Sandra Verhagen

Delft University of Technology | TU · Department of Geoscience and Remote Sensing

In this work we introduce the LAMBDA 4.0 toolbox, which provides an enhanced implementation for integer estimation, validation, and success rate evaluation. This free and open-source toolbox is a major update to LAMBDA 3.0 (2012), while it also integrates the functionalities from Ps-LAMBDA 1.0 (2013), thus respectively merging both estimation and e...

In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GNSS carrier phase ambiguity residuals, thereby assuming that the GNSS data belong to the very general class of elliptically contoured (EC) distributions. Examples of distributions belonging to this class are the multivariate n...

Until now, RTK (real-time kinematic) and NRTK (Network-based RTK) have been the most popular cm-level accurate positioning approaches based on Global Navigation Satellite System (GNSS) signals in real-time. The tropospheric delay is a major source of RTK errors, especially for medium and long baselines. This source of error is difficult to quantify...

With the advancement of multi-constellation and multi-frequency global navigation satellite systems (GNSSs), more observations are available for high precision positioning applications. Although there is a lot of progress in the GNSS world, achieving realistic precision of the solution (neither too optimistic nor too pessimistic) is still an open p...

In this contribution, we extend the principle of integer bootstrapping (IB) to a vectorial form (VIB). The mathematical definition of the class of VIB-estimators is introduced together with their pull-in regions and other properties such as probability bounds and success rate approximations. The vectorial formulation allows sequential block-by-bloc...

Guaranteeing safety of navigation within the Netherlands Continental Shelf (NCS), while efficiently using its ocean mapping resources, is a key task of Netherlands Hydrographic Service (NLHS) and Rijkswaterstaat (RWS). Resurvey frequencies depend on seafloor dynamics and the aim of this research is to model the seafloor dynamics to predict changes...

The single-receiver integer ambiguity resolution-enabled variant of precise point positioning (PPP), namely PPP-RTK, has proven to be crucial in reducing the long convergence time of PPP solutions through the recovery of the integerness of the user-ambiguities. The proliferation of global navigation satellite systems (GNSS) supports various improve...

Tropospheric wet delay, the main source of which is water vapor, is one of the major factors affecting the accuracy of positioning techniques using microwave. Tropospheric tomography is a powerful method to reconstruct the water vapor content in four-dimensional (4D) space. This paper studies the effect of using function-based and voxel-based tropo...

The technology of integer ambiguity resolution-enabled precise-point-positioning (also referred to as PPP-AR) has been proven capable of providing comparable accuracy, efficiency, and productivity to long-baseline real-time kinematic positioning (RTK) during the last decade. Commercial PPP-AR services have been provided by different institutions an...

This contribution implements the Kriging interpolation in predicting the tropospheric wet delays using global navigation satellite system networks. The predicted tropospheric delays can be used in strengthening the precise point positioning models and numerical weather prediction models. In order to evaluate the performances of the Kriging interpol...

Tropospheric water vapor is a key parameter in meteorology studies. Because of its irregular spatiotemporal distribution, modeling this parameter is a challenging subject. Global Positioning System (GPS) troposphere tomography is a new and powerful technique to assess the spatiotemporal distribution of water vapor in this layer. The efficiency of t...

The benefits of an increased number of global navigation satellite systems (GNSS) in space have been confirmed for the robustness and convergence time of standard precise point positioning (PPP) solutions, as well as improved accuracy when (most of) the ambiguities are fixed. Yet, it is still worthwhile to investigate fast and high-precision GNSS p...

A single-receiver integer ambiguity resolution-enabled precise point positioning (PPP-RTK) user experiences a long convergence time when the rather weak single-constellation dual-frequency ionosphere-float model is used. Nowadays, the rapid development of Global Navigation Satellite Systems (GNSS) provides a multitude of available satellites and fr...

Tropospheric tomography is one of the most important techniques to reconstruct three-dimensional (3D) images of the tropospheric water vapor fields using a local GNSS network. In the conventional tropospheric tomography method, called voxel-based tropospheric tomography, the 3D space is divided into many voxels and the amount of water vapor is esti...

The long convergence time required to achieve high-precision position solutions with integer ambiguity resolution-enabled precise point positioning (PPP-RTK) is driven by the presence of ionospheric delays. When precise real-time ionospheric information is available and properly applied, it can strengthen the underlying model and substantially redu...

The water vapor content in the atmosphere can be reconstructed using the all-weather condition troposphere tomography technique. In common troposphere tomography, the water vapor of each voxel is represented by an unknown parameter. This means that when the desired spatial resolution is high or study area is large, there will be a huge number of un...

