Adjustment Computations Statistics And Least Squares In Surveying And Gis PdfBy Inpretofal In and pdf 03.04.2021 at 16:16 9 min read
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- Adjustment Computations: Statistics and Least Squares in Surveying and GIS
- Adjustment Computations, 6th Edition
- Adjustment Computations: Statistics and Least Squares in Surveying and GIS
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A short summary of this paper. As a corollary, every measurement contains error. These statements are fundamental and universally accepted. It follows logically, therefore, that surveyors, who are measurement specialists, should have a thorough understanding of errors. They must be familiar with the different types of errors, their sources, and their expected magnitudes. Armed with this knowledge they will be able to 1 adopt procedures for reducing error sizes when making their measurements and 2 account rigorously for the presence of errors as they analyze and adjust their measured data.
This book is devoted to creating a better understanding of these topics. In recent years, the least squares method of adjusting spatial data has been rapidly gaining popularity as the method used for analyzing and adjusting surveying data. This should not be surprising, because the method is the most rigorous adjustment procedure available.
It is soundly based on the mathematical theory of probability; it allows for appropriate weighting of all observations in accordance with their expected precisions; and it enables complete statistical analyses to be made following adjustments so that the expected precisions of adjusted quantities can be determined. Procedures for employing the method of least squares and then statistically analyzing the results are major topics covered in this book.
In years past, least squares was seldom used for adjusting surveying data because the time required to set up and solve the necessary equations was too great for hand methods. Now computers have eliminated that disadvantage. Besides advances in computer technology, some other recent developments have also led to increased use of least squares. But perhaps the most compelling of all reasons for the recent increased interest in least squares adjustment is that new accuracy standards for surveys are being developed that are based on quantities obtained from least squares adjustments.
Thus, surveyors of the future will not be able to test their measurements for compliance with these standards unless they adjust their data using least squares. Clearly, modern surveyors must be able to apply the method of least squares to adjust their measured data, and they must also be able to perform a statistical evaluation of the results after making the adjustments.
This book originated in as a set of lecture notes for a course taught to a group of practicing surveyors in the San Francisco Bay area by Professor Paul R. The notes were subsequently bound and used as the text for formal courses in adjustment computations taught at both the University of California-Berkeley and the University of Wisconsin-Madison.
In , a second edition was produced that incorporated many changes and suggestions from students and others who had used the notes. The second edition, published by Landmark Enterprises, has been distributed widely to practicing surveyors and has also been used as a textbook for adjustment computations courses in several colleges and universities.
For the fourth edition, new chapters on the three-dimensional geodetic network adjustments, combining GPS baseline vectors and terrestrial observations in an adjustment, the Helmert transformation, analysis of adjustments, and state plane coordinate computations are added. These are in keeping with the modern survey firm that collects data in three dimensions and needs to analyze large data sets. Additionally, Chapter 4 of the third edition has been divided into two new chapters on confidence intervals and statistical testing.
This edition has greatly expanded and modified the number of problems for each chapter to provide readers with ample practice problems. For instructors who adopt this book in their classes, a Solutions Manual to Accompany Adjustment Computations is also available from the publisher.
Two new appendixes have been added, including one on map projection coordinate systems and another on the companion CD. The software included on the CD for this book has also been greatly expanded and updated. A Mathcad electronic book added to the companion CD demonstrates the computations for many of the example problems in the text. To obtain a greater understanding of the material contained in this text, these electronic worksheets allow the reader to explore the intermediate computations in more detail.
For readers not having the Mathcad software package, hypertext markup language html files are included on the CD for browsing. For any given set of measured data, it will compute the mean, median, mode, and standard deviation, and develop and plot the histogram and normal distribution curve. Level nets, horizontal surveys trilateration, triangulation, traverses, and horizontal network surveys , GPS networks, and traditional threedimensional surveys can be adjusted using software in this package.
It also contains programs to compute the least-squares solution for a variety of coordinate transformations, and to determine the least squares fit of a line, parabola, or circle to a set of data points. Each of these programs computes residuals and standard deviations following the adjustment. The third program package, called MATRIX, performs a collection of basic matrix operations, such as addition, subtraction, transpose, multiplication, inverse, and more.
Using this program, systems of simultaneous linear equations can be solved quickly and conveniently, and the basic algorithm for doing least squares adjustments can be solved in a stepwise fashion.
Additionally, the Mathcad worksheets demonstrate the use of functions in developing modular programs. This current edition now consists of 26 chapters and several appendixes.
The chapters are arranged in the order found most convenient in teaching college courses on adjustment computations. It is believed that this order also best facilitates practicing surveyors who use the book for self-study. In earlier chapters we define terms and introduce students to the fundamentals of errors and methods for analyzing them.
The next several chapters are devoted to the subject of error propagation in the various types of traditional surveying measurements. Then chapters follow that describe observation weighting and introduce the least-squares method for adjusting observations. Application of least squares in adjusting basic types of surveys are then presented in separate chapters. Adjustment of level nets, trilateration, triangulation, traverses, and horizontal networks, GPS networks, and traditional three-dimensional surveys are included.
