Adjustment Models in 3D Geomatics and Computational Geophysics

With MATLAB Examples

Bashar Alsadik

• Publisher: Elsevier
• Year: 2019
• Print ISBN: 9780128175880
• eBook ISBN: 9780128175897
• Topic: Physical Sciences
• Subtopic: Geophysics

Adjustment Models in 3D Geomatics and Computational Geophysics: With MATLAB Examples, Volume Four introduces a complete package of theoretical and practical subjects in adjustment computations relating to Geomatics and geophysical applications, particularly photogrammetry, surveying, remote sensing, GIS, cartography, and geodesy. Supported by illustrating figures and solved examples with MATLAB codes, the book provides clear methods for processing 3D data for accurate and reliable results. Problems cover free net adjustment, adjustment with constraints, blunder detection, RANSAC, robust estimation, error propagation, 3D co-registration, image pose determination, and more.- Covers both the theory and practice of using adjustment techniques in a wide variety of modern applications in Geomatics- Presents topics on the Kalman filter, Robust estimation, Levenberg Marquardt technique, and many other vital applications in the context of Geomatics and photogrammetry- Provides 75 solved problems in detail, especially related to 3-dimensional applications of Geomatics- Offers MATLAB codes to strengthen understanding and give readers up-to-date knowledge on information science

Chapter 1

Statistical Introduction

Abstract

In this chapter, an introduction of the adjustment computations in geomatics is presented supported with statistical definitions, concepts, and derivations. The chapter introduces the error types and their relation to accuracy and precision terms, and the statistical accuracy indices of the variance and standard errors. Then the connection between the probability normal distribution curve and the geomatical observations is illustrated with both numerical and MATLAB examples. Probable error at different confidence limits is given with a simple approach of blunders rejection. This chapter also also illustrates the most important method of adjustment using the least squares principle and its mathematical derivation. Finally, the computation of the weighted mean is shown in a numerical example.

Keywords

Least squares principle; Probable error; Accuracy and precision; Systematic error; Random error; Cumulative distribution function (CDF); Weighted mean

1.1 Introduction

In geomatics, different kinds of measurements (termed as observations in the book) are applied. The imperfections in instrumentation, weather conditions, and limitations of the operator′s skills produce field observations that encompass different kinds of errors. Accordingly, understanding the adjustment of observations and theory of errors are essential to process and solve geomatical problems. Because we need confidence in applied engineering or a s...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Chapter 1: Statistical Introduction
• Chapter 2: Propagation of Errors
• Chapter 3: Least Squares Adjustment Procedures
• Chapter 4: Observation Models and Least Squares Adjustment
• Chapter 5: Adjustment Using General Observation Model (Av + B Δ = F)
• Chapter 6: Adjustment With Constraints
• Chapter 7: Unified Approach of Least Squares
• Chapter 8: Fitting Geometric Primitives With Least Squares
• Chapter 9: 3D Transformation and Coregistration
• Chapter 10: Kalman Filter
• Chapter 11: Introduction to the adjustment With Levenberg–Marquardt Method
• Chapter 12: Postanalysis in Adjustment Computations
• Appendix A: MATLAB Code of General 2D Geodetic Network Adjustment
• References
• Index