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Adjustment theory

Adjustment theory




P.J.G. Teunissen

Adjustment theory 

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


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Apokatastasis

Apokatastasis




Arjan Smit

Almost 13,000 years ago the earth was struck by a sudden, worldwide catastrophe. Giant mammals like the mammoth became extinct. Civilizations vanished, leaving only a few traces. The map of the world changed considerably. After a final convulsion the ice age definitely came to a close. The author presents a new and startling theory about the events that likely happened in those days, using elements of geology, archaeology, palaeontology, astronomy and mythology, which assent to his theory. These indications show that the earths crust shifted as a whole over a large distance within a very short time. The finds provide us with a delicate surprise that had not been detected before. Especially in our time of great changes, this book should be read. What is the connection to the Maya, who let their Long Count Calendar end at December 21st, 2012? To what were they referring? ` A hypothesis, made clear from the beginning of the book, is explained so well that it is difficult not to search for the truth independently. I can imagine that everything may have happened like this. The writer deserves a lot of thanks for this, as it is an art to implant a new idea into somebodys head. (J.M.) `This book provides a lot of interesting information that differs from existing theories. Science should seriously regard these ideas and not a priori ban different views. Some parts are hard to understand, but in this book clues are mentioned that cannot simply be pushed aside. (J.E.) `If one is interested in the genesis of the earth in its current shape, this is a very interesting book. Writer has been immersed in a lot of scientific studies on the subject and provides an original, clear and realistic vision. (T.S.V.)








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Dynamic data processing

Dynamic data processing




P.J.G. Teunissen

Dynamic data processing

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


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Ebb and Flood Channel Systems in the Netherlands Tidal Water

Ebb and Flood Channel Systems in the Netherlands Tidal Water




J. van der Veen

Colofon
This publication is an initiative of the Section Hydraulic Engineering
of the Faculty of Civil Engineering and Geosciences
of Delft University of Technology and was realised with support
of the Netherlands Centre for Coastal Research (NCK)
and Delft Cluster.
Internet: http://www.hydraulicengineering.tudelft.nl
Netherlands Centre for Coastal Research
In 1992 the coastal research groups of Delft University of Technology
(TUD), Utrecht University (UU), WL | Delft Hydraulics
and Rijkswaterstaat (RIKZ) engaged in a strategic co-operation
programme, NCK (Netherlands Centre for Coastal Research).
Some time later the Netherlands Institute of Applied Geoscience
TNO (TNO-NITG) and the University Twente (UT)
joined NCK, recently followed by the Netherlands Institute
for Sea Research (NIOZ) and the Netherlands Institute for
Ecology-Centre for Estuarine and Marine Ecology (NIOOCEMO).
Internet: http://www.nck-web.org
Delft Cluster
Five Delft knowledge institutes, active in the field of civiland
hydraulic engineering, have combined forces to form Delft
Cluster. Collaboration is in the form of an open network,
whose aim is to develop and distribute knowledge in the field of
sustainable development of densely populated delta areas. The
core of Delft Cluster consists of GeoDelft, International Institute
for Infrastructural, Hydraulic and Environmental Engineering
(IHE), Netherlands Organisation for Applied Scientific
Research (TNO), Delft University of Technology (TUD),
WL | Delft Hydraulics.
Internet: http://www.delftcluster.nl








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Hydrography

Hydrography



Hydrography

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:

Properties of water, waves, ocean currents and general circulation.

Tide-generating forces, tidal analysis and prediction.

Batch and recursive least squares estimation and quality control.

Coordinate systems, horizontal and vertical datums, ellipsoidal computations.

Radio frequency definitions, propagation of electromagnetic waves, time keeping systems.

Underwater acoustics, propagation of underwater sound, sonar parameters and sonar equations.

Law of the Sea, baselines, maritime zones and boundaries, third party settlement.

Geometry of positioning, concepts, classification and requirements of positioning systems, standards for hydrographic surveys.

Terrestrial and satellite positioning systems, speed determination.

Underwater acoustic positioning systems, calibration of systems.

Acoustic (single- and multibeam) and airborne sounding methods, sidescan and oblique sonars.


http://www.vssd.nl/hlf/a030.htm











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Network quality control

Network quality control




P.J.G. Teunissen

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 URL http://www.vssd.nl/hlf/a034.htm








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Testing theory

Testing theory




P.J.G. Teunissen

Testing Theory, an introduction

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


http://www.vssd.nl/hlf/a030.htm











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