Precise point positioning (PPP) is one of the well-known applications of Global Navigation Satellite System (GNSS) and provides precise positioning solutions using accurate satellite orbit and clock products. The tropospheric delay due to the neutral atmosphere for microwave signals is one of the main sources of measurement error in PPP. As one com...

The realization of the integer ambiguity resolution (IAR) enabled precise point positioning (PPP) method, the so-called PPP-RTK, is enabled by providing singlereceiver PPP users with satellite phase biases to recover the integerness of the user ambiguities. Successful IAR can greatly reduce the solution convergence time. However, the unknown ionosp...

This paper presents an analysis of the ionospheric corrections required to get a significant improvement in PPP-RTK performance. The main aim was to determine the improvement in the position precision and time-to-first-fix in the PPP-RTK user side using ionospheric corrections computed from a network. The study consists of two main steps. The first...

The spatial sampling often used to process and represent bathymetric data are of fixed grid resolution where the least depth value is stored in each grid cell. This results in Digital Elevation Models (DEMs) that are used to depict the underlying features of the seafloor. With the discretion of the user, the resulting DEMs used may either be of coa...

The integer ambiguity resolution-enabled precise point positioning (PPP) method, the so-called PPP-RTK, is a state-of-the-art Global Navigation Satellite Systems (GNSS) technique that allows to determine position solutions with high accuracy in a short amount of time. The main idea behind PPP-RTK is to extend the PPP technique by providing single-r...

Since GPS tends to fail for indoor positioning purposes, alternative methods like indoor positioning systems (IPS) based on Bluetooth low energy (BLE) are developing rapidly. Generally, IPS are deployed in environments covered with obstacles such as furniture, walls, people and electronics influencing the signal propagation. The major factor influe...

Extensive studies have concluded that the GNSS observations are heteroscedastic and physically correlated. Typically, the observation precisions are elevation dependent and between-frequency cross-correlations and time correlations exist. The influence of these stochastic characteristics on the GNSS positioning has been numerically well understood....

The Krafla volcanic system has geothermal areas within the Krafla caldera and at Bjarnarflag in the Krafla fissure swarm, 9-km south of the Krafla caldera. Arrays of boreholes extract geothermal fluids for power plants in both areas. We collected and analyzed InSAR, GPS, and leveling data spanning 1993–2015 in order to investigate crustal deformati...

This chapter presents the estimation and filtering principles as used in global navigation satellite system (GNSS ) data processing. Estimation and filtering are concerned with retrieving or recovering parameters of interest from noisy measurements. The least-squares (LS) principle is the standard approach for estimating unknown parameters from unc...

Ambiguity Resolution (AR) is a key technique in GNSS precise positioning. In case of weak models (i.e., low precision of data), however, the success rate of AR may be low, which may consequently introduce large errors to the baseline solution in cases of wrong fixing. Partial Ambiguity Resolution (PAR) is therefore proposed such that the baseline p...

Ambiguity Resolution (AR) plays a vital role in precise GNSS positioning. Correctly-fixed integer ambiguities can significantly improve the positioning solution, while incorrectly-fixed integer ambiguities can bring large positioning errors and, therefore, should be avoided. The ratio test is an extensively used test to validate the fixed integer a...

Integer ambiguity estimation and validation are crucial steps when solving the carrier-phase based GNSS model. For the validation, different ambiguity acceptance tests have been proposed. For those tests often fixed critical values are used, with the important disadvantage that the performance of the tests varies a lot depending on measurement set-...

Global Navigation Satellite Systems (GNSS) have become ubiquitous in positioning, guidance and navigation. GNSS-based attitude determination and relative navigation are the important and promising applications. In this contribution we explore the potential of Low Earth Orbiting (LEO) satellite navigation in formation using arrays of GNSS sensors. W...

The ambiguity acceptance test is an important quality control procedure in high precision GNSS data processing. Although the ambiguity acceptance test methods have been extensively investigated, its threshold determine method is still not well understood. Currently, the threshold is determined with the empirical approach or the fixed failure rate (...

Ambiguity validation as an important procedure of integer ambiguity resolution is to test the correctness of the fixed integer ambiguity of phase measurements before being used for positioning computation. Most existing investigations on ambiguity validation focus on test statistic. How to determine the threshold more reasonably is less understood,...

Integer ambiguity resolution is an indispensable procedure for all high precision GNSS applications. The correctness of the estimated integer ambiguities is the key to achieving highly reliable positioning, but the solution cannot be validated with classical hypothesis testing methods. The integer aperture estimation theory unifies all existing amb...

The goal of carrier-phase ambiguity resolution is to exploit that the carrier-phase observations start to act as very precise pseudoranges. With the development of modern GNSS (GPS, BDS, Galileo, Glonass), more than 30 satellites are visible, however, it might be impossible to reliably fix all the ambiguities due to the computation time. Additional...

