On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations : The Seewinkel network

Microwave electromagnetic signals from the Global Navigation Satellite System (GNSS) are affected by their travel through the atmosphere: the troposphere, a non-dispersive medium, has an especial impact on the measurements. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The correlation structure of residuals from GNSS relative position estimation provides a unique opportunity to study specific properties of the turbulent atmosphere. Prior to such a study, the residuals have to be filtered from unwanted additional effects, such as multipath. In this contribution, we propose to investigate the property of the atmospheric noise by using a new methodology combining the empirical mode decomposition with the Hilbert–Huang transform. The chirurgical “designalling of the noise” aims to filter both the white noise and low-frequency noise to extract only the noise coming from tropospheric turbulence. Further analysis of the power spectrum of phase difference can be performed, including the study of the cut-off frequencies and the two slopes of the power spectrum of phase differences. The obtained values can be compared with theoretical expectations. In this contribution, we use Global Positioning System (GPS) phase observations from the Seewinkel network, specially designed to study the impact of atmospheric turbulence on GPS phase observations. We show that (i) a two-slope power spectrum can be found in the residuals and (ii) that the outer scale length can be taken to a constant value, close to the physically expected one and in relation with the size of the eddies at tropospheric height.[Figure not available: see fulltext.] © 2020, The Author(s)

Surface approximation of coastal regions: LR B-spline for detection of deformation pattern

Geospatial data acquisition of terrains produces huge, noisy and scattered point clouds. An efficient use of the acquired data requires structured and compact data representations. Working directly in a point cloud is often not appealing. To face this challenge, approximation with tensor product B-spline surfaces is attractive. It reduces the point cloud description to relatively few coefficients compared to the volume of the original point cloud. However, this representation lacks the ability to adapt the resolution of the shape to local variations in the point cloud. The result is frequently that noise is approximated and that surfaces have unwanted oscillations. Locally Refined (LR) B-spline surfaces were introduced to face this challenge and provide a tool for approximating Geographic Information System point clouds. In our LR B-spline based approximation algorithm, iterative least-squares approximation is combined with a Multilevel B-spline Approximation to reduce memory consumption. We apply the approach to data sets from coastal regions in Norway and the Netherlands, and compare the obtained approximation with a raster method. We further highlight the potential of LR B-spline volumes for spatio-temporal visualisation of deformation patterns.publishedVersio

LR B-splines to approximate bathymetry datasets: An improved statistical criterion to judge the goodness of fit

The task of representing remotely sensed scattered point clouds with mathematical surfaces is ubiquitous to reduce a high number of observations to a compact description with as few coefficients as possible. To reach that goal, locally refined B-splines provide a simple framework to perform surface approximation by allowing an iterative local refinement. Different setups exist (bidegree of the splines, tolerance, refinement strategies) and the choice is often made heuristically, depending on the applications and observations at hand. In this article, we introduce a statistical information criterion based on the t-distribution to judge the goodness of fit of the surface approximation for remote sensing data with outliers. We use a real bathymetry dataset and illustrate how concepts from model selection can be used to select the most adequate refinement strategy of the LR B-splines.publishedVersio

Surface approximation of coastal regions: LR B-spline for detection of deformation pattern

Geospatial data acquisition of terrains produces huge, noisy and scattered point clouds. An efficient use of the acquired data requires structured and compact data representations. Working directly in a point cloud is often not appealing. To face this challenge, approximation with tensor product B-spline surfaces is attractive. It reduces the point cloud description to relatively few coefficients compared to the volume of the original point cloud. However, this representation lacks the ability to adapt the resolution of the shape to local variations in the point cloud. The result is frequently that noise is approximated and that surfaces have unwanted oscillations. Locally Refined (LR) B-spline surfaces were introduced to face this challenge and provide a tool for approximating Geographic Information System point clouds. In our LR B-spline based approximation algorithm, iterative least-squares approximation is combined with a Multilevel B-spline Approximation to reduce memory consumption. We apply the approach to data sets from coastal regions in Norway and the Netherlands, and compare the obtained approximation with a raster method. We further highlight the potential of LR B-spline volumes for spatio-temporal visualisation of deformation patterns

LR B-splines to approximate bathymetry datasets: An improved statistical criterion to judge the goodness of fit

The task of representing remotely sensed scattered point clouds with mathematical surfaces is ubiquitous to reduce a high number of observations to a compact description with as few coefficients as possible. To reach that goal, locally refined B-splines provide a simple framework to perform surface approximation by allowing an iterative local refinement. Different setups exist (bidegree of the splines, tolerance, refinement strategies) and the choice is often made heuristically, depending on the applications and observations at hand. In this article, we introduce a statistical information criterion based on the t-distribution to judge the goodness of fit of the surface approximation for remote sensing data with outliers. We use a real bathymetry dataset and illustrate how concepts from model selection can be used to select the most adequate refinement strategy of the LR B-splines