The subject of error ellipses is covered in a separate chapter. Procedures for applying least squares in curve fitting and in computing coordinate transformations are also presented. The more advanced topics of blunder detection, the method of general least squares, and computer optimization are covered in the last chapters. As with previous editions, matrix methods, which are so well adapted to adjustment computations, continue to be used in this edition.
For those students who have never studied matrices, or those who wish to review this topic, an introduction to matrix methods is given in Appendixes A and B. Those students who have already studied matrices can conveniently skip this subject.
Least-squares adjustments often require the formation and solution of nonlinear equations. Procedures for linearizing nonlinear equations by Taylor's theorem are therefore important in adjustment computations, and this topic is presented in Appendix C. As noted in the preface, the book has been used in continuing education classes taught to practicing surveyors as well as in classes taken by students at the University of California-Berkeley, the University of Wisconsin-Madison, and the Pennsylvania State University-Wilkes-Barre.
The students in these classes have provided data for many of the example problems and have supplied numerous helpful suggestions for improvements throughout the book.
The authors gratefully acknowledge their contributions. Earlier To improve future editions, the author will gratefully accept any constructive criticisms of this edition and suggestions for its improvement.
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 positioning system GPS equipment, digital metric cameras, and satellite imaging systems are only some of the new instruments that are now available for rapid generation of vast quantities of measured 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 upon 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.
Before data can be utilized, however, 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. Procedures for performing these two steps in processing measured data are principal subjects of this book. 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 theodolite or 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. Surveyors may, for example, measure angles and lengths of lines between points directly and use these measurements to compute station coordinates. From these coordinate values, other distances and angles that were not measured 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, 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 book. 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.
If a better scale graduated in minutes were available and read under magnification, however, 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 con- ditions that exist when the observations are taken, and human limitations e.
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. As discussed above, errors stem from three sources, which are classified as instrumental, natural, and personal 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.
Adjustment Computations: Statistics and Least Squares in Surveying and GIS
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Adjustment Computations, 6th Edition
In the vertical adjustment, benchmarks are held fixed. GPS Satellite Surveying. This work presents basic methods in least squares adjustment computation.
Adjustment Computations: Statistics and Least Squares in Surveying and GIS
Но Беккер слишком устал, чтобы обращать внимание на оскорбления. Проваливай и умри. Он повернулся к Росио и заговорил с ней по-испански: - Похоже, я злоупотребил вашим гостеприимством.
Какова твоя роль во всем. Сьюзан объяснила, что перехватываемые сообщения обычно исходят от правительств потенциально враждебных стран, политических фракций, террористических групп, многие из которых действуют на территории США. Эти сообщения обычно бывают зашифрованы: на тот случай, если они попадут не в те руки, - а благодаря КОМИНТ это обычно так и происходит.
General Least--Squares Method and Its Application to Curve Fitting and Coordinate Adjustment Computations: Statistics and Least Squares in Surveying and GIS PDF. Alert. Research Feed. Statistical methods in surveying by trilateration.
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ГЛАВА 32 Дэвид Беккер остановился в коридоре у номера 301. Он знал, что где-то за этой витиеватой резной дверью находится кольцо. Вопрос национальной безопасности. За дверью послышалось движение, раздались голоса. Он постучал.
Он говорил авторитетно и увлеченно, не обращая внимания на восторженные взгляды студенток. Беккер был смуглым моложавым мужчиной тридцати пяти лет, крепкого сложения, с проницательным взглядом зеленых глаз и потрясающим чувством юмором. Волевой подбородок и правильные черты его лица казались Сьюзан высеченными из мрамора. При росте более ста восьмидесяти сантиметров он передвигался по корту куда быстрее университетских коллег. Разгромив очередного партнера, он шел охладиться к фонтанчику с питьевой водой и опускал в него голову.
Нет, вообще-то я… - Из туристического бюро. - Нет, я… - Слушайте, я знаю, зачем вы пришли! - Старик попытался сесть в кровати.
Это было сделано тайно. - Мидж, - сказал Бринкерхофф, - Джабба просто помешан на безопасности ТРАНСТЕКСТА. Он ни за что не установил бы переключатель, позволяющий действовать в обход… - Стратмор заставил. - Она не дала ему договорить.
Мы еще не проиграли. Если Дэвид успеет найти кольцо, мы спасем банк данных. Стратмор ничего не. - Позвоните в банк данных! - приказала Сьюзан. - Предупредите их о вирусе.
Повернувшись, она увидела, как за стеной, в шифровалке, Чатрукьян что-то говорит Хейлу. Понятно, домой он так и не ушел и теперь в панике пытается что-то внушить Хейлу. Она понимала, что это больше не имеет значения: Хейл и без того знал все, что можно было знать. Мне нужно доложить об этом Стратмору, - подумала она, - и как можно скорее.
Я отправил Дэвида в Испанию. ГЛАВА 11 Испания. Я отправил Дэвида в Испанию.
Дэвид только что позвонил Стратмору и рассказал о немецком туристе. Новость не обрадовала коммандера.