45 research outputs found
Digital Filtering Algorithms for Decorrelation within Large Least Squares Problems
The GOCE (Gravity Field and steady-state Ocean Circulation Explorer) mission is dedicated to the determination of the Earth's gravity field. During the mission period of at least one year the GOCE satellite will collect approximately 100 million highly correlated observations. The gravity field will be described in terms of approximately 70,000 spherical harmonic coefficients. This leads to a least squares adjustment, in which the design matrix occupies 51 terabytes while the covariance matrix of the observations requires 72,760 terabytes of memory. The very large design matrix is typically computed in parallel using supercomputers like the JUMP (Juelich Multi Processor) supercomputer in JĂŒlich, Germany. However, such a brute force approach does not work for the covariance matrix. Here, we have to exploit certain features of the observations, e.g. that the observations can be interpreted as a stationary time series. This allows for a very sparse representation of the covariance matrix by digital filters. This thesis is concerned with the use of digital filters for decorrelation within large least squares problems. First, it is analyzed, which conditions the observations must meet, such that digital filters can be used to represent their covariance matrix. After that, different filter implementations are introduced and compared with each other, especially with respect to the calculation time of filtering. This is of special concern, as for many applications the very large design matrix has to be filtered at least once. One special problem arising by the use of digital filters is the so-called warm-up effect. For the first time, methods are developed in this thesis for determining the length of the effect and for avoiding this effect. Next, a new algorithm is developed to deal with the problem of short data gaps within the observation time series. Finally, it is investigated which filter methods are best adopted for the application scenario GOCE, and several numerical simulations are performed.Digitale Filteralgorithmen zur Dekorrelation in groĂen kleinste-Quadrate Problemen Die GOCE (Gravity Field and steady-state Ocean Circulation Explorer) Mission ist der Bestimmung des Erdschwerefeldes gewidmet. WĂ€hrend der Missionsdauer von mindestens einem Jahr wird der GOCE Satellit circa 100 Millionen hoch korrelierte Beobachtungen sammeln. Das Erdschwerefeld wird durch circa 70.000 sphĂ€risch harmonische Koeffizienten beschrieben. Dies fĂŒhrt zu einem kleinste-Quadrate Ausgleich, wobei die Designmatrix 51 Terabytes benötigt wĂ€hrend die Kovarianzmatrix der Beobachtungen 72.760 Terabytes erfordert. Die sehr groĂe Designmatrix wird typischerweise parallel berechnet, wobei Supercomputer wie JUMP (Juelich Multi Processor) in JĂŒlich (Deutschland) zum Einsatz kommen. Ein solcher Ansatz, bei dem das Problem durch geballte Rechenleistung gelöst wird, funktioniert bei der Kovarianzmatrix der Beobachtungen nicht mehr. Hier mĂŒssen bestimmte Eigenschaften der Beobachtungen ausgenutzt werden, z.B. dass die Beobachtungen als stationĂ€re Zeitreihe aufgefasst werden können. Dies ermöglicht es die Kovarianzmatrix durch digitale Filter zu reprĂ€sentieren. Diese Arbeit beschĂ€ftigt sich mit der Nutzung von digitalen Filtern zur Dekorrelation in groĂen kleinste-Quadrate Problemen. Zuerst wird analysiert, welche Bedingungen die Beobachtungen erfĂŒllen mĂŒssen, damit digitale Filter zur ReprĂ€sentation ihrer Kovarianzmatrix benutzt werden können. Danach werden verschiedene Filterimplementierungen vorgestellt und miteinander verglichen, wobei spezielles Augenmerk auf die Rechenzeit fĂŒr das Filtern gelegt wird. Dies ist von besonderer Bedeutung, da in vielen Anwendungen die sehr groĂe Designmatrix mindestens einmal gefiltert werden muss. Ein spezielles Problem, welches beim Benutzen der Filter entsteht, ist der sogenannte Warmlaufzeiteffekt. Zum ersten Mal werden in dieser Arbeit Methoden entwickelt, um die LĂ€nge des Effekts zu bestimmen und um den Effekt zu vermeiden. Als NĂ€chstes wird ein neuer Algorithmus zur Lösung des Problems von kurzen DatenlĂŒcken in der Beobachtungszeitreihe entwickelt. SchlieĂlich wird untersucht, welche Filtermethoden man am besten fĂŒr das Anwendungsszenario GOCE verwendet und es werden verschiedene numerische Simulationen durchgefĂŒhrt
Assessing the potential for precision medicine in body weight reduction with regard to type 2 diabetes mellitus therapies: A metaâregression analysis of 120 randomized controlled trials
Aims: To assess the potential for precision medicine in type 2 diabetes by quantifying the variability of body weight as response to pharmacological treatment and to identify predictors which could explain this variability. Methods: We used randomized clinical trials (RCTs) comparing glucoseâlowering drugs (including but not limited to sodiumâglucose cotransporterâ2 inhibitors, glucagonâlike peptideâ1 receptor agonists and thiazolidinediones) to placebo from four recent systematic reviews. RCTs reporting on body weight after treatment to allow for calculation of its logarithmic standard deviation (log[SD], i.e., treatment response heterogeneity) in verum (i.e., treatment) and placebo groups were included. Metaâregression analyses were performed with respect to variability of body weight after treatment and potential predictors. Results: A total of 120 RCTs with a total of 43 663 participants were analysed. A slightly larger treatment response heterogeneity was shown in the verum groups, with a median log(SD) of 2.83 compared to 2.79 from placebo. After full adjustment in the metaâregression model, the difference in body weight log(SD) was â0.026 (95% confidence interval â0.044; 0.008), with greater variability in the placebo groups. Scatterplots did not show any slope divergence (i.e., interaction) between clinical predictors and the respective treatment (verum or placebo). Conclusions: We found no major treatment response heterogeneity in RCTs of glucoseâlowering drugs for body weight reduction in type 2 diabetes. The precision medicine approach may thus be of limited value in this setting
Swarm accelerometer data processing from raw accelerations to thermospheric neutral densities
