the rules cited earlier, the least squares adjustment is strictly based on the theory of the propagation of measurement errors. The theory states that, for any set of measured values, the best set of corrections to apply to the measured values is one such that the sum of the squares of all of the corrections is minimized. The least squares adjustment is the most commonly used method of adjusting measured values.
The simplest example of the least squares adjustment theory is the average. If the least squares theory is applied to a single set of things that are measured many times, calculus renders the arithmetic average as the least squares solution. If the distance between two points were measured many times, then the average (obtained by summing all of the measurements and dividing by the number of measurements made) would represent the most probable measured distance. Every person has, at one time or another, used a least squares adjustment without knowing it.
The least squares adjustment is applied directly to measured values and, in surveying, is simplest when the precision of angular measure- ments is comparable to the precision of the distance measurements. If the procedure used to measure the angles (distances) is much more precise than the procedure used to measure the distances (angles), then special steps within the least squares adjustment must be taken for the results to be valid.
Unlike the rules, the angles of the traverse are not adjusted prior to be- ginning the least squares procedure. Angles and distances are adjusted simultaneously, based on the theories of probability. The procedure renders consistent and reliable results in proportion to the quality of the measurements made.
6.10. MODERN PERIOD
From the mid-1970s to today, the increased use of electronic distance measuring devices (EDMs) has greatly increased the accuracy of the distances reported on modern surveys. Unlike the toise or the chain, the EDM does not rely on repetitively “laying out” a standard length. Most EDMs measure distances by emitting a laser light that is reflected back to the instrument by a special mirror. The distance to the reflector is determined by comparing the departing signal with the returning one.
The accumulation of error with every length of chain, so inherent with the old methods of measurement, is almost absent with the EDM. It is only necessary to be able to see from one end of the line segment being measured to the other in order to measure the distance.
The high precision of the EDM has matched the precision long pos- sible in angular measurement. This “matching of precision” is perfectly suited to the least squares adjustment method of analyzing measured values. When the distance values were obtained by chaining, even when strict procedures were used, the angular values were usually more reliable. The Land Surveyor had to determine the relative degree of difference in reliability in order to use the least squares adjustment method properly. This difficulty, which discouraged the use of least squares, was eliminated by the EDM.
Distances of several thousand feet are measured as quickly and as easily as a few feet. This has also led to a more widespread acceptance and use of the state plane projection system by the Professional Land Surveyor. Full use of state plane system requires that the work be tied into control stations that may be miles from the job site. Before the accuracy and ease of long-distance measurement were provided by the EDM, one could hardly fault the Land Surveyor in private practice for opting not to spend several extra days on a job just to tie it to the state plane system.
GPS instrumentation has increased this long distance measurement capability to distances that are truly global. The near distance precision of GPS-based systems is marginally less than that of the EDM, but on the scale of miles it is unparalleled. This development alone has all but mandated the acceptance of state plane controlled surveys by the professional community.
The introduction of the computer has allowed the Land Surveyor to use formerly very cumbersome, but theoretically superior, computa- tional methods of detecting error distribution and balancing traverses. Now, instead of using guesswork in identifying and correcting for er- rors, complex and sophisticated mathematical procedures are available to every Land Surveyor. The formerly time-consuming tasks of com- puting traverses, areas, distances, and a thousand other things are now performed in fractions of a second. This relief from tedium has allowed the Land Surveyor the opportunity to look at every problem from many different sides.
Modern surveys are performed with a degree of precision that was nearly impossible just a few decades ago. Accuracies of better than one in 70,000 are now commonplace. Angles and distances can be measured with equivalent degrees of accuracy. This results in a greater consistency or reliability of computed dimensions. This is perhaps best illustrated by the standard deviations for typical modern instrumenta- tion listed in Table A.5 in the appendix of tables.
The future of survey measurements—that is, the tools and procedures—that will be available to the Land Surveyor are unlimited.