In a post below the question was asked as to the impact on results of the usual surveys performed by surveyors of the incorrect assumption, contained in much GPS reduction software, that the WGS 84 and NAD 83 coordinate systems are identical. I believe the answer is that there is no significant impact. Below I give the formula I use to reach this conclusion and where it comes from so that one can reach their own conclusion.

Determining coordinates with GPS is a two step process. The first step is to compute one or more GPS vectors. The second step is to use these vectors to compute coordinates of stations being positioned. A vector (ie the coordinate differences between two stations) contains no information on the origin of a coordinate system's axes. It only contains information on the orientation of the axes. The orientation of computed GPS vectors reflect the orientation of the coordinate system axes of the coordinate system to which the satellite coordinates were referenced during the vector computation. When using broadcast orbits this is the coordinate axes of the current WGS coordinate system. These axes are not oriented the same as the NAD 83 coordinate axes. When performing the second step, coordinate computation, the known NAD 83 coordinates of one or more stations are held fixed and the computed coordinates of other stations using the vectors are taken to be NAD 83 coordinates.

The question is: Since the NGS 83 and current WGS 84 coordinate axes are rotated relative to one another, how big is the error introduced from treating the computed coordinates as NAD 83 coordinates? Looking at the case of using a single vector with a known NAD 83 coordinate for the station at one end, and computing the NAD 83 coordinates of the station at the other end, it is clear that the error will depend on how much the two coordinate systems are rotated relative to one another and the length of the vector. So. what is the size of the rotation between the WGS 84 and NAD 83 axes? To within something like a milliarc second or two it is the same as the rotation between the NAD 83 and the ITRF 97 coordinate axes. This rotation, in the form of rotation components, is given on the NGS web site.

Using these components I get as a reasonable approximation formula for estimating the maximum error in computed NAD 83 coordinates for stations in a GPS survey to be:

Error = .015 x D cm

where D is the horizontal extent of the stations of the survey used in the coordinate computation

For a GPS survey 20 km in extent this gives a maximum error of about 3 mm where one reference station with know NAD 83 coordinates is held fixed on one side of the survey. Holding the NAD 83 coordinates of 2 or more stations located at different points in the survey will mean the maximum error will be less. I don't think an error of a few millimeters in the computed coordinates of a survey will normally cause any problem.

In the ORGI work, the error using a single baseline 200 km long would be 3 cm, which can be significant. Of course, as has been noted previously, using several vectors coming into the station from different directions would reduce the error.

Reduction software could be very simply fixed to nearly completely remove the error due to the orientation difference even for lines several hundred kilometers long. All that would need to be done would be to apply to the computed vectors the rotation components between NAD 83 and ITRF 97 given on the NGS web site before coordinate computation. Whether WGS 84 (G873) or one of the recent ITRF coordinate systems were used for satellite coordinates in the vector computations this would reduce the maximum error by a factor of about 10.

Some of this is beginning to soak in. Your persistence in explaining this is definately giving me a better understanding of how the systems compare. It does seem to support the reason we all learn to build networks tied to more than a single control station.

I do still have the question on the table as to what controls the "control" stations, considering a dynamic planet with plate tectonics, uplifts, subsidence, etc.

And, another question I'd doubt you will want to answer: If Trimble had a message board such as this, would you now be willing to entitle a thread "Trimble GPS Software Is Wrong"?

J.D.

I got the same results when comparing coordinates (basically none)...So all the our software is wrong..
But are our results wrong...No Way...They are letter perfect for our uses...
When you squish it, you get the answer you need , especially when you follow the recommended procedures of the manufacure.. (discount the ORGI, cause it was WAY out of the box, but very usefull)
I sent JD a message today...I got the same results he did on comparing the two systems...Our software maybe wrong, technically, but it still provides answers at the level we need to do field surveys...
"In the Dirt" is not a good idea....It's the law...

TM