The Swarm satellites were launched on November 22, 2013, and carry accelerometers and GPS receivers as part of their scientific payload. The GPS receivers do not only provide the position and time for the magnetic field measurements, but are also used for determining non-gravitational forces like drag and radiation pressure acting on the spacecraft. The accelerometers measure these forces directly, at much finer resolution than the GPS receivers, from which thermospheric neutral densities can be derived. Unfortunately, the acceleration measurements suffer from a variety of disturbances, the most prominent being slow temperature-induced bias variations and sudden bias changes. In this paper, we describe the new, improved four-stage processing that is applied for transforming the disturbed acceleration measurements into scientifically valuable thermospheric neutral densities. In the first stage, the sudden bias changes in the acceleration measurements are manually removed using a dedicated software tool. The second stage is the calibration of the accelerometer measurements against the non-gravitational accelerations derived from the GPS receiver, which includes the correction for the slow temperature-induced bias variations. The identification of validity periods for calibration and correction parameters is part of the second stage. In the third stage, the calibrated and corrected accelerations are merged with the non-gravitational accelerations derived from the observations of the GPS receiver by a weighted average in the spectral domain, where the weights depend on the frequency. The fourth stage consists of transforming the corrected and calibrated accelerations into thermospheric neutral densities. We present the first results of the processing of Swarm C acceleration measurements from June 2014 to May 2015. We started with Swarm C because its acceleration measurements contain much less disturbances than those of Swarm A and have a higher signal-to-noise ratio than those of Swarm B. The latter is caused by the higher altitude of Swarm B as well as larger noise in the acceleration measurements of Swarm B. We show the results of each processing stage, highlight the difficulties encountered, and comment on the quality of the thermospheric neutral density data set.Astrodynamics & Space Mission
TOLEOS: Thermosphere Observations from Low-Earth Orbiting Satellites
The objective of the TOLEOS project is to process the CHAMP, GRACE, and GRACE-FO accelerometer measurements with improved processing standards to obtain thermosphere density and crosswind data products. These new data products will cover the entirety of the accelerometer missions and complement the existing ESA databases for Swarm and GOCE. The improvements in the processing focus on the radiation pressure modelling, which is expected to have a significant effect on the density and crosswind data, in particular at altitudes above 450 km during solar minimum conditions. Substantial validation activities are performed since the projectâs start in June 2021 and will continue until the end of the project in July 2022
Preliminary Validation of Thermosphere Observations from the TOLEOS Project
OBSERVATIONS of upper atmospheric neutral mass density (NMD) and wind are critical to understand the coupling mechanisms between Earthâs ionosphere, thermosphere, and magnetosphere. The ongoing Swarm DISC (data, innovation, and science cluster) project TOLEOS (thermosphere observations from low-Earth orbiting satellites) aims to provide better calibrated NMD and crosswind data from CHAMP, GRACE, and GRACE-FO (follow-on) satellite missions. The project uses state-of-the-art models, calibration techniques, and processing standards to improve the accuracy of these data products and ensure inter-mission consistency. Here, we present preliminary results of the quality of the data in comparison to the high accuracy drag temperature model DTM2020, and physics-based TIE-GCM (thermosphere ionosphere electrodynamics general circulation model) and CTIPe (coupled thermosphere ionosphere plasmasphere electrodynamics) models
Lower-thermosphereâionosphere (LTI) quantities: current status of measuring techniques and models
The lower-thermosphere-ionosphere (LTI) system consists of the upper atmosphere and the lower part of the ionosphere and as such comprises a complex system coupled to both the atmosphere below and space above. The atmospheric part of the LTI is dominated by laws of continuum fluid dynamics and chemistry, while the ionosphere is a plasma system controlled by electromagnetic forces driven by the magnetosphere, the solar wind, as well as the wind dynamo. The LTI is hence a domain controlled by many different physical processes. However, systematic in situ measurements within this region are severely lacking, although the LTI is located only 80 to 200 km above the surface of our planet. This paper reviews the current state of the art in measuring the LTI, either in situ or by several different remote-sensing methods. We begin by outlining the open questions within the LTI requiring high-quality in situ measurements, before reviewing directly observable parameters and their most important derivatives. The motivation for this review has arisen from the recent retention of the Daedalus mission as one among three competing mission candidates within the European Space Agency (ESA) Earth Explorer 10 Programme. However, this paper intends to cover the LTI parameters such that it can be used as a background scientific reference for any mission targeting in situ observations of the LTI.Peer reviewe
Digital filtering algorithms for decorrelation within large least squares problems
The GOCE (Gravity Field and steady-state Ocean Circulation Explorer) mission is dedicated to the determination of the Earth's gravity field. During the mission period of at least one year the GOCE satellite will collect approximately 100 million highly correlated observations. The gravity field will be described in terms of approximately 70,000 spherical harmonic coefficients. This leads to a least squares adjustment, in which the design matrix occupies 51 terabytes while the covariance matrix of the observations requires 72,760 terabytes of memory. The very large design matrix is typically computed in parallel using supercomputers like the JUMP (Juelich Multi Processor) supercomputer in JĂŒlich, Germany. However, such a brute force approach does not work for the covariance matrix. Here, we have to exploit certain features of the observations, e.g. that the observations can be interpreted as a stationary time series. This allows for a very sparse representation of the covariance matrix by digital filters.