Single-frequency (SF) Precise Point Positioning (PPP) is a promising technique for real-time positioning and navigation at sub-meter (about 0.5 m) accuracy level because of its convenience and low cost. With satellite orbit and clock error being greatly mitigated by the precise products from the International GNSS Service (IGS), ionospheric delay b...

Both the underlying model strength and biases are two crucial factors for successful integer GNSS ambiguity resolution (AR) in real applications. In some cases, the biases can be adequately parameterized and an unbiased model can be formulated. However, such parameterization will, as trade-off, reduce the model strength as compared to the model in...

Performance verification of GNSS-based safety-of-life systems requires demonstration that the probability of an excessive positioning error is as small as 10 − 7 or even smaller. Integrity concepts are based on the requisite that the system provides conservative performance estimates for alert generation. The GNSS Integrity Monitoring and Analysis...

Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. However, before conducting ambiguity resolution, one needs to infer how reliable the fixed solut...

The Compass Navigation Satellite system, which currently provides more than 12 satellites with three carrier signals, already satisfies the requirement of stand-alone positioning in the Asia–Pacific regional area. First an initial introduction and performance assessment of dual-frequency un-differenced precise point positioning (PPP) for GPS and Co...

The evolving BeiDou Navigation Satellite System constellation brings new opportunities for high-precision applications. In this contribution the focus will be on one such application, namely precise and instantaneous relative navigation of a formation of LEO satellites. The aim is to assess the ambiguity resolution performance with the future GPS a...

Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. However, before conducting ambiguity resolution, one needs to infer how reliable the fixed solut...

With the advent of augmentation systems such as WAAS and EGNOS, satellite navigation gets more and more used for so-called Safety of Life (SoL) applications, with civil aviation being the most prominent example. The integrity of the position solution resulting from the satellite navigation signals is crucial, but difficult to test due to the extrem...

Next generation Global Navigation Satellite Systems will open the door to a whole new field of applications, for example in Earth observation, construction, and safety-of-life navigation. This implies very high requirements not only on precision and availability, but also on reliability. Integer carrier phase ambiguity resolution is the key to (nea...

This contribution focuses on geodetic sensor systems and sensor networks for positioning and applications. The key problems in this area will be addressed together with an overview of applications. Global Navigation Satellite Systems (GNSS) and other geodetic techniques play a central role in many applications like engineering, mapping and remote s...

The coming decade will bring a proliferation of Global Navigation Satellite Systems (GNSSs) that are likely to enable a much wider range of demanding applications compared to the current GPS-only situation. One such important area of application is single-frequency real-time kinematic (RTK) positioning. Presently, however, such systems lack real-ti...

The performance of the popular ambiguity ratio test is analyzed. Based on experimental and simulated data, it is demonstrated that the current usage of the ratio test with fixed critical value is not sustainable in light of the enhanced variability that future global navigation satellite system (GNSS) ambiguity resolution will bring. As its replace...

GNSS, InSAR and LIDAR are identified as important techniques when it comes to monitoring and remote sensing of our planet Earth and its atmosphere. In fact, these techniques can be considered as key elements of the Global Geodetic Observing System. Examples of applications are: environmental monitoring; volcano monitoring, land slides, tectonic mot...

Carrier phase integer ambiguity resolution is the key to high-precision Global Navigation Satellite System (GNSS) positioning, navigation, and attitude determination. It is the process of resolving the unknown cycle ambiguities of the carrier phase data as integers. After ambiguity resolution, precise baseline estimates become available, which can...

Integer ambiguity resolution is the key to obtain very accurate positioning solutions out of the GNSS observations. The Integer Least Squares (ILS) principle, a derivation of the least-squares principle applied to a linear system of equations in which some of the unknowns are subject to an integer constraint,was demonstrated to be optimal among the...

The goal of Network RTK is to provide users with precise ionospheric corrections in order to conduct fast GPS ambiguity resolution and to get cm-level positioning results over medium-distance baselines. In this paper it is shown that a Network RTK user should apply the ratio test with fixed failure rate, having a threshold value that depends on the...

With the advent of augmentation systems such as WAAS and EGNOS, satellite navigation gets more and more used for so-called Safety of Life (SoL) applications, with civil aviation being the most prominent example. For SoL applications reliability performance of the system is typically expressed in tenns of accuracy, availability, continuity of servic...

The Japan Aerospace Exploration Agency (JAXA) is developing a system to provide a high-quality, long duration microgravity environment using a capsule that can be released from a high-altitude balloon. Since 1981, an average of 100 million dollars is spent every year on microgravity research by space agencies in the United States, Europe, and Japan...

