[PDF] Practical Least Squares eBook

Author : Bruce P. Gibbs
Publisher : John Wiley & Sons
Page : 559 pages
File Size : 14,7 MB
Release : 2011-03-29
Category : Technology & Engineering
ISBN : 1118003160

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This book is intended primarily as a handbook for engineers who must design practical systems. Its primary goal is to discuss model development in sufficient detail so that the reader may design an estimator that meets all application requirements and is robust to modeling assumptions. Since it is sometimes difficult to a priori determine the best model structure, use of exploratory data analysis to define model structure is discussed. Methods for deciding on the “best” model are also presented. A second goal is to present little known extensions of least squares estimation or Kalman filtering that provide guidance on model structure and parameters, or make the estimator more robust to changes in real-world behavior. A third goal is discussion of implementation issues that make the estimator more accurate or efficient, or that make it flexible so that model alternatives can be easily compared. The fourth goal is to provide the designer/analyst with guidance in evaluating estimator performance and in determining/correcting problems. The final goal is to provide a subroutine library that simplifies implementation, and flexible general purpose high-level drivers that allow both easy analysis of alternative models and access to extensions of the basic filtering. Supplemental materials and up-to-date errata are downloadable at http://booksupport.wiley.com.

Author : Charles L. Lawson
Publisher : SIAM
Page : 348 pages
File Size : 46,75 MB
Release : 1995-12-01
Category : Mathematics
ISBN : 0898713560

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This Classic edition includes a new appendix which summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method.

Author : Tilo Strutz
Publisher : Springer Vieweg
Page : 0 pages
File Size : 35,34 MB
Release : 2015-12-16
Category : Technology & Engineering
ISBN : 9783658114558

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The subject of data fitting bridges many disciplines, especially those traditionally dealing with statistics like physics, mathematics, engineering, biology, economy, or psychology, but also more recent fields like computer vision. This book addresses itself to engineers and computer scientists or corresponding undergraduates who are interested in data fitting by the method of least-squares approximation, but have no or only limited pre-knowledge in this field. Experienced readers will find in it new ideas or might appreciate the book as a useful work of reference. Familiarity with basic linear algebra is helpful though not essential as the book includes a self-contained introduction and presents the method in a logical and accessible fashion. The primary goal of the text is to explain how data fitting via least squares works. The reader will find that the emphasis of the book is on practical matters, not on theoretical problems. In addition, the book enables the reader to design own software implementations with application-specific model functions based on the comprehensive discussion of several examples. The text is accompanied with working source code in ANSI-C for fitting with weighted least squares including outlier detection. Among others the book covers following topics * fitting of linear and nonlinear functions with one- or multi-dimensional variables * weighted least-squares * outlier detection * evaluation of the fitting results * different optimisation strategies * combined fitting of different model functions * total least-squares approach with multi-dimensional conditions

Author : Per Christian Hansen
Publisher : JHU Press
Page : 325 pages
File Size : 33,14 MB
Release : 2013-01-15
Category : Mathematics
ISBN : 1421408589

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A lucid explanation of the intricacies of both simple and complex least squares methods. As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues. In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis that help readers to understand and evaluate the computed solutions • many examples that illustrate the techniques and algorithms Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.

Author : John Olusegun Ogundare
Publisher : John Wiley & Sons
Page : 724 pages
File Size : 31,18 MB
Release : 2018-11-13
Category : Mathematics
ISBN : 1119501393

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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.

Author : John Wolberg
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 47,58 MB
Release : 2006-02-08
Category : Mathematics
ISBN : 3540317201

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Develops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods

Author : Ora Miner Leland
Publisher : Theclassics.Us
Page : 58 pages
File Size : 25,56 MB
Release : 2013-09
Category :
ISBN : 9781230461946

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 edition. Excerpt: ...and that they be independent of one another, so that no one of them could be obtained by combining any of the others. If a dependent condition were included, by mistake, it would be indicated during the solution of the normal equations by a derived equation having all of its coefficients zero, or nearly so, so that the corresponding correlate would be indeterminate. The necessary number of independent angle and side equations will be given by formulas (107) and (124), namely, Number of Angle Equations = L'--S' + 1 (107) Number of Side Equations =L-2S +3 (124) in which L and S are the total numbers of lines and stations, and L' is the number of full lines and S' is the number of occupied stations. (For a station to be considered as occupied, at least two lines must be unbroken at that station.) The best method of writing the angle and side equations so as to be certain of their independence as well as their number, is to draw a sketch of the system or figure to be adjusted, adding one station at a time, with its lines to the previous stations, and writing the equations introduced by that station and those lines. For each station so added, there will be as many angle equations as new full lines, less one, and as many side equations as new lines, less two. As has been stated, small angles should be used in the side equations where practicable, although it is best to use each but once. In angle equations, on the contrary, they should be avoided. 1 These local conditions are avoided in the figure adjustment by using directions instead of angles, as will be shown later on. For example, the equations for Fig. 22, page 96, will be written. In this case, L = 13, L' =12, S = S' = 7, and there are six angle and two side equations. The complete...