Data fitting and uncertainty a practical introduction to weighted least squares and beyond ; with 23 tables and 71 test questions and examples ; [with online-service

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. The content: Introduction to Data-Fitting Problems – Estimation of Model Parameters by Least-Squares – Weights and Outliers – Uncertainty of Results – Matrix Algebra – The Idea Behind Least Squares – Supplemental Tools and Methods Target Groups: engineers, computer scientists, physicists and software programmers undergraduates of engineering, computer science, physics About the author: Dr.-Ing. habil. Tilo Strutz is professor at Hochschule für Telekommunikation Leipzig (University of Applied Sciences, Deutsche Telekom AG). His expertise is ranging from general signal processing to image processing to data compression. Front Matter....Pages I-XIII Front Matter....Pages 1-1 Introduction to Data-Fitting Problems....Pages 3-24 Estimation of Model Parameters by the Method of Least Squares....Pages 25-46 Weights and Outliers....Pages 47-104 Uncertainty of Results....Pages 105-124 Front Matter....Pages 125-125 Matrix Algebra....Pages 127-145 The Idea behind Least Squares....Pages 146-166 Supplemental Tools and Methods....Pages 167-190 Back Matter....Pages 191-244