As spatial technologies expand in both use and capability, so does our need for professionals who understand how to check and adjust for errors in spatial data. Conceptual knowledge is one thing, but practical skills are what counts when accuracy is at stake; Adjustment Computations provides the real-world training you need to identify, analyze, and correct for potentially crucial errors. D R . CHARLES D. GHILANI is a Professor Emeritus of Engineering. He taught in the B.S. Surveying Engineering and A.S. Surveying Technology programs at Pennsylvania State University. He holds a Ph.D. and M.S. in Civil and Environmental Engineering from the University of Wisconsin-Madison, and a B.S. degree in mathematics and education from the University of Wisconsin-Milwaukee. He is an honorary member of the Pennsylvania Society of Land Surveyors (P.S.L.S.), the president of the American Association for Geodetic Surveying, and the editor of Surveying and Land Information Science . He has received the Milton S. Eisenhower Distinguished Teaching Award in 2013, and the 2017 Surveying and Geomatics Educator's Society Educator Award.
We currently live in what is often termed the information age . Aided by new and emerging technologies, data are being collected at unprecedented rates in all walks of life. For example, in the field of surveying, total station instruments, global navigation satellite systems (GNSSs) equipment, digital metric cameras, laser-scanning systems, LiDAR, mobile mapping systems, and satellite imaging systems are only some of the new instruments that are now available for rapid generation of vast quantities of observational data.
Geographic information systems (GISs) have evolved concurrently with the development of these new data acquisition instruments. GISs are now used extensively for management, planning, and design. They are being applied worldwide at all levels of government, in business and industry, by public utilities, and in private engineering and surveying offices. Implementation of a GIS depends on large quantities of data from a variety of sources, many of them consisting of observations made with the new instruments such as those noted above and others collected by instruments no longer used in practice.
However, before data can be utilized whether for surveying and mapping projects, for engineering design, or for use in a geographic information system, they must be processed. One of the most important aspects of this is to account for the fact that no measurements are exact. That is, they always contain errors .
The steps involved in accounting for the existence of errors in observations consist of (1) performing statistical analyses of the observations to assess the magnitudes of their errors, and study their distributions to determine whether they are within acceptable tolerances, and if the observations are acceptable, (2) adjusting them so they conform to exact geometric conditions or other required constraints. Procedures for performing these two steps in processing measured data are principal subjects of this text.
1.2 DIRECT AND INDIRECT MEASUREMENTS
Measurements are defined as observations made to determine unknown quantities. They may be classified as either direct or indirect. Direct measurements are made by applying an instrument directly to the unknown quantity and observing its value, usually by reading it directly from graduated scales on the device. Determining the distance between two points by making a direct measurement using a graduated tape, or measuring an angle by making a direct observation from the graduated circle of a total station instrument are examples of direct measurements.
Indirect measurements are obtained when it is not possible or practical to make direct measurements. In such cases the quantity desired is determined from its mathematical relationship to direct measurements. For example, surveyors may observe angles and lengths of lines between points directly and use these observations to compute station coordinates. From these coordinate values, other distances and angles that were not observed directly may be derived indirectly by computation. During this procedure, the errors that were present in the original direct observations are propagated (distributed) by the computational process into the indirect values. Thus, the indirect measurements (computed station coordinates, distances, directions, and angles) contain errors that are functions of the original errors. This distribution of errors is known as error propagation . The analysis of how errors propagate is also a principal topic of this text.
1.3 MEASUREMENT ERROR SOURCES
It can be stated unconditionally that (1) no measurement is exact, (2) every measurement contains errors, (3) the true value of a measurement is never known, and thus (4) the exact size of the error present is always unknown. These facts can