Mixed-integer models arise in several geodetic problems, including precise positioning and remote sensing in Global Navigation Satellite Systems (GNSS), as well as deformation monitoring through Interferometric Synthetic Aperture Radar (InSAR) or fringe phase observations from Very Long Baseline Interferometry (VLBI). These problems generally involve two types of unknowns: integer ambiguities a ∈ Z^n and real-valued parameters b ∈ R^p, whose accuracy can be significantly improved by correctly resolving the ambiguities. However, in some cases, a large number of ambiguity components are involved and need to be correctly resolved; therefore the ambiguity resolution process becomes a bottleneck for the computations.

One research question is therefore how to effectively tackle the challenges of high-dimensional ambiguity resolution and its computational complexity, while ensuring a successful resolution of the ambiguities. Additionally, a second question arises regarding whether it is possible to solve this challenging problem in the domain of real-valued parameters, e.g. positioning coordinates, given that those are usually the parameters of interest for the user. In response to such questions, this doctoral dissertation is structured in two main parts: the first one looks in the integer ambiguity domain, presenting new flexible estimators and algorithms, ultimately merged into the new Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) 4.0 toolbox; the second one focuses on the real-valued parameter domain where the integerness of ambiguities is still taken into account, where novel dual estimators are presented and an optimal, globally convergent solution is constructed using the branch-and-bound method.@en

The use of Global Navigation Satellites Systems is increasing rapidly. More and more applications use positioning and/or timing information form a Global Navigation Satellite System (GNSS). Also more and more people and applications rely on high-precision positioning based on GNSS. The high-precision solution of GNSS is achieved with the use of example augmentation data. For example real-time kinematic (RTK)-GNSS enables centimetre-level positioning. Commonly the augmentation data is sent with the use of internet. At the moment an unsecure internet link is used to sent this augmentation data from the reference station to the user. The aim of this study was to find out if it is possible to manipulate the augmentation data for DGNSS using a cyber attack without being detected, and what the consequences could be for the final estimated parameters of interest. The parameters of interest can be the position and/or the timing. The augmentation data is sent using the Networked Transport of RTCM via Internet Protocol (NTRIP). What is found is that this is an unsecure connection. For an attacker it is possible to use a man-in-the middle attack, where the augmentation data is sent from the reference station, via the hacker, to the user. The data is not encrypted and therefore it is possible for the hacker to see and alter the data. Based on a man-in-the-middle attack this study found that it is possible to manipulate the DGNSS augmentation data, without detection. The model that is used to manipulate the augmentation data is based on a Single Point Positioning model. As long as the manipulation is in the range of the design matrix of the used model, it is not detectable. This means that the manipulation only contributes to the so called influential bias and not, or minimal, to the testable bias. As the name suggest, the result of this manipulation is that the final solution is manipulated due to the effect in the influential bias, and without detection since the testable bias is not changed. GNSS processing is based on non-linear observation equations. This means that those models are linearised before the final solution is estimated based on the least squares estimation. The effect of this non-linearity is minimal, but it means that a (very) small part of the manipulation contributes to the testable bias. This study points out that this small increase of the testable bias is insignificant when the observations are tested based on an overall model test and the w-test. The conclusion of this study is that it is possible to spoof the augmentation data when NTRIP is used to sent the augmentation data. Furthermore, the consequence of augmentation data spoofing is that it can be exactly manipulated by the hacker, based on a certain direction and distance, as long as the magnitude of the manipulation is in the order of 2 to 3 meter.

