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John Olusegun Ogundare

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Herausgeber: John Wiley & Sons
Kategorie: Wissenschaft und neue Technologien
Sprache: Englisch

Beschreibung

Provides a modern approach to least squares estimation and data analysis for undergraduate land surveying and geomatics programs Rich in theory and concepts, this comprehensive book on least square estimation and data analysis provides examples that are designed to help students extend their knowledge to solving more practical problems. The sample problems are accompanied by suggested solutions, and are challenging, yet easy enough to manually work through using simple computing devices, and chapter objectives provide an overview of the material contained in each section. Understanding Least Squares Estimation and Geomatics Data Analysis begins with an explanation of survey observables, observations, and their stochastic properties. It reviews matrix structure and construction and explains the needs for adjustment. Next, it discusses analysis and error propagation of survey observations, including the application of heuristic rule for covariance propagation. Then, the important elements of statistical distributions commonly used in geomatics are discussed. Main topics of the book include: concepts of datum definitions; the formulation and linearization of parametric, conditional and general model equations involving typical geomatics observables; geomatics problems; least squares adjustments of parametric, conditional and general models; confidence region estimation; problems of network design and pre-analysis; three-dimensional geodetic network adjustment; nuisance parameter elimination and the sequential least squares adjustment; post-adjustment data analysis and reliability; the problems of datum; mathematical filtering and prediction; an introduction to least squares collocation and the kriging methods; and more. * Contains ample concepts/theory and content, as well as practical and workable examples * Based on the author's manual, which he developed as a complete and comprehensive book for his Adjustment of Surveying Measurements and Special Topics in Adjustments courses * Provides geomatics undergraduates and geomatics professionals with required foundational knowledge * An excellent companion to Precision Surveying: The Principles and Geomatics Practice Understanding Least Squares Estimation and Geomatics Data Analysis is recommended for undergraduates studying geomatics, and will benefit many readers from a variety of geomatics backgrounds, including practicing surveyors/engineers who are interested in least squares estimation and data analysis, geomatics researchers, and software developers for geomatics.

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Leseprobe

Understanding Least Squares Estimation and Geomatics Data Analysis

John Olusegun Ogundare, PhD, PEng

Instructor of Geomatics EngineeringDepartment of Geomatics Engineering TechnologySchool of Construction and the EnvironmentBritish Columbia Institute of Technology (BCIT) – Burnaby, Canada

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Library of Congress Cataloging‐in‐Publication Data

Names: Ogundare, John Olusegun, author.Title: Understanding least squares estimation and geomatics data analysis / John Olusegun Ogundare.Description: 1st edition. | Hoboken, NJ : John Wiley & Sons, 2018. | Includes bibliographical references and index. |Identifiers: LCCN 2018033050 (print) | LCCN 2018042480 (ebook) | ISBN 9781119501404 (Adobe PDF) | ISBN 9781119501442 (ePub) | ISBN 9781119501398 (hardcover)Subjects: LCSH: Estimation theory. | Least squares.Classification: LCC QA276.8 (ebook) | LCC QA276.8 .O34 2018 (print) | DDC 519.5/44–dc23LC record available at https://lccn.loc.gov/2018033050

Cover Design: WileyCover Illustration: © naddi/iStockphoto

Preface

Paradigm changes are taking place in geomatics with regard to how geomatics professionals function and use equipment and technology. The rise of “automatic surveying systems” and high precision Global Navigation Satellite System (GNSS) networks are changing the focus from how data are captured to how the resultant (usually redundant) data are processed, analyzed, adjusted, and integrated. The modern equipment and technology are continually capturing and storing redundant data of varying precisions and accuracies, and there is an ever‐increasing need to process, analyze, adjust, and integrate these data, especially as part of land (or geographic) information systems. The methods of least squares estimation, which are the most rigorous adjustment procedures available today, are the most popular methods of analyzing, adjusting, and integrating geomatics data. Although the concepts and theories of the methods have been developed over several decades, it is not until recently that they are gaining much attention in geomatics professions. This is due, in part, to the recent advancement in computing technology and the various attempts being made in simplifying the theories and concepts involved. This book is to complement the efforts of the geomatics professionals in further simplifying the various aspects of least squares estimation and geomatics data analysis.

