In the September 2010 issue of Missouri Surveyor, Professional Land Surveyor Stan Emerick composed an article entitled, "Quixotial Quest Part II," in which he discussed proposed changes to Missouri Minimum Standards for Property Boundary Surveys (see page 28, Missouri Surveyor, Septemer 2010). Following is the response that I submitted to Stan on October 4, 2010:
Having read your article in The Missouri Surveyor, entitled "The Quixotial Quest Part II," I have no argument with your analysis of traverse measurements or your suggested modifications to field procedures, but I must disagree with your analysis of satellite-based measurements and your suggested modifications to the current standards.
In your article you stated:
"For analysis, we looked at three basic approaches to utilizing GPS technology: Static Surveys (including OPUS solutions), Real Time Kinematic Surveys (RTK, utilizing base stations and rovers) and Virtual Reference Systems (VRS, a network of continually operating reference stations). Each employee a slightly different method of determining positions, but all work on the same general framework, the computation of positional values by resection."
and
"In the other system, positional values are determined by resection from satellites, whose primary component measurement is distance. With the exception of some real-time kinematic surveys, the value of any given point in a survey is nearly independent of any other given point. The only connection they share is the condition of the satellites at the time of the survey and any atmospheric influences that the signals might have endured."
The concept of satellite-based observations being based on resection does not fit with my understanding of satellite-based technology. To refresh my memory on the precise meaning of resection, I consulted a few surveying texts. One reference defined resection as a means of determining the position of an unknown point by occupying the point and measuring the horizontal angles between at least three, and preferably more, control points. The other references that I consulted indicated similar definitions with all emphasizing the determination of position by either horizontal angles or directions, from which the horizontal angles could be computed. From these definitions we see that resection is based on the measurement of horizontal angles, not distances, as you have stated. So, resection is definitely the wrong word to use.
I agree that satellite-based measurements are more analogous to distance measurements, as in trilateration, although I wouldn’t use that word to describe it either. I cannot agree, though, with your statement that "positional values are determined by resection from satellites." Aside from resection being the improper word to use, your statement implies that the direct result of satellite-based observations is a positional value. This is true if point positioning is being used. Point positioning with a single receiver to a degree of precision acceptable for surveying applications, however, simply is not available to the ordinary civilian user.
The high precision measurements obtained for survey applications are achieved by relative positioning, which requires two receivers collecting data from the same satellites at the same time. At each epoch interval, measurements are recorded to each of the satellites from which the receivers can detect a signal. For as long as the receivers continue to collect data, measurements continue to be recorded at each epoch interval, so that a significant number of measurements are available. These measurements are the raw data just as traverse observations are raw data. For this raw data to be meaningful it must be processed just as traverse observations must be reduced to be meaningful. Provided that enough measurements have been obtained to produce a solution, processing techniques are employed to make computations using all of the available data, resulting in a vector solution that defines the orientation of one receiver relative to the other receiver. This vector is the basic piece of usable information obtained from the observation process, having both magnitude and direction, just as a traverse observation from one control point to the next has magnitude and direction, each with a corresponding uncertainty based on the quality of the measurements obtained. It is then from this vector solution that the positional values can be computed.
The process just described is applicable for all satellite-based observations used in surveying applications, whether static or real time kinematic (single base or network). The main difference in the techniques is the time at which the processing takes place. In static applications the processing takes place at a later time, whereas in real time kinematic applications the processing takes place in real time. The computers do all the work, so it’s easy to misunderstand what is actually taking place.
So, your statement that "the value of any given point in a [satellite-based] survey is nearly independent of any other given point" is totally false for relative positioning. The value of any given point is dependent upon at least one other point. If two points can be traced back to a common point, then a positional relationship between the two points is determinable.
You also state that "GPS or sky-based surveys ... normally are not viewed as tools for measuring direction." With satellite-based measurements, even without a fixed position, it is possible to determine a usable direction, so I would have to disagree with this statement. Azimuth determinations are made by satellite-based observations all the time, replacing the less convenient methods of solar and polaris observations.
Your article seems to emphasize the differences between ground-based traverse measurements and satellite-based measurements, based upon the concept of traverse closure and a manual analysis of component distance and direction errors. If, however, we recognize the limited application of traverse closure and turn to an analysis of positional accuracy/uncertainty and/or relative positional accuracy/uncertainty, then I think the similarities become more apparent and the results more comparable. If we consider that there are really only two classes of methods in collecting survey information, the real differences in analysis are revealed.
The first class of methods consists of those methods which employ redundant observations, providing a mathematical check and a measure of quality. Methods in this class would include: ground-based closed traverses; networked ground-based traverse observations; ground-based surveys in which sideshots are observed from more than one instrument setup; static or rapid static satellite-based surveys in which vectors form a closed figure or connect points whose positions have been precisely determined; real time kinematic satellite-based surveys in which each point is observed from more than one base setup; and satellite-based observations submitted for OPUS processing.
The second class of methods consists of those methods which do not employ redundant observations, thereby providing no mathematical check and no verification of quality. Methods in this class would include: ground-based open traverses; ground-based single setup radial observations; static or rapid static satellite-based surveys in which vectors do not form a closed figure and do not connect points whose positions have been precisely determined; and satellite-based real time kinematic surveys in which only one base setup is used or in which points are occupied only once.
With the first class of methods, the redundancy makes it possible for a least squares analysis or other statistical analysis to be performed to evaluate the quality of the measurements actually obtained. This analysis includes information about the quality of individual measurements (whether ground-based observations or satellite-based vectors), the relative positional accuracy/uncertainty between points and the positional accuracy/uncertainty of points relative to the overall survey. These results, then, provide information as to whether the accuracy requirements have been satisfied or not.
With the second class of methods, any evaluation of the quality of the measurements must be based on the accuracies that one might expect to obtain using those procedures, because no checks are available on the actual measurements. These expected accuracies may be based on prior field testing or established specifications that can be relied upon to provide a certain level of quality of results.
You may have noticed that I did not include real time kinematic networks in either of the two classes delineated above. Into which class of methods real time kinematic networks would be placed depends upon how the resulting position is determined. If the position is determined as the result of multiple vectors, then the network method would fit in the first class of methods which employ redundant observations. If, however, the position is determined by a single vector from a single network station, then the network method would fit in the second class of methods, which have no mathematical check or verification of quality. The information that I have read would seem to indicate that real time kinematic networks have a network determined correction, but a position that is ultimately based on a single vector from a network station, which would place it in the second class of methods.
It should be noted that your "suggested modifications to field procedures," if implemented, would produce surveys that fit into the first class of methods described above.
Having said all of this, I believe that you see why I must disagree with your suggested modifications to the current minimum standards that refer to resected survey measurement or resected survey method, since they are based on a misunderstanding of satellite-based observations.
As for your other suggested modifications to the current minimum standards, the only ones that I like are the changes to "the required relative position tolerance and traverse closure," stating the accuracy standards as a constant and a scale factor and eliminating the Suburban Property Standard.
An additional note of one thing that I think really needs to be corrected in the current minimum standards for property boundary surveys is the terrible misuse of the word "tolerance." It should be noted that a tolerance is a "not-to-exceed" value. In other words, it is the standard to be met. The current minimum standards use the word interchangeably as the standard to be met and the accuracy achieved in the performance of the survey. There is a distinction and it needs to be clarified.
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Original composition by Steven E. Weible
