Calculating the position of a point—the fundamental objective of survey—is not the only consideration in producing survey results. It is also important to know the precision of the location of the point. All
Measurements have random errors and the size of these errors can vary. If the measurements used to position a point have small random errors, or are precise, then the position error for the point will be small. If one makes redundant measurements as a check on position, because of the random errors in the measurements, there will almost certainly never be a single point position. Instead there will be lots of possible positions that can be calculated using different selections of the measurements in the set. Therefore, it will usually not be possible to calculate the true position for the point, and it will be necessary to determine the most probable position. In general, the most probable value for the true measurement is the average or mean value. If each measurement in turn is compared with the average value, the difference is called the residual. To compute the position of a point using a large number of measurements, the use of the mathematical calculation known as least-squares gives the most probable position. (Where the sum of the squares of the residuals is the smallest, the sum of the residuals for each measurement, will be smaller than that for any other position.) The least-squares calculation produces a single solution regardless of how many measurements have been made, the type of measurements, or how they were collected. This technique also provides information on how well the measurements fit together and can be used to help find mistakes.
By using this type of program, a number of possibilities exist for the archaeologist who wishes to conduct survey work under water. In one application, the interobject distances are measured to develop site plans. In the more common application, a control network is set up around the site and this is used to survey objects. The interobject technique first requires only distances between points to be known, so it is not necessary to introduce survey reference points. It is therefore a very useful method for surveying control points or a series of site tags that are used for other types of survey, particularly when establishing photographic control. It does not require every distance to be known, but the more distances that are measured the better the results will be.
There are a number of important advantages to using this approach. First, because survey reference points are unnecessary, the need for elaborate survey stakes and the time required to put them in place is avoided. In the other application, the objective, like the way the computer program Web was used on the Mary Rose project, is to establish basic control points and then measure the objects. The control network must be rigid and fixed in a location that allows access to all possible locations of objects. This is the more common situation, particularly when dealing with a large complex site, where measuring interobject distances would be unfeasible.