Analysis of the temporal correlations of TLS range observations from plane fitting residuals

Terrestrial laser scanners (TLS) record a large number of points within a short time. Temporal correlations between observations are unavoidable but often neglected in stochastic modelling. The main consequences are an overestimated precision of the point clouds and potential wrong test decisions when used for deformation analysis with rigorous statistical procedures. Regarding physical considerations, a fractional Gaussian noise, defined by a so-called Hurst exponent, or a combination of fractional Gaussian noises could be used to model the noise of range measurements from a sensor perspective; Temporal correlations are expected to have a long-range dependency due to the high recording rate of the TLS. Scanning settings and configurations can affect the global correlation parameters. These effects can be quantified from the residuals of a least-squares surface approximation from the TLS point cloud. Based on simulation results, real data correlation analysis from indoor and outdoor experiments can be better understood which makes the identification of the dominant correlating noise source possible. Our methodology combines two Hurst-estimators: the Whittle maximum likelihood and the generalised Hurst estimator; It paves the way for a simple and global model for describing the temporal noise of TLS range correlations, usable in point clouds analysis independently of the object under consideration

Original 3D-Punktwolken oder Approximation mit B-Splines: Verformungsanalyse mit CloudCompare

In diesem Beitrag wird anhand von 3D-Punktwolken gezeigt, wie sich Verformungen bzw. Deformationen mithilfe von Flächenmodellierung beschreiben lassen. Exemplarisch werden hierfür 3D-Puntkwolken eines terrestrischen Laserscanner (TLS) genutzt, die im Zuge eines Belastungsversuch an einer historischeren Eisenbahnbrücke bei Verden (Aller), Niedersachsen, erfasst wurden. Zur Approximation der 3D-Punktwolken in unterschiedlichen Epochen werden B-Spline-Flächen genutzt. Im Rahmen der Schätzung von B-Spline-Flächen mit der Methode der kleinsten Quadrate werden neben Informationen über den Knotenvektor, auch die optimale Anzahl von Kontrollpunkten benötigt. Diese Kontrollpunkte bilden eine konvexe Hülle, innerhalb der die approximierte Fläche oder Kurve liegt. Ihre Anzahl hat somit einen starken Einfluss auf die gesamte Approximation und die sich anschließende Bestimmung von Verformungen (Deformationsanalyse). Zur Bestimmung der optimalen Anzahl der Kontrollpunkte werden Informationskriterien genutzt unter der Voraussetzung, dass das Messrauschen einer Normalverteilung entspricht. Eine verbesserte stochastische Beschreibung der polaren Messelemente: Horizontalrichtung, Vertikalwinkel und Schrägstrecke des TLS liefert die Möglichkeit einer zuverlässigeren Beurteilung der Genauigkeit der Flächenmodellierung von verrauschten, diskreten 3D-Punkten. Dies führt zu aussagekräftigeren Testgrößen, wie der Kongruenztestgröße in der Deformationanalyse. In diesem Beitrag liegt der Fokus auf der Diskussion der Ergebnisse basierend auf der Approximation mit B-Spline Flächen gegenüber den Ergebnissen aus rein punktwolkenbasierten Verfahren unter Nutzung der OpenSource Software CloudCompare (CC). Es wird gezeigt wie lokale Verfeinerung der Approximation vorteilshaft ist

Mitigation of ionospheric effects on Swarm GPS observations and kinematic orbits

The Swarm mission launched on November 22, 2013 consists of three identical satellites in near-polar orbits, Swarm A and C flying almost side-by-side at an initial altitude of 460 km, Swarm B flying in a higher orbit of about 530 km. Each satellite is equipped with a high precision 8-channels dual-frequency GPS receiver for precise orbit determination. This also offers excellent opportunities to study the ionosphere and to provide temporal gravity field information derived from the kinematic orbits of the satellites for the gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO). However, observations from on-board GPS receiver are strongly disturbed by ionospheric scintillations, which degrades the kinematic orbits at the geomagnetic equator and at polar areas and thus the gravity field. Due to the different property of ionospheric scintillations, the GPS carrier phase observations suffer also from different types of disturbances. In this contribution, in order to improve the quality of the kinematic orbits, we propose a new method to filter the high-frequency noise and repair the systematic errors in the phase observations, instead of eliminating or down-weighting the disturbed observations. The kinematic orbits and derived gravity field can be significantly improved. The systematic errors along the geomagnetic equator bands in the gravity field are also successfully eliminated.Deutsche Forschungsgemeinschaft (DFG)/LEO Potential Field Missions (CONTIM)/SPP1788 Dynamic Earth/E