Data Fitting and Uncertainty: A Practical Introduction to Weighted Least Squares and Beyond

ISBN-13: 9783658114558 / Angielski / Miękka / 2015 / 281 str.

Tilo Strutz

Opis

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

Spis treści

Framework of Least-Squares Method.- Introduction to Data-Fitting Problems.- Estimation of Model Parameters by the Method of Least Squares.- Weights and Outliers.- Uncertainty of Results.- Mathematics, Optimisation Methods, and Add ons.- Matrix Algebra.- The Idea behind Least Squares.- Supplemental Tools and Methods.- A Comparison of Approaches to Outlier Detection.- Implementation.

O autorze

Dr.-Ing. habil. Tilo Strutz is professor at Leipzig University of Telecommunications (Deutsche Telekom). His expertise is ranging from general signal processing to special problems of image processing and data compression.

Blurb

The primary goal of this book is to provide a recipe explaining the functioning of data fitting via least squares and the emphasis here is on practical matters, not on theoretical problems. In addition, the book enables the reader to design own software implementation with application-specific model functions based on the comprehensive discussion of several examples. It includes a self-contained introduction and presents the method in a logical and accessible fashion. The subject of data fitting bridges many disciplines, especially those dealing traditionally with statistics as, for instance, physics, mathematics, engineering, biology, economy, or psychology, but also more recent fields as computer vision. This book is addressed to engineers and computer scientists or corresponding undergraduates, which 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 new details and interpretations or might appreciate the book as useful reference. The text is accompanied with working source code in ANSI-C for the fitting with weighted least squares including outlier detection.

Content

• fitting of linear and non-linear functions with one- or multidimensional 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 

Target Groups
• engineers, computer scientists, physicists and software programmers
• undergraduates of engineering, computer science, physics
• natural scientists, economists

About the Author:
Dr.-Ing. habil. Tilo Strutz is professor at Leipzig University of Telecommunications (Deutsche Telekom). His expertise is ranging from general signal processing to special problems of image processing and data compression.