Page 140 - Green - Maritime Archaeology: A Technical Handbook. 2nd ed

Chapter 4: Conventional Survey 119 B. LEAST-SQUARES ADJUSTMENT TECHNIQUE
The least-squares adjustment program is a mathematical method of calculating the best fit of a series of data measurements. If, for example, every unique distance between four points is measured, giving a total of six measurements, there will inevitably be some error in each of these mea- surements depending on the accuracy of the measuring system. If the measurements are used to plot the position of the points on a plan in a con- ventional manner with a compass, there will be a resulting uncertainty in the position of each of the plotted points. The least-squares adjustment program calculates the best fit from this given data using rigorous statisti- cal techniques. It also provides a statistical estimation of the errors involved in the measurements. Through a series of mathematical iterations, the dis- tances are systematically varied by small amounts in order to seek a unique best fit that requires the least amount of adjustment to the measurements. It is obviously not necessary to have a complete understanding of the math- ematical theory or the program, but this method offers a very interesting solution to the problem of surveying sites under water.
The concept of least-squares adjustment has been known and under- stood for a number of years. With the advent of small and powerful com- puters, programs have been developed that can be used to make these calculations. It is generally recognized that Cross (1981) popularized the least-squares concept and was influential in the development of the Web, Site Surveyor, and most acoustic position fixing system programs. The Department of Maritime Archaeology at the Western Australian Maritime Museum developed an early least-squares adjustment program in 1987 by Duncan (see Atkinson et al., 1988). The initial program was written by Duncan as part of the underwater, acoustic, position-fixing project (HPASS described later). It was obvious that the program had ap-plications in under- water surveying and the results were published in Atkinson et al. (1989) together with the source code. At the same time Rule (1989) was develop- ing the Web program and this, in turn, was superseded by the more sophis- ticated program, Site Surveyor (see Section VII.D).
There are two basic approaches to using computer adjustment programs. One is where a series of points on a site are systematically surveyed, the points being the points of interest on the site and not artificial reference points. This type of survey is commonly a predisturbance survey or the survey of control points. The other option is to use predetermined control points and to use these control points to conduct an ongoing survey, typi- cally during an extensive excavation. The latter example requires a prelim- inary and careful survey of the control points which act as the basis for the survey.