Precise Point Positioning (PPP) is a Global Navigation Satellite System (GNSS) processing method with the objective of providing high positioning accuracy without the need for a nearby base station or dense network of reference stations operated by the user. To reach this objective, PPP uses the very precise carrier phase measurements in addition to the coarse pseudorange measurements, and precise satellite orbits and clock offsets. Before the carrier phase measurements can contribute to the position solution, the carrier phase biases must be estimated from the measurements. Additionally, to compute an accurate position, a number of approaches are used in PPP to reduce the error contributions. A sparse global network of reference stations estimates very accurate satellite orbits and clock offsets, and provides these to the user. A priori models are used to correct for the hydrostatic troposphere delay, relativistic effects, carrier phase wind-up, phase center offsets and variations. We will mainly consider users on or close to the surface of the Earth, which means that site displacement effects (e.g. ocean loading and solid Earth tides) also should be taken into account. The troposphere wet delay is often estimated from the data, and, in conventional PPP, the ionosphere delays are eliminated by combining dual-frequency observations in a reduced number of ionosphere-free observations. The accuracy provided by PPP based on GPS is very high; just a few mm for 24h of static data. However, PPP can still be improved in a number of areas which are addressed in this dissertation: - The need to both eliminate the ionosphere delays and estimate the carrier phase ambiguities results in a relatively weak model. This leads to long (re)initialization times before an accurate position can be computed. In this dissertation a different approach is proposed, implemented and tested that does not form the ionosphere-free combination, but estimates the ionosphere-delays from the observations. First the (linearized) GNSS observation equations are introduced and the functional PPP model is derived. From this we determine the estimable parameters, and treat the possibility of constraining the ionosphere estimation by use of external ionosphere data. This is achieved by correcting the observations with ionosphere model values and estimating only the residual ionosphere delay. Finally, a dynamic model for the residual ionosphere delays is determined and positioning results are presented. - An accurate stochastic model for PPP is lacking, which leads to a suboptimal weighting of the different observation types, an inadequate quality description of the solution, and unreliable hypothesis testing. In this dissertation the stochastic properties of the PPP model are studied starting with the accuracy of the (real-time) satellite orbit and clock offsets, and continuing with the accuracy and correlation of the GNSS observations. For the latter a newly developed method is introduced based on the geometry-free model. This analysis also includes an estimation procedure to model pseudorange multipath errors as an auto-regressive process, which can also be used to construct a dynamic model for time-correlated parameters. Finally, an almost unbiased variance component estimation algorithm is applied to the complete PPP model, and an accurate quality description of the positioning results is obtained. - Integrity monitoring, which uses hypothesis testing to detect errors in the model which are not covered by the expected uncertainties, is not well developed for PPP. This subject is related to the previous points, since an accurate stochastic model is required for integrity monitoring and estimating and constraining the ionosphere delay, is key to high integrity performance. The geometry-free model is used again in time-differenced form to analyze the integrity aspects of (multi-frequency) GNSS models and their power to detect errors such as cycle-slips on the carrier phase measurements. The null hypothesis and alternative hypotheses are presented and the Minimal Detectable Bias (MDB) is derived for different kinds of errors. Analytical expressions are provided supported by numerical results. The geometry-free analysis of pseudorange and carrier phase measurement noise revealed a good agreement with the theoretical expressions linking the measurement noise to the receiver tracking loop parameters and signal-to-noise ratio. However, strong variations of the pseudorange code measurements over longer time periods were also observed, which dominate the error budget if not accounted for. Modeling of multipath time series as an autoregressive process AR(k) of order k, showed that the estimated AR(1) parameter is almost always significant to a very high level, which indicates strong time correlation of the multipath time series. Indeed the AR(1) model fits the data much better than a white noise or AR(0) model does, significantly reducing the residual variance. Analysis of the real-time precise products showed that compared to the satellite orbit prediction, satellite clock prediction is relatively poor and thus dominates the combined error. The quality of newer products with shorter delays is much higher and approaches the post-processed products. There also exists strong correlation between the orbit and clock products, resulting from the estimation process, but also due to the use of specific phase center offsets. Users should thus obtain the satellite orbit and clock products from the same provider and not mix products. Analysis of the time-differenced geometry-free model revealed the strong impact of constraining the ionosphere variations over time on the integrity performance. Instantaneous detection of individual slips in dual- and triple-frequency data was found to have a high probability of success under moderate ionosphere conditions. Detection of phase-slips in single-frequency data is more difficult and may lead to a delay in the detection. The size of the smallest pseudorange outliers which can still be detected is, except for single-frequency data, insensitive to the ionosphere conditions; the precision of the code measurements is the only determining factor. Testing for a simultaneous phase-slip on each frequency leads to a very elongated MDB ellipse or (hyper)ellipsoid if the ionosphere is not constrained, indicating that specific combinations of slips are very difficult to detect. Constraining the ionosphere delay shrinks the MDB ellipse when the precision of the ionospheric pseudo observable increases. The positioning results show that without proper modeling, the pseudorange observations cannot contribute significantly to the carrier phase solution without degrading the accuracy. Furthermore the formal quality description of the solution poorly fits the empirical position errors if time-correlated effects are neglected. After solving both these issues, the strength of the combined model was demonstrated by the excellent convergence performance in both the static and kinematic case. Constraining the atmosphere delays to model values further improves the initial convergence of the position estimation.@en

Over the past few decades, Terrestrial Laser Scanners are increasingly being used in a broad spectrum of applications, from surveying to civil engineering, medical modeling and forensics. Especially surveying applications require on one hand a quickly obtainable, high resolution point cloud but also need observations with a well described quality, from which it is possible to reliably derive the quality of the end-product. As any measurement, TLS scans are subject to measurement noise. Currently, the manufacturers provide documentation containing only global technical specifications including precision of measurements performed on reference surfaces under laboratory conditions. After brief introduction of the principal of Laser Scanning, in this thesis an overview of the major quality influencing factors is provided, grouped in four main categories: (i.) scanner mechanism, (ii.) atmospheric conditions and environment, (iii.) object properties and (iv.) scanning geometry. In many cases, the user has limited control on the scanner mechanism, the atmospheric conditions or the object properties. The only factor on which the user has control on is the scanning geometry, as the user determines the scan location and thereby the view-point of a point cloud. This dissertation presents the research on the influence of scanning geometry on the point cloud quality. This thesis proposes a theoretical study of the scanning geometry effects on individual point quality, as well as practical assessments. The impact of scanning geometry on individual point quality is analyzed, based on local planar features. The quality investigated in this thesis relates to the random errors or precision of individual points and does not deal with systematic errors or biases. Different planar fitting techniques are presented and compared. The quality of each local fit is described using a Least Squares estimation. The main quality describers used in this work are presented for each method. By using these quality describers, the influence of the scanning geometry on the point quality is characterized both quantitatively and qualitatively. The scanning geometry is defined using two parameters: the incidence angle and the range. The incidence angle is defined as the angle between one laser beam vector and the normal vector to the surface. The range is defined as the distance between the scanner and the surface. It is shown that and how the received signal strength of the measurements decreases with increasing incidence angle and range. The presented approach allows the quantification of the contribution of noise induced by the scanning geometry, based solely on point cloud data. No additional or external measurements are needed. The contribution of the two scanning geometry parameters on the point quality has been quantified using contribution coefficients. The effect of scanning geometry on the point quality is quantified and tested on a reference test board and two point clouds sampling a standard room. It is shown that the theoretical models developed are consistent with this experimental assessment. It is shown that it is possible to reduce the total error of the measurements by placing the scanner at another position in the room, which is not necessarily an obvious position. Inspired by these results, a new method that determines near optimal view-points in a scene based on terrestrial laser scanner capabilities is presented. Using a simple approach, an improvement of the measurement set-up can be easily achieved using a small amount of computation, memory and time@en