1117 -0.0023 0.0064 0.4
16 137 101.2016 0.0003 0.0064 0.0
16 138 41.0134 -0.0070 0.0064 1.1
[/pre]
> One item that lends credence to the analysis is the dramatic change in uncertainty for the length of the shortest line in your second table.
>
> Do you look for such relationships to verify your output?
When I look at the results of an adjustment, I look carefully at what the residuals testing (by category of observation) shows as figures of merit in the Chi-Square test.
For example, here's the statistical summary from that adjustment. The error factors should be nominally 1.00
[pre]
Adjustment Statistical Summary
==============================
Convergence Iterations = 5
Number of Stations = 166
Number of Observations = 792
Number of Unknowns = 489
Number of Redundant Obs = 303
Observation Count Sum Squares Error
of StdRes Factor
Angles 169 15.691 0.493
Distances 235 55.976 0.789
Zeniths 226 55.691 0.803
Elev Diffs 6 0.348 0.389
GPS Deltas 156 110.962 1.364
Total 792 238.669 0.888
Warning: The Chi-Square Test at 5.00% Level Exceeded Lower Bound
Lower/Upper Bounds (0.920/1.080)
[/pre]
In this case, the Chi-Square test indicated that the angles were more accurately measured than the standard errors I assigned to them and the associated standard errors of instrument and target centering. But those values were all quite tight and the test value of 0.888 wasn't that far below the lower bounds to make me think there was a major problem. Basically the statistical summary just told me that the work may have been a little bit better than I thought. There are worse problems to have.
> ...When I look at the results of an adjustment, I look carefully at what the residuals testing (by category of observation) shows as figures of merit in the Chi-Square test.....
In recent releases of StarNet that statistical summary comes up in its own window when you run the adjustment. So it's always right there.
After the summary I look at the individual residuals next, which I have set to sort by residual size, so that the largest residuals are at the top of the list. If you have a lot of data it is possible to have a few bad measurements and still get a good summary.
Once I'm happy with the residuals I can look at error ellipses and relative connections but by that time its almost an afterthought. They are what they are, for the most part, as long as they aren't too big. It's more of a general check on procedures.
As a side note, the newest version of StarNet will output a kml file (presuming you are on a grid) so that you get a point plot in Google Earth, which is the greatest enhancement to StarNet since it went to Windows, IMO.
> As a side note, the newest version of StarNet will output a kml file (presuming you are on a grid) so that you get a point plot in Google Earth, which is the greatest enhancement to StarNet since it went to Windows, IMO.
Version 6 does have the option of exporting a dxf file of the network, which, if computed in a projection of a geodetic datum, can be overlaid on aerial orthophotos referenced to the same datum via [REDACTED]. It isn't perfect, but it's certainly easy.
As for examining the entire list of residuals: yes, definitely.
>... My only beef with this method is that unless you have tied each corner from more than one setup (usually not practical), I think you are relying somewhat on the a-priori error estimates you have assigned your sideshot observations ....
That is absolutely true. And there will be no residuals on single ties (technically there will be, they will just be zero). There will be an error estimate based only on the a-priori estimates.
So double tie wherever time and budget allow!
> >... My only beef with this method is that unless you have tied each corner from more than one setup (usually not practical), I think you are relying somewhat on the a-priori error estimates you have assigned your sideshot observations ....
> That is absolutely true. And there will be no residuals on single ties (technically there will be, they will just be zero). There will be an error estimate based only on the a-priori estimates.
>
> So double tie wherever time and budget allow!
But, let's not let the perfect be the enemy of the good. If the question is whether the a priori error estimates of the various classes of GPS vectors are reasonable or not and you have what amounts to an independent validation of a sufficiently large sample from each class, I wouldn't lose any sleep over each GPS vector not having a redundant check as long as there aren't other factors of concern present. These concerning factors would include clutter and obstructions around the station and noisy vector solution statistics.
The kml thing is a couple of clicks and you are looking at your points in Google Earth. I think that the convenience may well be worth the price of the upgrade. I used to plot points in Google Earth one by one and save those as a kml. But only sometimes and only after the final adjustment because it was time consuming.
> The kml thing is a couple of clicks and you are looking at your points in Google Earth. I think that the convenience may well be worth the price of the upgrade. I used to plot points in Google Earth one by one and save those as a kml. But only sometimes and only after the final adjustment because it was time consuming.
I'll probably think about upgrading to the current version of Star*Net when I change operating systems since I'm still running XP Pro. I'll probably ask a few questions about how MicroSurvey manages their license via the USB key since while it would be nice to think that it is done as efficiently and securely as under the StarPlus system, it wouldn't surprise me if it isn't.
Modular Design of Network - Star*Net
One thing that Star*Net makes readily possible is a sort of modular design of a survey adjustment, a subset of important observations that can be independently adjusted. Because all of the input data is accessible via an ascii text editor, it's just a cut-and-paste job to extract the GPS vectors in the main "spine" of the control network and create a separate input file containing them alone.
I'm particularly interested in these stations because they are how NAD83 was extended from the OPUS-derived NAD83 position of Point 1. Many other control points were then surveyed by GPS vectors from Points 3 and 13.
