Textbooks from VSSD

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Series on Mathematical Geodesy and Positioning

ISBN 9040719748 ISBN 9040719756 ISBN 9040719764 ISBN 9040719772 ISBN 9040723591

 

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landmeetkunde

Adjustment theory, an introduction

P.J.G. Teunissen

2004 / viii+193 p. / ISBN 978-90-407-1974-5 / Euro 18.00

Available at www.amazon.com

Ebook ISBN 9789065622150  

Adjustment theory can be regarded as the part of the mathematical geodesy that deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. It is essential for a geodesist, its meaning comparable to what mechanics means to a civil-engineer or mechanical engineer. Historically, the first methods of combining redundant measurements originate from the study of three problems in geodesy and astronomy, namely to determine the size and shape of the Earth, to explain the long-term inequality in the motions of Jupiter and Saturn, and to find a mathematical representation of the motions of the Moon. Nowadays, the methods of adjustment are used for a much greater variety of geodetic applications, ranging from, for instance, surveying and navigation to remote sensing and global positioning.

The two main reasons for performing redundant measurements are the wish to increase the accuracy of the results computed and the requirement to be able to check for errors. Due to the intrinsic uncertainty in measurements, measurements redundancy generally leads to an inconsistent system of equations. Without additional criteria, such a system of equations is not uniquely solvable. In this introductory course on adjustment theory, methods are developed and presented for solving inconsistent systems of equations. The leading principle is that of least-squares adjustment together with its statistical properties.

The inconsistent systems of equations can come in many different guises. They could be given in parametric form, in implicit form, or as a combination of these two forms. In each case the same principle of least- squares applies. The algorithmic realizations of the solution will differ however. Depending on the application at hand, one could also wish to choose between obtaining the solution in one single step or in a step-by-step manner. This leads to the need of formulating the system of equations in partitioned form. Different partitions exist, measurement partitioning, parameter partitioning, or a partitioning of both measurements and parameters. The choice of partitioning also affects the algorithmic realization of the solution.

In this introductory text the methodology of adjustment is emphasized, although various samples are given to illustrate the theory. The methods discussed form the basis for solving different adjustment problems in geodesy.

Contents: Introduction / Linear estimation theory: an introduction / The model with observation equations / The model with condition equations / vR-Variates / Mixed model representations / Partitioned model representations / Nonlinear models, linearization, iteration / Appendices / Literature / Index

Available PDF files: Introduction (60 Kb) / Chapter 4. vR-Variates (300 Kb)

landmeetkunde

Hydrography

C.D. de Jong, G. Lachapelle, S. Skone, I.A. Elema,

2003 / x+351 pp. / ISBN 978-90-407-2359-9 / hardback / Euro 30,25

Available at www.amazon.com

Ebook ISBN 9789065622181  

This book is based on the lecture notes for the graduate and undergraduate courses in hydrography as offered at the Department of Geomatics Engineering of the Universitiy of Calgary and the Department of Mathematical Geodesy and Positioning of Delft University of Technology. The purpose of the book is to present an introduction to and an overview of the broad field of hydrography.

Since there is only a weak interdependence between the eleven chapters, each of them can be studied separately. When used for a course, it is therefore also possible to consider only a selected number of chapters. The eleven chapters cover the following topics:

  1. Properties of water, waves, ocean currents and general circulation.
  2. Tide-generating forces, tidal analysis and prediction.
  3. Batch and recursive least squares estimation and quality control.
  4. Coordinate systems, horizontal and vertical datums, ellipsoidal computations.
  5. Radio frequency definitions, propagation of electromagnetic waves, time keeping systems.
  6. Underwater acoustics, propagation of underwater sound, sonar parameters and sonar equations.
  7. Law of the Sea, baselines, maritime zones and boundaries, third party settlement.
  8. Geometry of positioning, concepts, classification and requirements of positioning systems, standards for hydrographic surveys.
  9. Terrestrial and satellite positioning systems, speed determination.
  10. Underwater acoustic positioning systems, calibration of systems.
  11. Acoustic (single- and multibeam) and airborne sounding methods, sidescan and oblique sonars.

