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C.C.J.M. Tiberius

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Doctoral thesis (2025) - S. Ciuban, P.J.G. Teunissen, C.C.J.M. Tiberius
Satellite-based Positioning, Navigation, and Timing (PNT) technologies, including Global Navigation Satellite Systems (GNSS) and emerging Low Earth Orbit (LEO) constellations, alongside Terrestrial Networked Positioning Systems (TNPS) and various other sensors for positioning (e.g., inertial measurement units, cameras, LiDAR), are used and of interest for safety-critical applications across automotive, aviation, rail, and maritime domains. An important positioning safety criterion for these applications is represented by the probability of positioning failure, defined as the probability that a position estimator falls outside an application-specific safety-region. Rigorous quantification of this probability, denoted PF, is essential to verify compliance with safety requirements and to support the design and evaluation of positioning algorithms and systems.

This thesis addresses the challenges associated with computing  PF when the position estimator results from a combined parameter estimation and statistical hypothesis testing procedure for model misspecifications in the positioning model. A key challenge is posed by the multimodality of the probability density function (PDF) of the position estimator, which renders analytical integration methods intractable. Another key challenge is represented by the stringent requirements that  PF must satisfy for safety-critical applications (e.g., below 10-5), which implies that the event of positioning failure F must be rare—rendering standard Monte Carlo techniques computationally too expensive. Therefore, a novel method is developed in this thesis which addresses these challenges and is grounded in rare event simulation techniques, specifically Importance Sampling and the Cross-Entropy method. This method enables the construction of a 'failure-tree' that decomposes PF into components conditioned on the hypothesis testing decisions, thereby supporting rigorous positioning safety analyses during the design stage of positioning algorithms, and systems, for safety-critical applications.