In the case of the project subject of the above example, there are five stations that form the main spine of the control network. All are positioned by redundant GPS vectors. This is a small project only about 0.5 mile x 0.5 mile in extent.
[pre]
Adjusted Observations and Residuals
===================================
Adjusted GPS Vector Observations (FeetUS)
From Component Adj Value Residual StdErr StdRes
To
(V1 Day297)
1Day297 Delta-N -0.0000 -0.0000 0.0163 0.0
1 Delta-E -0.0000 -0.0000 0.0072 0.0
Delta-U -0.0000 -0.0000 0.0420 0.0
Length 0.0000
(V1 Day298(0) 21:20 00026709.ssf)
1 Delta-N 1561.1307 -0.0088 0.0201 0.4
3 Delta-E -281.3296 -0.0145 0.0090 1.6
Delta-U 132.9175 -0.0708 0.0908 0.8
Length 1591.8362
(V7 Day298(0) 20:50 00026705.ssf)
1 Delta-N 1561.1307 0.0197 0.0132 1.5
3 Delta-E -281.3296 -0.0100 0.0070 1.4
Delta-U 132.9175 0.0327 0.0402 0.8
Length 1591.8362
(V9 Day300(1) 15:54 00026713.ssk)
3 Delta-N -1561.1185 0.0083 0.0067 1.2
1 Delta-E 281.3399 -0.0132 0.0058 2.3
Delta-U -133.0382 -0.0190 0.0193 1.0
Length 1591.8362
(V20 Day300(1) 19:41 00026742.ssk)
3 Delta-N 464.5624 -0.0114 0.0183 0.6
7 Delta-E -120.4771 -0.0235 0.0153 1.5
Delta-U 48.1472 0.0100 0.0863 0.1
Length 482.3392
(V32 Day303(0) 18:17 00026763.ssf)
3 Delta-N 946.4558 0.0011 0.0057 0.2
13 Delta-E 2492.4943 0.0022 0.0059 0.4
Delta-U 45.0809 0.0002 0.0178 0.0
Length 2666.5219
(V34 Day303(0) 19:38 00026771.ssk)
3 Delta-N 743.5773 -0.0014 0.0198 0.1
16 Delta-E 2340.2928 0.0070 0.0154 0.5
Delta-U 43.0456 0.0327 0.0857 0.4
Length 2455.9582
(V39 Day308(1) 19:30 00026776.ssk)
13 Delta-N -202.8679 0.0007 0.0186 0.0
16 Delta-E -152.2152 -0.0063 0.0144 0.4
Delta-U -2.0626 -0.0266 0.0754 0.4
Length 253.6319
(V56 Day308(1) 22:29 00026795.ssk)
13 Delta-N -481.7145 0.0104 0.0146 0.7
7 Delta-E -2613.0047 0.0192 0.0134 1.4
Delta-U 2.7335 -0.0136 0.0575 0.2
Length 2657.0378
[/pre]
And here are the uncertainties (as 95%-confidence error ellipses) of the various control points. Note that these are uncertainties with respect to the local segment of the CORS network.
[pre]
Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%
Station Semi-Major Semi-Minor Azimuth of Elev
Axis Axis Major Axis
1 0.040151 0.016824 171-50 0.082295
3 0.041834 0.019444 171-55 0.087238
7 0.050779 0.032433 173-56 0.130179
13 0.043944 0.023448 171-24 0.093559
16 0.054019 0.032737 170-45 0.142377
1Day297 0.000000 0.000000 0-00 0.000000
[/pre]
If I hold the OPUS-derived coordinates of Station 1 as fixed and error-free (just for purposes of demonstration), and readjust the main network, these are the uncertainties with the basic Network Uncertainty of the OPUS point stripped out:
[pre]
Station Coordinate Error Ellipses (FeetUS)
Confidence Region = 95%
Station Semi-Major Semi-Minor Azimuth of Elev
Axis Axis Major Axis
1 0.000000 0.000000 0-00 0.000000
3 0.011752 0.009744 174-27 0.028947
7 0.031296 0.027493 6-53 0.100866
13 0.017915 0.016273 160-53 0.044506
16 0.036162 0.028053 167-59 0.116184
[/pre]
I have a Microsurvey StarNet Pro dongle, it works fine. You need to register it on a computer connected to the Internet but after that it works anywhere.
Modular Design of Network - Star*Net
> Adjusted Observations and Residuals
> ===================================
>
> Adjusted GPS Vector Observations (FeetUS)
>
> From Component Adj Value Residual StdErr StdRes
> To
> (V1 Day297)
> 1Day297 Delta-N -0.0000 -0.0000 0.0163 0.0
> 1 Delta-E -0.0000 -0.0000 0.0072 0.0
> Delta-U -0.0000 -0.0000 0.0420 0.0
> Length 0.0000
What's "U"? Same as "Z"? Elevation?
> I have a Microsurvey StarNet Pro dongle, it works fine. You need to register it on a computer connected to the Internet but after that it works anywhere.
That sounds benign enough.
Modular Design of Network - Star*Net
> What's "U"? Same as "Z"? Elevation?
"U" is for Up. The components of the vector can be expressed as: North, East, Up. In the context of GPS vectors, X,Y, and Z conventionally refer to a global cartesian coordinate system typically used to describe GPS vectors.