My motivation to write this book came from three perspectives: First, my over 15 years of experience in teaching students in the Diploma and Bachelor of Geomatics Engineering Technology (currently, Bachelor of Science in Geomatics) at the British Columbia Institute of Technology (BCIT). Second, my over 10 years as a special examiner and a subject‐matter expert for Canadian Board of Examiners for Professional Surveyors (CBEPS) on coordinate systems and map projections, and advanced surveying. Third, as an expert for CBEPS on least squares estimation and data analysis. As a subject‐matter expert, I have observed after reviewing syllabus topics, learning outcomes, study guides, and reference and supplementary materials of CBEPS Least Squares Estimation and Data Analysis that there is a definite need for a comprehensive textbook on this subject.

Currently available undergraduate‐level books on least squares estimation and data analysis are either inadequate in concepts/theory and content or inadequate in practical and workable examples that are easy to understand. To the best of my knowledge, no specific book in this subject area has synergized concepts/theory and practical and workable examples. Because of this, students and geomatics practitioners are often distracted by having to go through numerous, sometimes irrelevant, materials to extract information to solve a specific least squares estimation problem. Because of this, they end up losing focus and fail to understand the subject and apply it efficiently in practice. My main goal in writing this book is to provide the geomatics community with a comprehensive least squares estimation and data analysis book that is rich in theory/concepts and examples that are easy to follow. This book is based on Data Analysis and Least Squares Estimation: The Geomatics Practice, which I developed and use for teaching students at BCIT for over 15 years. It provides the geomatics undergraduates and professionals with the foundational knowledge that is consistent with the baccalaureate level and also introduces students to some more advanced topics in data analysis.

Compared with other geomatics books in this field, this book is rich in theory/concepts and provides examples that are simple enough for the students to attempt and manually work through using simple computing devices. The examples are designed to help the students extend their knowledge to solving more practical problems. Moreover, this book assumes that the usually overdetermined geomatics measurements can be formulated generally as three main mathematical models (general, parametric, and conditional), and the number of examples can be limited to the adjustment of these three types of mathematical models.

The book consists of 16 chapters and 6 appendices. Chapter 1 explains survey observables, observations and their stochastic properties, reviews matrix structure and construction, and discusses the needs for geomatics adjustments.

Chapter 2 discusses analysis and error propagation of survey observations, including the application of the heuristic rule for covariance propagation. This chapter explores the concepts and laws of systematic error and random error propagations and applies the laws to some practical problems in geomatics. The use of interactive computing environment for numerical solution of scientific problems, such as Matrix Laboratory (MATLAB) software, is introduced for computing Jacobian matrices for error and systematic error propagations.

In Chapter 3, the important elements of statistical distributions commonly used in geomatics are discussed. The discussion includes an explanation on how statistical problems in geomatics are solved and how statistical decisions are made based on statistical hypothesis tests. The chapter introduces the relevant statistical terms such as statistics, concepts of probability, and statistical distributions.

Chapter 4 discusses the differences among the traditional adjustment methods (transit, compass and Crandall’s) and the least squares method of adjustment, including their limitations, advantages, and properties. The concepts of datum definition and the different constraints in least squares adjustment are also introduced in this chapter.

Chapter 5 presents the formulation and linearization of parametric model equations involving typical geomatics observables, the derivation of basic parametric least squares adjustment models, variation functions, and normal equations and solution equations. This chapter also discusses the application of variance–covariance propagation laws in determining the stochastic models of adjusted quantities, such as adjusted parameters, adjusted observations, and observation residuals. The discussion ends with an explanation of how to formulate weight constraint parametric least squares adjustment models, including the solution equations and the associated stochastic models.

