Noise Modelling for GRACE Follow-On Observables in the Celestial Mechanics Approach

A key to understanding the dynamic system Earth in its current state is the continuous observation of its time-variable gravity field. The satellite missions Gravity Recovery And Climate Experiment (GRACE) and its successor GRACE Follow-On take an exceptional position in sensing these time-variable components because of their unique observing concept, which is based on ultra precise measurements of distance changes between a pair of satellites separated by a few hundred kilometres. These observations allow for a modelling of the Earth’s gravity field, typically on a basis of monthly snapshots. One of the key components of any model is the accurate specification of its quality. In temporal gravityfield modelling from GRACE Follow-On data one has to cope with several noise sources contaminating not only the observations but also the observation equations via mis-modellings in the underlying background force models. When employing the Celestial Mechanics Approach (CMA), developed at the Astronomical Institute of the University of Bern (AIUB), for gravity field modelling from satellite data a Least-Squares Adjustment (LSQA) is performed to compute monthly models of the Earth’s gravity field. However, as a consequence of the various contaminations with noise, the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. One way to deal with such deficiencies in the observations and modelling is to extend the parameter space, i.e., the model, by additional quantities, such as pseudo-stochastic parameters, which are co-estimated in the LSQA. These parameters are meant to absorb any kind of noise while retaining the signal in the gravity field and orbit parameters. In the CMA such pseudo-stochastic parameters are typically set-up as Piece-wise Constant Accelerations (PCAs) in regular intervals of e.g., 15 min. The stochastic behaviour of these parameters is unknown because they reflect an accumulation of a variety of noise sources. In the CMA fictitious artificial zero-observations are appended to the vector of observations together with an empirically determined variance to introduce a stochastic model for the PCAs. In order to also co-estimate a stochastic model for the pseudo-stochastic parameters in the LSQA Variance Component Estimation (VCE) is used in this work as a well established tool to assign variance components to individual groups of observations. In the simplest case the magnitude of the constraints of the pseudo-stochastic parameters can be determined fully automatically. Additionally, VCE is applied as an on-the-fly data reviewing method to account for gross outliers in the observations. Addressing the problem of noise contamination from the point of the GRACE Follow-On satellite mission’s observations, this work presents the incorporation of several noise models into the CMA to not only obtain high-quality time-variable gravity field models but also an accurate description of their stochastic behaviour. The noise models applied stem from pre-launch simulations or the formal covariance propagation of a kinematic point positioning process. Furthermore, the derivation and application of empirical noise models obtained from post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the observations, expressed in position residuals to the kinematic positions and in the inter-satellite link range-rate residuals, is implemented. Additionally, the current operational processing scheme of GRACE Follow-On data is expounded, including the normal equation handling in the CMA with BLAS and LAPACK routines. All implementations are compared and validated with the operational GRACE Follow-On processing at the AIUB by examining the stochastic behaviour of the respective post-fit residuals and by investigating areas on Earth where a low noise is expected. Finally, the influence and behaviour of the different noise modelling techniques is investigated in a combination of monthly gravity fields computed by various institutions as it is done by the Combination Service for Time-variable Gravity fields (COST-G).Ein wesentlicher Baustein für das Verständnis des Systems Erde ist die kontinuierliche Überwachung des zeit-variablen Anteils des Erdschwerefeldes. Die beiden Satellitenmissionen Gravity Recovery And Climate Experiment (GRACE) und GRACE Follow-On spielen hierbei eine gewichtige Rolle, da sie mit ihrem Beobachtungskonzept, das auf einer hochpräsizen Abstandsmessung zwischen einem Satellitenpaar beruht, diesen zeit-variablen Anteil besonders hoch auflösen können. Diese Messungen ermöglichen es, monatliche Schwerefeldmodelle zu bestimmen. Eine der wichtigsten Komponenten eines jeden Modells ist die akkurate Beschreibung seiner Unsicherheiten. Bei der Modellierung von zeit-variablen Schwerefeldern aus GRACE Follow-On Daten treten Effekte auf, die einerseits die Beobachtungen direkt kontaminieren, und andererseits auch durch Hintergrundmodelle der Kräfte in die Beobachtungsgleichungen einfliessen. Der Ansatz des Celestial Mechanics Approach (CMA), der am Astronomischen Institut der Universität Bern (AIUB) entwickelt wurde und in dieser Arbeit angewandt wird, beruht auf einer Kleinste-Quadrate-Parameterschätzung, um aus entsprechenden Satellitendaten Orbit- und Schwerefeldmodelle abzuleiten. Dabei ist zu beobachten, dass die formale Fehlerabschätzung der Parameter deutlich besser ausfällt als es zu erwarten wäre. Eine Möglichkeit mit Unsicherheiten in den Beobachtungen und der Modellierung umzugehen ist es, den Parameterraum zu erweitern. Das bedeutet, dass zusätzliche Grössen bestimmt werden, wie z.B. pseudo-stochastische Parameter. Diese Grössen sind dazu gedacht, Unsicherheiten zu absorbieren, aber gleichzeitig das Signal in den Schwerefeld- und Orbitparametern zu erhalten. Im CMA werden diese pseudo-stochastischen Parameter als stückweise konstante Beschleunigungen (PCAs) für regelmässige Intervalle (von z.B. 15 min) geschätzt. Das stochastische Verhalten dieser Parameter ist unbekannt, da sie eine Summe an Fehlerquellen ausgleichen sollen. Im CMA wird daher ein empirisch ermitteltes stochastisches Modell für die PCAs eingeführt. Um so ein Modell auch schätzen zu können, wird in dieser Arbeit auf die Methode der Varianzkomponentenschätzung (VCE) zurückgegriffen, die sich dadurch auszeichnet, Varianzkomponenten für unterschiedliche Beobachtungsgruppen zu bestimmen. Im einfachsten Falle zeigt sich, dass die Magnitude des stochastisches Modells der PCAs zusammen mit allen Parametern berechnet werden kann. Zusätzlich werden die Varianzkomponenten als Mass eingeführt, um Ausreisserin den Daten zu glätten. Die Problemstellung des Beobachtungsrauschens wird in dieser Arbeit durch unterschiedliche Rauschmodelle betrachtet. Damit soll sichergestellt werden, dass die geschätzten Schwerefeldmodelle nicht nur das zeit-variable Schwerefeldsignal beschreiben, sondern auch nachvollziehbare Informationen zu den zugehörigen Unsicherheiten bieten. Die Rauschmodelle stammen einerseits aus Simulationen zum Instrumentenverhalten, die vor dem Start durchgeführt wurden, und andererseits im Fall der kinematischen Positionsbeobachtungen aus einer formalen Kovarianzfortpflanzung. Des Weiteren wird auf die Ableitung von empirischen Rauschmodellen aus Post-Fit-Residuen eingegangen, die aus dem berechneten Orbit und den kinematischen Positionen bzw. Inter-satellite Link Range-Rates bestimmt werden. Auch wird die operationelle GRACE Follow-On Prozessierung ausgeführt, verbunden mit einer verbesserten Handhabung der Normalgleichungen mittels BLAS- und LAPACK-Routinen. Alle Neuerungen werden mit den operationellen GRACE Follow-On Lösungen verglichen und validiert. Hierbei werden insbesondere das stochastische Verhalten der Post-Fit-Residuen untersucht, ebenso wie Gebiete der Erde, in denen aufgrund physikalischer Prozesse kaum Rauschen zu erwarten ist. Zuletzt wird im Rahmen des Combination Service for Time-variable Gravity fields (COST-G) noch darauf eingegangen wie sich unterschiedliche Rauschmodellierungen in einer Kombination von Schwerefeldmodellen, die mit verschiedenen Ansätzen und Softwarepaketen bestimmt wurden, verhalten