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landmeetkunde

Testing theory, an introduction

P.J.G. Teunissen

2006 / vii+147 p. / ISBN 978-90-407-1975-2 / Euro 18.00

Available at www.amazon.com

Ebook ISBN 9789065622167

The present lecture notes are a follow up on Adjustment theory. Adjustment theory deals with the optimal combination of redundant measurements together with the estimation of unknown parameters. There are two main reasons for performing redundant measurements. First, the wish to increase the accuracy of the results computed. Second, the requirement to be able to check for mistakes or errors. The present book addresses this second topic.

Although one always will try one's best to avoid making mistakes, they can and will occasionally happen. It is therefore of importance to have ways of detecting and identifying such mistakes. Mistakes or errors can come in many different guises. They could be caused by mistakes made by the observer, or by the fact that defective instruments are used, or by wrong assumptions about the functional relations between the observables. When passed unnoticed, these errors will deteriorate the final results. The goal of this introductory course on testing theory is therefore to convey the necessary knowledge for testing the validity of both the measurements and the mathematical model. Typical questions that will be addressed are: 'How to check the validity of the mathematical model? How to search for certain mistakes or errors? How well can errors be traced? And how do undetected errors affect the final results?'

The theory is worked out in detail for the important case of linear(ized) models. Both the parametric form (observation equations) and the implicit form (condition equations) of linear models are treated. As an additional aid in understanding the basic principles involved, a geometric interpretation is given throughout. Attention is also paid to the performance of the testing procedures. The closely related concept of reliability is introduced and diagnostic measures are given to determine the size of the minimal detectable biases.

In this introductory text the methodology of testing is emphasized, although various examples are given to illustrate the theory. The methods discussed form the basis for geodetic quality control and they provide the ingredients for the formulation of guidelines for the reliable design of measurement set-ups.

Contents: Introduction / Basic concepts of hypothesis testing / Testing of simple hyptheses / Testing of composite hypotheses / Hypothesis testing in linear models / Appendices / Literature / Index

Available PDF files: 0. Introduction (60 Kb)

landmeetkunde

Dynamic data processing

P.J.G. Teunissen

2001 / viii + 241 p. / ISBN 978-90-407-1976-9 /  Euro 22,50

Available at www.amazon.com

Ebook ISBN 9789065622174  

This book is a follow-up on Adjustment theory. It extends the theory to the case of time-varying parameters with an emphasis on their recursive determination. Least-squares estimation will be the leading principle used. A least-squares solution is said to be recursive when the method of computation enables sequential, rather than batch, processing of the measurement data. The recursive equations enable the updating of parameter estimates for new observations without the need to store all past observations. Methods of recursive least-squares estimation are therefore particularly useful for applications in which the time-varying parameters need to be instantly determined. Important examples of such applications can be found in the fields of real-time kinematic positioning, navigation and guidance, or multivariate time series analysis. The goal of this book is therefore to convey the necessary knowledge to be able to process sequentially collected measurements for the purpose of estimating time-varying parameters.

When determining time-varying parameters from sequentially collected measurement data, one can discriminate between three types of estimation problems: filtering, prediction and smoothing. Filtering aims at the determination of current parameter values, while smoothing and prediction aim at the determination of respectively past and future parameter values. The emphasis in this book will be on recursive least-squares filtering. The theory is worked out for the important case of linear(ized) models. The measurement-update and time-update equations of recursive least-squares are discussed in detail. Models with sequentially collected data, but time-invariant parameters are treated first.

In this case only the measurement-update equations apply. State-space models for dynamic systems are discussed so as to include time-varying parameters. This includes their linearization and the construction of the state transition matrix. Elements from the theory of random functions are used to describe the propagation laws for linear dynamic systems. The theory is illustrated by means of many worked out examples. They are drawn from applications such as kinematic positioning, satellite orbit determination and inertial navigation.

Contents: Introduction / 1. Least-squares: a review / 2. Recursive least-squares: the static case / 3. Recursive least-squares: the static case / 4. State-space models for dynamic systems / 5. Random functions / 6. Recursive least squares: the dynamic case / Literature / Index

PDF files: Contents (44 Kb) and Introduction and Chapter 1 (1.5 Mb)

landmeetkunde

Global Positioning System, een inleiding (in Dutch)