In Chapter 6, the concepts of parametric least squares adjustment are applied to various geomatics problems, which include differential levelling, station adjustment, traverse, triangulation, trilateration, resection, and curve fitting. The general formulation of parametric model equations for various geomatics problems, including the determination of stochastic properties of adjusted quantities and the adjustment of weight constraint problems, is also discussed in this chapter.

Chapter 7 discusses the confidence region estimation, which includes the construction of confidence intervals for population means, variances, and ratio of variances, and the construction of standard and confidence error ellipses for absolute and relative cases. Before these, some of the basic statistical terms relating to parameter estimation in geomatics, such as mean squared error, biased and unbiased estimators, mathematical expectation, and point and interval estimators, are defined.

Chapter 8 discusses the problems of network design and pre‐analysis. In this chapter, different design variables and how they relate to each other, including their uses and importance, are discussed. The chapter also presents the procedures (with numerical examples) for performing simple pre‐analysis of survey observations and for performing network design (or simulation) in one‐, two‐ and three‐dimensional cases.

Chapter 9 introduces the concepts of three‐dimensional geodetic network adjustment, including the formulation and solution of parametric model equations in conventional terrestrial (CT), geodetic (G), and local astronomic (LA) systems; numerical examples are then provided to illustrate the concepts.

Chapter 10 presents, with examples, the concepts of and the needs for nuisance parameter elimination and the sequential least squares adjustment.

Chapter 11 discusses the steps involved in post‐adjustment data analysis and the concepts of reliability. It also includes the procedures for conducting global and local tests in outlier detection and identification and an explanation of the concepts of redundancy numbers, reliability (internal and external), and sensitivity, and their applications to geomatics.

Chapters 12 and 13 discuss the least squares adjustments of conditional models and general models. Included in each of these chapters are the derivation of steps involved in the adjustment, the formulation of model equations for different cases of survey system, the variance–covariance propagation for the adjusted quantities and their functions, and some numerical examples. Also included in Chapter 13 are the steps involved in the adjustment of general models with weight constraints on the parameters.

Chapter 14 discusses the problems of datum and their solution approaches and an approach for performing free network adjustment. It further describes the steps for formulating free network adjustment constraint equations and explains the differences between inner constraint and external constraint network adjustments and how to transform adjusted quantities from one minimal constraint datum to another.

Chapter 15 introduces the dynamic mode filtering and prediction methods, including the steps involved and how simple filtering equations are constructed and solved. The differences between filtering and sequential least squares adjustment are also discussed in this chapter.

Chapter 16 presents an introduction to least squares collocation and the kriging methods, where the theories and steps of least squares collocation and kriging are explained, including their differences and similarities. The book ends with six appendices: Appendices A–C contain sample statistical distribution tables, Appendix D illustrates general partial differentials of typical survey observables, Appendix E presents some important matrix lemmas and identities, and Appendix F lists the commonly used abbreviations in this book.

The topics in this book are designed to meet the needs of the students at the diploma, bachelor, and advanced levels and to support the aspiration of those who work in the geomatics industry and those who are in the process of becoming professional surveyors. Certain aspects of this book are designed to aid the learning and teaching activities: the chapter objectives provide an overview of the material contained in that chapter, and the sample problems with suggested solutions assist readers in understanding the principles discussed.

In general, I expect those who use this book to be familiar with introductory probability and statistics and to have good background in differential calculus, matrix algebra, geometry, and elementary surveying. On this basis, I recommend its use for second‐ and third‐year technological and university undergraduate courses. Some of the topics, such as least squares collocation and kriging methods, will be useful to graduate students and the geomatics practitioners. It is also a valuable tool for readers from a variety of geomatics backgrounds, including practicing surveyors/engineers who are interested in least squares estimation and data analysis, geomatics researchers, software developers for geomatics, and more. Those who are interested in precision surveying will also want to have the book as a reference or complementary material. The professional land surveyors who are gradually discovering the power of least squares method or who are pursuing their continued professional development will likely use the book as a reference material.