The positioning safety is assessed in several representative scenarios. The importance of accounting for estimation–testing dependence is emphasized in a scenario involving cooperative positioning of automated vehicles, where neglecting this dependence results in probabilities of positioning failure being underestimated by an order of magnitude. Furthermore, positioning safety analyses for Unmanned Aerial Vehicles (UAVs) across multiple European airspace regions reveal substantial variability in the probabilities of positioning failure due to changes in receiver-satellite geometry over time, highlighting the importance of comprehensive simulation-based assessments. Additionally, an example is shown in which the probability of positioning failure is computed while accounting for multidimensional model misspecifications (e.g., multiple simultaneous outliers, or faults, in the observations). Collectively, the contributions and findings of this thesis highlight a rigorous approach to computing probabilities of positioning failure and conducting positioning safety analyses. ...
The Delft real-time GNSS single-frequency precise point positioning (RT-SF-PPP) algorithm is extended to include velocity and receiver clock drift as unknown states to be estimated from Global Navigation Satellite Systems (GNSS) measurements. Carrier-phase ambiguities are assumed constant over time. Two different variance models are used, one obtains variance as a function of satellite elevation, and the other obtains variance as a function of carrier-to-noise density ratio as estimated by the receiver. The elevation based variance model was used in the original RT-SF-PPP algorithm, and adapted to include Doppler measurements. The carrier-to-noise density ratio based variance model components are estimated from double difference (DD) observation combinations using measurements obtained from a shortbaseline experiment with two receivers setup over multiple days. Two velocity observables are used and related to velocity and clock drift through the extended functional model of the original algorithm: the receiver generated Doppler and a time-derivative of the carrier-phase observable: the time-differenced carrier-phase (TDCP). Algorithmic performance is evaluated by the horizontal RMSE, which represents accuracy as the variance plus bias squared, precision and reliability. This was validated using three different experiments: a stationary receiver on top of a roof, a buoy freely adrift in the North Sea, and a receiver mounted on a car driving a regional road. It was found that in terms of position in the static experiment and under calm water conditions during the drifting buoy experiment the horizontal RMSE was between 0.429 and 0.530 [m], and under rough water conditions and a road partly flanked by fences and trees between 0.682 and 0.812 [m]. Furthermore in terms of velocity it was found that the TDCP observable in combination with the carrier-to-noise density based variance model has a horizontal RMSE between 0.014 and 0.068 [m/s] over all experiments, and using the Doppler observable with either variance model a RMSE between 0.033 and 0.122 [m/s]. The algorithm was even found by means of external reliability to be capable of detecting faults at the boundary of 0.5 [m] for position and 0.1 [m/s] for velocity in the TDCP observable case. ...
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. ...
Under urban sprawl the trend of new established complex structures has rapidly increased. In this context maintenance plays a major role and monitoring of such structures represents a first important step in combating disasters. Over the last years low-cost Global Navigation Satellite System (GNSS) equipment has faced rapid and important development opening a new door to reliable and high accurate positioning applications such as structural health monitoring. This study presents a methodology for gathering, processing and analysing 1 Hz dual frequency GNSS data acquired by a network of newly released low-cost dual frequency GNSS receivers installed on a 90 metres tall steel-concrete structure in order to sense possible wind-induced displacements. At the same time, it represents one of the first studies testing the positioning capabilities of low-cost dual frequency GNSS equipment for monitoring large-scale building infrastructure. The main tools exploited in this study are PPK relative positioning together with a multipath correction procedure based on GPS satellite constellation repeatability. In addition to these, several corrections are discussed and applied on the position estimates in order to achieve millimetre position accuracy, highly needed for sensing wind-induced displacements of large-scale structures. By artificially inducing some horizontal deformations it was found that the newly released low-cost dual frequency GNSS receiver can track centimetre order permanent deformations of tall buildings. In the context of not being able to identify strong statistical correlation between possible wind-induced deformations of the case study building and and wind data patterns, the study proves that wind-induced deflections of tall structures might be traceable only if they are larger than the magnitude of the carrier phase multipath effect that is “leaking” in the position estimates. ...
Under urban sprawl the trend of new established complex structures has rapidly increased. In this context little importance has been given to maintenance, even if this represents an important step in combating and avoiding disasters and developing improved future structural designs. Over the last years low-cost Global Navigation Satellite System (GNSS) equipment has faced rapid and important development opening a new door to reliable and high accuracy positioning applications such as structural health monitoring (SHM). This study focuses on assessing, from a geodetic perspective, the capabilities of a pair of low-cost dual frequency GNSS receivers for capturing the kinematic response of structures to wind. An experiment has been carried out with a stainless steel cantilever beam, aiming to highlight the advantages of employing a differential GNSS system for monitoring low frequency changes in the structure’s body. Hence, in this context the nominal precision of the GNSS system in East, North and Up direction of 4, 5 and 10 millimeter (1σ), was further improved to 3, 4 and 8 miilimeters in the presence of a Global Positioning System (GPS) based multipath (MP) correction. However, it is safer to consider that the true displacement retention potential of the low-cost GNSS receivers corresponds to 3 times (3σ) the aforementioned standard deviation values, resulting in slightly larger than 1 centimeter detectable horizontal displacements, and up to 2.4 centimeters vertical displacements. To support this, wind-induced beam displacements of up to 1.9 centimeters were identified and attested based on a cross correlation analysis with meteorological information. Next, the architecture of a GNSS based SHM system is proposed that can detect structural displacements in real time and rise safety alarms. Therefore, with real time kinematic (RTK) differential positioning and a position outlier and slip statistical testing procedure, a clear strategy for the estimation and identification of uni- or tri-dimensional displacement quantities in real time is proposed, to rise alarms about the magnitude and the direction of identified displacements. Hence, there is no doubt that newly released low-cost dual frequency GNSS receivers represent an alternative to high-end geodetic equipment for SHM, by offering an optimal balance between precision and cost efficiency. ...
Road damage detection is important for road safety and road maintenance planning. Road surface anomalies, like potholes, cracks and ravelling, affect driving conditions, such as driving comfort and safety, noise emission, load loss of trucks, increase of fuel consumption and traffic circulation. Locali- sation of these anomalies allows for targeted road maintenance, which contributes to the improvement of driver safety, comfort and the optimisation of road maintenance.
The current technique to detect road damage is that road inspectors determine road damage in road images. However, the results are susceptible to human subjectivity. An improvement on image based road damage detection is using LiDAR data, because the geometry of road damage is measured too. To mitigate the issue of human subjectivity, an automated method for road damage detection was developed for the profile laser scanner on the IV-Infra car. This laser scanner is mounted at the back of the vehicle so that its profile lines are perpendicular to the driving direction. The proposed method consists of: (I) feature extraction with a sliding window algorithm; (II) K-means clustering to create training data; (III) Random Forest classification and (IV) morphological operations to remove noise and identify larger damage patches. This method was tested on an 800-meter long provincial road with different road defects and road types. Most occurring road damages are cracks, craquel and raveling. The results of this method were validated in two ways: using a road inspectors damage classification and a custom-made validation set based on orthophotos. An overall accuracy of 73% is achieved for the fully automated process. When training of the Random Forest was based on an improved, semi-automated training data, the overall accuracy was 58%, this gives visual clear results. This is explained by more noise are presented in the results based on the fully automatic method, which is overlapped with the coarse road inspector’s data. Optical inspection shows that the semi-automated method identified almost all damages of the custom-made validation set, although a shift between the point cloud and the validation is found. Still, the method has some difficulties with detecting the transverse cracks. This problem can be solved by integrating the two other mounted laser scanners of the Iv-Car, but pre-processing is needed to organise the point cloud. Also, an improvement in georeferencing the validation data would help to optimise the method and training data. Nevertheless, promising results are achieved by this method. ...

