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.
JOHN OLUSEGUN OGUNDARE, PHD, is a professional geomatics engineer and an instructor in the Department of Geomatics at British Columbia Institute of Technology (BCIT), Canada. He has been in the field of geomatics for over thirty years, as a surveyor in various geomatics engineering establishments in Africa and Canada and as a geomatics instructor or teaching assistant in universities and polytechnic institutions in Africa and Canada. Dr. Ogundare is also the author of Precision Surveying: The Principles and Geomatics Practice (Wiley, 2015).
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...