John Olusegun OgundareBurnaby, BC, Canada

Acknowledgments

This book has benefited from various input in the form of comments, critique and suggestions, from numerous students, educators, and professionals, and the author would like to acknowledge and thank all of them for their help. The author is particularly indebted to the British Columbia Institute of Technology (BCIT) in Canada, for providing the support for the development of the manual on Data Analysis and Least Squares Estimation: The Geomatics Practice, on which this book is based. Without this support, this book would not have been possible. The helpful suggestions by the BCIT Geomatics students for continued improvements of the many versions of the manual are also much appreciated.

Special thanks are due to Dr. J.A.R. Blais (Professor Emeritus, Geomatics Engineering Department of the University of Calgary), who provided the author with some valuable comments, suggestions, and reference materials on the last two chapters of this book, on “Introduction to Dynamic Mode Filtering and Prediction” and “Introduction to Least Squares Collocation and The Kriging Methods.” The help received from his past technical papers on these topics are also gratefully acknowledged. Others who reviewed material or have assisted in some way in the preparation of this book are Dr. K. Frankich (retired BCIT Geomatics instructor) for allowing the author access to his least squares lecture notes, which he delivered to the BCIT Geomatics students for over several years before his retirement; the faculty members of the Geomatics Department at BCIT, especially Dr. M.A. Rajabi; and Dr. M. Santos of the University of New Brunswick in Canada. The author is grateful to all of them and also to the reviewers, who pointed out problems and identified some areas of improvement for this book.

The Canadian Board of Examiners for Professional Surveyors (CBEPS) is gratefully acknowledged for giving the author the permission to reproduce some of their past exam questions on least squares estimation and data analysis in this book. To those who may have been inadvertently omitted, the author is also grateful.

In spite of the diligent effort of the author, some errors and mistakes are still possible in this edition. The author, therefore, will gratefully accept corrections, comments, and critique to improve future editions.

Finally, the author is grateful to his wife, Eunice, and his children, Joy and Isaac, for their patience, understanding, and support.

About the Author

John Olusegun Ogundare is a practising professional geomatics engineer in British Columbia, Canada; an educator; and author of Precision Surveying: The Principles and Geomatics Practice, published by Wiley & Sons, Inc., Hoboken. He received his BSc and MSc degrees in surveying engineering from the University of Lagos, Nigeria, and an MScE and a PhD in high precision and deformation analysis from the University of New Brunswick (UNB) in Canada. He has been in the field of geomatics for over 30 years as a surveyor in various survey engineering establishments in Africa and Canada and as a surveying instructor or teaching assistant in universities and polytechnic institutions also in Africa and Canada.

For over 10 years, John has served as a special examiner for the Canadian Board of Examiners for Professional Surveyors (CBEPS), which includes setting and marking exams on two of their subjects: Coordinate Systems and Map Projections (formerly known as Map Projections and Cartography) and Advanced Surveying. As a subject‐matter expert, he has served as a consultant to the Canadian Council of Land Surveyors (CCLS) on those subjects. He has also served as a subject‐matter expert in least squares estimation and data analysis for CBEPS, evaluating several Canadian geomatics programs to determine compliance with CBEPS requirements. He sits on the CBEPS Board of Directors and the CBEPS Exemptions and Accreditation Committee. This board with the help of the committee establishes, assesses, and certifies the academic qualifications of individuals who apply to become land surveyors in Canada.

For over 20 years, John has been teaching courses in geomatics technology diploma and degree programs at the British Columbia Institute of Technology (BCIT) in Canada. Some of the courses he teaches or has taught include Advanced Topics in Precision Surveys, Least Squares Adjustments and Data Analysis, Geodetic Positioning, Engineering Surveys, and Coordinate Systems and Mathematical Cartography. He also mentors students pursuing their Bachelor of Science (formerly Bachelor of Technology) in Geomatics in their technical projects and reports. Some of his BCIT‐funded works included providing manuals for CBEPS‐accredited courses, which he developed and teaches to full‐time and web‐based students. He has served for over 10 years as a member of the quality committee of the BCIT School of Construction and the Environment and for over 5 years as a member of the School Research committee.