This thesis is concerned with the use of digital filters for decorrelation within large least squares problems. First, it is analyzed, which conditions the observations must meet, such that digital filters can be used to represent their covariance matrix. After that, different filter implementations are introduced and compared with each other, especially with respect to the calculation time of filtering. This is of special concern, as for many applications the very large design matrix has to be filtered at least once. One special problem arising by the use of digital filters is the so-called warm-up effect. For the first time, methods are developed in this thesis for determining the length of the effect and for avoiding this effect. Next, a new algorithm is developed to deal with the problem of short data gaps within the observation time series. Finally, it is investigated which filter methods are best adopted for the application scenario GOCE, and several numerical simulations are performedDigitale Filteralgorithmen zur Dekorrelation in groĂen kleinste-Quadrate Problemen
Die GOCE (Gravity Field and steady-state Ocean Circulation Explorer) Mission ist der Bestimmung des Erdschwerefeldes gewidmet. WĂ€hrend der Missionsdauer von mindestens einem Jahr wird der GOCE Satellit circa 100 Millionen hoch korrelierte Beobachtungen sammeln. Das Erdschwerefeld wird durch circa 70.000 sphĂ€risch harmonische Koeffizienten beschrieben. Dies fĂŒhrt zu einem kleinste-Quadrate Ausgleich, wobei die Designmatrix 51 Terabytes benötigt wĂ€hrend die Kovarianzmatrix der Beobachtungen 72.760 Terabytes erfordert. Die sehr groĂe Designmatrix wird typischerweise parallel berechnet, wobei Supercomputer wie JUMP (Juelich Multi Processor) in JĂŒlich (Deutschland) zum Einsatz kommen. Ein solcher Ansatz, bei dem das Problem durch geballte Rechenleistung gelöst wird, funktioniert bei der Kovarianzmatrix der Beobachtungen nicht mehr. Hier mĂŒssen bestimmte Eigenschaften der Beobachtungen ausgenutzt werden, z.B. dass die Beobachtungen als stationĂ€re Zeitreihe aufgefasst werden können. Dies ermöglicht es die Kovarianzmatrix durch digitale Filter zu reprĂ€sentieren.
Diese Arbeit beschĂ€ftigt sich mit der Nutzung von digitalen Filtern zur Dekorrelation in groĂen kleinste-Quadrate Problemen. Zuerst wird analysiert, welche Bedingungen die Beobachtungen erfĂŒllen mĂŒssen, damit digitale Filter zur ReprĂ€sentation ihrer Kovarianzmatrix benutzt werden können. Danach werden verschiedene Filterimplementierungen vorgestellt und miteinander verglichen, wobei spezielles Augenmerk auf die Rechenzeit fĂŒr das Filtern gelegt wird. Dies ist von besonderer Bedeutung, da in vielen Anwendungen die sehr groĂe Designmatrix mindestens einmal gefiltert werden muss. Ein spezielles Problem, welches beim Benutzen der Filter entsteht, ist der sogenannte Warmlaufzeiteffekt. Zum ersten Mal werden in dieser Arbeit Methoden entwickelt, um die LĂ€nge des Effekts zu bestimmen und um den Effekt zu vermeiden. Als NĂ€chstes wird ein neuer Algorithmus zur Lösung des Problems von kurzen DatenlĂŒcken in der Beobachtungszeitreihe entwickelt. SchlieĂlich wird untersucht, welche Filtermethoden man am besten fĂŒr das Anwendungsszenario GOCE verwendet und es werden verschiedene numerische Simulationen durchgefĂŒhrt