The definitive guide to bringing accuracy to measurement, updated and supplemented
Adjustment Computations is the classic textbook for spatial information analysis and adjustment computations, providing clear, easy-to-understand instruction backed by real-world practicality. From the basic terms and fundamentals of errors to specific adjustment computations and spatial information analysis, this book covers the methodologies and tools that bring accuracy to surveying, GNSS, GIS, and other spatial technologies. Broad in scope yet rich in detail, the discussion avoids overly-complex theory in favor of practical techniques for students and professionals. This new sixth edition has been updated to align with the latest developments in this rapidly expanding field, and includes new video lessons and updated problems, including worked problems in STATS, MATRIX, ADJUST, and MathCAD.
All measurement produces some amount of error; whether from human mistakes, instrumentation inaccuracy, or environmental features, these errors must be accounted and adjusted for when accuracy is critical. This book describes how errors are identified, analyzed, measured, and corrected, with a focus on least squares adjustment—the most rigorous methodology available.
Apply industry-standard methodologies to error analysis and adjustment
Translate your skills to the real-world with instruction focused on the practical
Master the fundamentals as well as specific computations and analysis
Strengthen your understanding of critical topics on the Fundamentals in Surveying Licensing Exam
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.
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Yes, you can access Adjustment Computations by Charles D. Ghilani in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Civil Engineering. We have over one million books available in our catalogue for you to explore.
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 be illustrated by the following. If an angle is measured with a scale divided into degrees, its value can be read only to perhaps the nearest tenth of a degree. However if a better scale graduated in minutes were available and read under magnification, the same angle might be estimated to tenths of a minute. With a scale graduated in seconds, a reading to the nearest tenth of a second might be possible. From the foregoing, it should be clear that no matter how well the observation is taken, a better one may be possible. Obviously in this example, observational accuracy depends on the division size of the scale. But accuracy depends on many other factors, including the overall reliability and refinement of the equipment used, environmental conditions that exist when the observations are taken, and human limitations (e.g., the ability to estimate fractions of a scale division). As better equipment is developed, environmental conditions improve, and observer ability increases, observations will approach their true values more closely, but they can never be exact.
By definition, an error is the difference between a measured value for any quantity and its true value, or
(1.1)
where ε is the error in an observation, y the measured value, and μ its true value.
As discussed above, errors stem from three sources, which are classified as instrumental, natural, and personal. These are described as follows:
Instrumental errors. These errors are caused by imperfections in instrument construction or adjustment. For example, the divisions on a theodolite or total station instrument may not be spaced uniformly. These error sources are present whether the equipment is read manually or digitally.
Natural errors. These errors are caused by changing conditions in the surrounding environment. These include variations in atmospheric pressure, temperature, wind, gravitational fields, and magnetic fields.
Personal errors. These errors arise due to limitations in human senses, such as the ability to read a micrometer or to center a level bubble. The sizes of these errors are affected by personal ability to see and by manual dexterity. These factors may be influenced further by temperature, insects, and other physical conditions that cause humans to behave in a less precise manner than they would under ideal conditions.
1.4 DEFINITIONS
From the discussion thus far it can be stated with absolute certainty that all measured values contain errors, whether due to lack of refinement in readings, instabilities in environmental conditions, instrumental imperfections, or human limitations. Some of these errors result from physical conditions that cause them to occur in a systematic way, whereas others occur with apparent randomness. Accordingly, errors are classified as either systematic or random. But before defining systematic and random errors, it is helpful to define mistakes. These three terms are defined as follows:
Mistakes. These are caused by confusion or by an observer's carelessness. They are not classified as errors and must be removed from any set of observations. Examples of mistakes include (a) forgetting to set ...
Table of contents
COVER
TITLE PAGE
TABLE OF CONTENTS
PREFACE
ACKNOWLEDGMENTS
CHAPTER 1: INTRODUCTION
CHAPTER 2: OBSERVATIONS AND THEIR ANALYSIS
CHAPTER 3: RANDOM ERROR THEORY
CHAPTER 4: CONFIDENCE INTERVALS
CHAPTER 5: STATISTICAL TESTING
CHAPTER 6: PROPAGATION OF RANDOM ERRORS IN INDIRECTLY MEASURED QUANTITIES
CHAPTER 7: ERROR PROPAGATION IN ANGLE AND DISTANCE OBSERVATIONS
CHAPTER 8: ERROR PROPAGATION IN TRAVERSE SURVEYS
CHAPTER 9: ERROR PROPAGATION IN ELEVATION DETERMINATION
CHAPTER 10: WEIGHTS OF OBSERVATIONS
CHAPTER 11: PRINCIPLES OF LEAST SQUARES
CHAPTER 12: ADJUSTMENT OF LEVEL NETS
CHAPTER 13: PRECISIONS OF INDIRECTLY DETERMINED QUANTITIES
CHAPTER 14: ADJUSTMENT OF HORIZONTAL SURVEYS: TRILATERATION
CHAPTER 15: ADJUSTMENT OF HORIZONTAL SURVEYS: TRIANGULATION
CHAPTER 16: ADJUSTMENT OF HORIZONTAL SURVEYS: TRAVERSES AND HORIZONTAL NETWORKS
CHAPTER 17: ADJUSTMENT OF GNSS NETWORKS
CHAPTER 18: COORDINATE TRANSFORMATIONS
CHAPTER 19: ERROR ELLIPSE
CHAPTER 20: CONSTRAINT EQUATIONS
CHAPTER 21: BLUNDER DETECTION IN HORIZONTAL NETWORKS
CHAPTER 22: THE GENERAL LEAST SQUARES METHOD AND ITS APPLICATION TO CURVE FITTING AND COORDINATE TRANSFORMATIONS