The difference between the classic and a conditional testing-estimation

A performance study in Delft (the Netherlands) and Dar es Salaam (Tanzania)

Heavy rainfall, combined with expanding (unplanned) urban settlements in flood prone areas, expose Dar es Salaam (Tanzania) to the risks of flooding. The urbanisation is so rapid in many areas that it is not beneficial to carry out expensive surveys which are quickly out of date. The work carried out by community-mapping project Dar Ramani Huria (Swahili for "Open map") aims to make a detailed map of Dar es Salaam, to enable the hydrologic models to approach the real situation more closely. However, the surveying methods used until recently are not sufficiently accurate. However, an alternative emerges in the form of community members using a low-cost, dual-frequency global navigation satellite system (GNSS) receiver during surveys. However, before this receiver can be implemented a detailed research has to be done. In this thesis the horizontal and vertical performance of the U-blox ZED-F9P receiver in Delft (the Netherlands) and Dar es Salaam is studied. The research is divided into two parts: performance and case study. For the performance study a series of post-processed kinematic (PPK) experiments were conducted in Delft and Dar es Salaam. The experiments have been designed in order to provide a variety of location, antenna-performance, baseline length, software package and movability. In addition, two re-initialisation experiments were conducted to measure how fast the interrupted GNSS signal is regained by the receiver. The case study focused on the desirability and feasibility, mainly focussing on accuracy, of implementation in the project of Dar Ramani Huria. Structured and unstructured interviews with employees of the Humanitarian OpenStreetMap Team (HOT) Tanzania were held to find out the requirements of implementation. The positioning performance of the receiver varies between the different experiments. The conclusions regarding the positioning performance are based on the scatter plots in the horizontal plane and the positioning over time for the three separate directional components; East, North and Up. The values for the horizontal performance (RMS East, RMS North) and for the vertical performance (RMS Up) of the fix solutions insofar as they fall inside the 95% confidence ellipse are decisive. Only the relevant experiments, namely those who can map a larger area with a single reference station are taken into consideration. The horizontal positioning performance ranges from 1.13 till 16.83 However the latter, high value is from the 9 baseline Dar es Salaam experiment with a very low percentage of fixed solutions. If we disregard the experiments with low percentage of fixed solutions then the horizontal positioning performance ranges van 1.13 till 9.42. The vertical positioning performance shows less accuracy ranging from 3.56 till 14.75. If we compare this performance with the requirements for Dar Ramani Huria’s project, even the strictest of 2cm, the performance is more than adequate according to the "few cm accuracy" requirement. The experiment with the high-end antenna shows with values 2.44mm (RMS East) and 3.42mm (RMS North) the best horizontal and with the value 3.75$mm(RMS Up) the best vertical performance. Another factor influencing the performance is the location, in particular the aspect of atmospheric delay that varies between Dar es Salaam and Delft. This research thesis concludes that the implementation of the receiver in Dar Ramani Huria's project is well possible and that the performance of the receiver is adequate. This conclusion is confirmed by what is actually occurring in the field: HOT Tanzania and Dar Ramani Huria already started using the GNSS receiver and carrying out surveys with this receiver. ...
Master thesis (2018) - Pang Pang, Christiaan Tiberius, Ramon Hanssen, Winnie Daamen, Peter de Bakker
Knowing 'where I am' is always essential and a prior to answer for a moving vehicle. Among numerous onboard sensors, a GNSS receiver for single-frequency Precise Point Positioning and camera are competitive due to the fairly lower cost and the potential to provide a lot of useful information.

