Tool tips.

Q: We recently ran a GPS traverse between two monuments of different orders about 21 miles apart. We set traverse monuments about two to three miles apart. When we got to the second monument, we missed the published state plane coordinates by about 0.5 ft. What gives?

Figure 1: Each line independently measured; limited redundancy, as the only figures are straight lines.
A:Many more details are required to do a thorough analysis of this situation. But this is not an uncommon experience for surveyors. There are several areas of investigation to be considered: the accuracy of the GPS receiver; the accuracy of the surveying system (including such things as accuracy of centering on points, measuring antenna heights, etc.); the possibility of systematic errors in the system and software being used; the possibility of systematic errors in the surveying procedures; and the expected closure between the two monuments being checked.

Manufacturers of GPS receivers state accuracies for the receivers in their instrument material. These accuracies will vary depending on the manufacturer, but for this discussion, let's use a value of ±(5 mm + 1 ppm). Hopefully, you were doing static observations and not RTK; if you were using RTK, the value may have to be more like ±(1 cm + 2ppm). In general, RTK is not recommended as a method of extending control. If the control stations you worked with were 21 miles apart, and we assume you did not set up your traverse stations in a straight line, let's assume there were eight lines at three miles apiece. The random error (the generally used standard for the manufacturer accuracy statements) for each line will then be about ±1 cm. For the eight lines, the expected random error from the GPS receivers only will be about 2.8 cm (1 cm √8) or 0.09 ft.

Random error from measurement of the antenna height and centering should also be considered. While there is much discussion (and argument) about how errors in antenna height measurement affect position, it is out of the scope of this column to go into the theory. Centering error, if the centering is done conscientiously and with an optical plummet, will be on the order of 1 mm per setup or 3 mm for the entire line.

Systematic errors, on the other hand, are a big unknown unless you are sure that your optical plummets were well-adjusted so as to bring the random error per setup to the 1 mm level. Optical plummet tribrachs are frequently out of adjustment in the 5-10 mm range, and it is not common to see errors of 4 or 5 cm! Also, a careful investigation of how the antenna heights are measured is recommended.

Surveyors tend to gravitate to a three- or four-tripod system similar to the so-called "forced centering" system of leaving tripods in place and moving equipment forward. Unfortunately, not changing the setup (or receiver) does not constitute an independent measurement. At the very minimum, the tripod should be completely uprooted and a new setup performed that does not use the same locations for the tripod feet. It is better to actually change tripods and tribrachs for every measurement, even if taken at the same point.

Figure 2: Each line independently measured; each figure can be checked for internal consistency.
Finally, there are errors of relatively small magnitude when using GPS for measurements that can only be picked up by repeating the process on a different day, preferably with a different constellation. Software that makes the conversion to state plane coordinates must be checked. A good way to do this is to run an example from the manual for state plane coordinates in your state.

You also have to consider the monuments themselves. Can you find out if they are part of the same adjustment? Since they are of different orders and almost 34 km apart, if one monument is the result of an adjustment that had an internal network consistency of 1:500,000 and the other 1:100,000, you can't expect the inversed distance between the coordinates to be better than 1:100,000, which in this case would be about ±0.33 m, or about ±1 ft. A solution for determining more about the consistency of monuments in your area would be to include more in a network observation.

The most useful tip to give regarding this issue is to verify that you are not running a GPS traverse that is weak. Because GPS measurements result in the calculation of three-dimensional vectors between two points at a time, a traverse that looks like the one in Figure 1 does not give you the redundancy that basic principles of surveying would indicate. Any errors along the way are not capable of being isolated. However, if your "traverse" is a series of braced quadrilaterals or triangles as in Figure 2, similar to the chain of figures run by geodetic or control surveyors, then the reliability of results can be evaluated and the errors isolated. As long as the measurements of each line are truly independent, the internal consistency of each sub-figure can be determined to evaluate the presence and magnitude of errors.