In this contribution we will provide an overview of the work that has been done on pulsar navigation and show a new direction in pulsar-based navigation research. Up until now the focus has been on X-ray pulsars, whereas our focus will be on the possibility of using radio pulsars. The radio frequency range has been neglected because the radio-frequ...

Traditionally in multi-spacecraft missions (e.g. formation flying, rendezvous) the GNSS-based relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibility to use multi-antenna data from each spacecraft, not only for attitude determination, but also to improve the relati...

GNSS-based precise relative positioning between spacecraft normally requires dual frequency observations, whereas attitude determination of the spacecraft, mainly due to the stronger model given by the a priori knowledge of the length and geometry of the baselines, can be performed precisely using only single frequency observations. When the Galile...

In this contribution we will provide an overview of the work that has been done on pulsar navigation and show a new direction in pulsar-based navigation research. Up until now the focus has been on X-ray pulsars, whereas our focus will be on the possibility of using radio pulsars. The radio frequency range has been neglected because the radio-frequ...

There is trend in spacecraft engineering toward distributed systems where a number of smaller spacecraft work as a larger multi-instrumented satellite. However, in order to make the small satellites work together as a single large platform, the precise relative positions and orientations of the elements of the formation have to be estimated. Global...

The inception of C2 brought with it new issues to be considered, such as the merger of C2-capable and legacy receivers and the processing of data collected by a C2-capable receiver with satellite clock values generated using a legacy receiver network. Since receiver and satellite hardware delays for C2 measurements may not be necessarily the same o...

In the next five to ten years, the evolution of Global Navigation Satellite Systems (GNSSs) will have a revolutionary impact on the positioning performance. More GNSSs will become available with improved signal characteristics. At the same time, enhancement of receiver technology and algorithms is ongoing. In light of these developments, it is inve...

The availability of the second civilian code C2 created a new issue to be considered: the bias relating P2 and C2 signals. Such an issue is important when merging C2-capable and legacy receivers and when processing data collected by a C2-capable receiver with satellite clock values generated using a legacy receiver network. The P2-C2 bias is essent...

GNSS (Global Navigation Satellite Systems)-based attitude determination is an important field of study, since it is a valuable technique for the orientation estimation of remote sensing platforms. To achieve highly accurate angular estimates, the precise GNSS carrier phase observables must be employed. However, in order to take full advantage of th...

Normally, dual frequency observations are required for precise relative positioning, but under critical circumstances even with multi-frequency observations a reliable solution might not always be available. We have developed a method to rigorously integrate multiantenna data at individual platforms such that the attitude solution can be used to en...

JAXA has been developing a system to provide a long duration, good quality microgravity environment based on a capsule, named the Balloon-based Operation Vehicle, that can be released from a balloon. In this paper we will describe the Balloon-based operation vehicle itself and the experiments using GPS performed - in cooperation with Delft Universi...

Real-time corrections at the decimeter level over an entire continent? The challenge lies in minimizing the ranging error from signals propagating through the Earth's atmosphere. European researchers describe how it can be done using a Wide Area Real-Time Kinematic concept that exploits the full geometry of the observations, a central processing fa...

Computing a position with Single Frequency Precise Point Positioning (SF-PPP) algorithms compels to the use of satellite clock corrections, and for use with real-time applications, only a limited set of sources for orbit and clock data is available, for example the predicted Ultra Rapid products of the International GNSS Service (IGS). Recently, re...

Precise Global Navigation Satellite System (GNSS) based attitude determination is based on the GNSS carrier phase measurements. In order to benefit from these precise phase measurements, their unknown integer number of cycles needs to be resolved. For attitude determination applications, this process of integer ambiguity resolution benefits signifi...

In the present contribution we study how the availability of next-generation multi-constellation Global Navigation Satellite Systems (GNSS), such as GPS and Galileo, will improve Wide Area Real-Time Kinematic (WARTK) ambiguity resolution for users receiving corrections as disseminated by the WARTK service provider. For this purpose, multi-frequency...

Traditionally the relative positioning and attitude determination problem are treated as independent. In this contribution we will investigate the possibilities of using multiantenna (i.e., triple and quadruple) data, not only for attitude determination but also for relative positioning. The methods developed are rigorous and have the additional ad...

Integer carrier phase ambiguity resolution is the key to fast and high-precision global navigation satellite system (GNSS) positioning and application. Apart from integer estimation, also acceptance tests are part of the ambiguity resolution process. A popular acceptance test is the so-called ratio-test. In this contribution we study the properties...

GNSS Attitude Determination is a valuable technique for the estimation of platform orientation. To achieve high accuracies on the angular estimations, the GNSS carrier phase data has to be used. These data are known to be affected by integer ambiguities, which must be correctly resolved in order to exploit the higher precision of the phase observab...