However, due to the degraded GNSS solution performance in city valleys, a tight integration is considered combining the two sensors at the observation level, ie. processing the GNSS ranges and the vision measurements in the image of the camera. The availability of High Definition Maps (HD Maps) aids vehicle positioning by providing extra information on the environment. In this project, landmark positions are retrieved through vision and the HD map, and can complement GNSS in city valleys. Additionally, the project focuses on building the mathematical model for the integration of observed landmark position (using a single camera, considering the ease of implementation and cost) and GNSS measurements, analyzing the performance as well as the feasibility for vehicle positioning. The project emphasizes the feasibility study of the proposed mathematical model, which is flexible and capable of using all available input automatedly, and providing a position solution with the best precision.

The uncertainty in the available landmark positions (for instance errors in the HD maps) is handled in two different ways: one is to include the landmark position coordinates as measurements into the model, the other one projects the uncertainty onto the measurements in the camera image. The latter method turns out to be much more efficient. To integrate vision and GNSS measurements, a conversion between an ECEF (earth-centered, earth-fixed coordinate frame), typically used for GNSS, and a world coordinate frame for the camera measurements, is required. A position offset between the GNSS antenna and camera is considered, since the camera lens center does not coincide with the GNSS antenna center. In the simulation and experiment, an extended integration is also presented and discussed which leaves out the position offset, for instance when the GNSS antenna is very close to the camera, which can further improve the redundancy and lower the computational load.

From the simulation and experiment, we conclude that the integration model is able to produce a position solution when one of the sensors is unable to produce a position solution and the other one still can; the extended integration model is able to produce a position solution even when both sensors individually fail to produce a position solution. Among these scenarios, the one when GNSS fails and vision operates, the integration model can produce a position solution within a quarter of a meter in local horizontal coordinates, and the GNSS measurements do not contribute much to the position solution. Compared to the integration model, the extended integration improves the model by reducing or eliminating the (typically heavy) correlation between the estimates, in particular those for the camera-antenna position offset, the GNSS receiver clock error and the vertical coordinate. Under the same scenarios, the extended integration improves the standard deviation in vertical coordinate and receiver clock error, within a quarter of a meter and one-third of a meter respectively.

Further study is recommended in the direction of applying full image processing procedures to obtain more realistic vision measurements, to include GNSS carrier phase observations to replace the current GNSS positioning based on Precise Point Positioning, in order to have a position solution of similar quality as the vision part. The dimension of system gets larger when carrier phase measurements (phase ambiguities) are added as well as two additional rotations for a camera; the extra rotations introduce a significant amount of nonlinearity in the model. A larger model with increased nonlinearity may call for an alternative model formulation.
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Student report (2017) - Menglin Pang, Peter de Bakker, Christiaan Tiberius
This report first elaborates on an experiment to evaluate the performance of single frequency base station performance along with baseline. The system is deployed on a single frequency base station, and low-cost antenna in both and base and rover setup. The experiment is based on taking measurements on six control points, which are selected by varying simple topographic information and baseline length difference, by connecting to the single frequency base station. To have better evaluation of the performance of six control points, three sets of data, fix, float and all the measurements are divided and a simplified outlier detection model is employed to process the position estimates per control point. Finally, combine the results extracted from each control points to see the baseline length influence.
The experiment is conducted on basis that the precise position of base station is known. While users may construct their base station with unknown location. The document also includes several methods on how to determine an unknown base station position by using NETPOS product, and compare advantages and disadvantages internally, by which user can choose the method accordingly. In the last part of the document, a detail instruction on implementation of low-cost base station and rover setup in the previous experiment, including the needed hardware setup and software configurations, is provided for the potential users. ...