G.J. Husti

2000 / 151 p. / ISBN 978-90-407-1977-6 / Euro 15,50

Het Global Positioning System (GPS) is een plaatsbepalingssysteem dat op afstandmeting naar satellieten is gebaseerd. De afstanden worden uit gemeten looptijden van radiogolven afgeleid. Het systeem is continu, 24 uur per dag, in bedrijf, overal ter wereld bruikbaar en werkt onder alle weersomstandigheden. Het is een militair systeem dat door de overheid van de Verenigde Staten kosteloos aan civiele gebruikers ter beschikking wordt gesteld; ook buiten de Verenigde Staten.
De ontwikkeling van GPS heeft in de laatste 10 jaar een enorme vlucht genomen. Bij de moderne meetmethoden t.b.v. geodetische puntsbepaling (grondslag- en detailmetingen), navigatie, geodynamica, en Geografische Informatie Systemen, is GPS niet meer weg te denken.

Men vindt deze ontwikkeling ook terug in het onderzoek en onderwijs bij de Afdeling Geodesie van de TU Delft. Het GPS onderzoek is sterk uitgebreid en het aantal collegeuren met GPS als onderwerp is aanzienlijk opgevoerd. In het onderwijs maken de studenten tegenwoordig reeds vanaf de basisstudie kennis met GPS.

J. van Buren schreef in Geodesia (2000-6): "Samenvattend kunnen we zeggen dat men voor een zeer gering bedrag een prettig leesbaar, Nederlandstalig boek kan aanschaffen met een schat aan achtergrondinformatie over satellietbepaling in het algemeen en GPS in het bijzonder."

Inhoud: Inleiding / Een overzicht van GPS / Coördinatenstelsels, tijdsystemen en satellietbanen / Invloed van de atmosfeer / Plaatsbepaling uit code-afstanden / Relatieve positie uit fasewaarnemingen / Datumtransformatie / Referentiestations / Overzicht van GLONASS / Literatuur / Index

PDF-bestand met inhoudsopgave en de hoofdstukken 1, 2 en 5 (593 Kb)

geodesie

Network quality control

P.J.G. Teunissen

2006 / viii + 128 pp. / ISBN 978-90-71301-98-8 / Euro 16,00

Available at www.amazon.com

Ebook ISBN 9789071301995  

 ISBN 9071301982  ISBN 90-71301-98-2 EAN 9789071301998

The aim of computing a geodetic network is to determine the geometry of the configuration of a set of points from spatial observations (e.g. GPS baselines and/or terrestrial measurements). The configuration of points usually consists of newly established points, of which the coordinates still need to be determined, and already existing points, the so-called control points, of which the coordinates are known. Network quality control deals with the qualitative aspects of network design, network adjustment, network validation and network connection.

By means of a network adjustment the relative geometry of the new points is determined and integrated into the geometry of the existing control points. Prior to the network adjustment, the geometry of the network is designed on the basis of precision and reliability criteria.

The adjustment and validation of the overall geometry can be divided in two phases, the free network phase and the connected network phase. In the free network phase, the known coordinates of the control points do not take part in the adjustment and validation. The possible use of a free network phase is based on the idea that a good geodetic network should be sufficiently precise and reliable in itself, without the need of external control. Moreover, it allows one to validate the quality of the external control.

In the connected network phase, the geometry of the free network is integrated into the geometry of the control points. Adjustment and validation in this second phase differs from the free network phase. The adjustment in the second phase is a constrained connection adjustment, since it is often not practical to see the coordinates of the control points change everytime a free network is connected to them. For the validation of the connected network however, the unconstrained connected adjustment is used as input. This allows one to take the intrinsic uncertainty of the coordinates of the control points in the connection phase into account.

The goal of this introductory text on network quality control is to convey the necessary knowledge for designing, adjusting and testing geodetic networks. For the purpose of network design, the precision and reliability theory is worked out in detail. This includes the minimal detectable biases and the bias-to-noise ratios. For the purpose of the network adjustment, the principles of unconstrained-, constrained-, and minimally constrained least-squares estimation, are treated. For the network testing, the principles of hypothesis testing are presented and worked out for the different network cases. For the free network phase this includes the overall model test, the w-test, and the data snooping procedure. For the connected network phase, it includes the T-test, with an emphasis on the detection and identification of errors in the control points.

Contents: 1 An overview • 2 Estimation and precision • 3 Testing and reliability • 4 Adjustment and validation of networks • Appendix - A1 Mean and variance of scalar random variables - A2 Mean and variance of vector random variables • References • Index

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Updated 16th October 2010, hlf@vssd.nl