Extrinsic Parameter Calibration for Line Scanning Cameras on Ground Vehicles with Navigation Systems Using a Calibration Pattern

Line scanning cameras, which capture only a single line of pixels, have been increasingly used in ground based mobile or robotic platforms. In applications where it is advantageous to directly georeference the camera data to world coordinates, an accurate estimate of the camera's 6D pose is required. This paper focuses on the common case where a mobile platform is equipped with a rigidly mounted line scanning camera, whose pose is unknown, and a navigation system providing vehicle body pose estimates. We propose a novel method that estimates the camera's pose relative to the navigation system. The approach involves imaging and manually labelling a calibration pattern with distinctly identifiable points, triangulating these points from camera and navigation system data and reprojecting them in order to compute a likelihood, which is maximised to estimate the 6D camera pose. Additionally, a Markov Chain Monte Carlo (MCMC) algorithm is used to estimate the uncertainty of the offset. Tested on two different platforms, the method was able to estimate the pose to within 0.06 m / 1.05$^{\circ}$ and 0.18 m / 2.39$^{\circ}$. We also propose several approaches to displaying and interpreting the 6D results in a human readable way.Comment: Published in MDPI Sensors, 30 October 201

Analysis and synthesis of bipedal humanoid movement : a physical simulation approach

textAdvances in graphics and robotics have increased the importance of tools for synthesizing humanoid movements to control animated characters and physical robots. There is also an increasing need for analyzing human movements for clinical diagnosis and rehabilitation. Existing tools can be expensive, inefficient, or difficult to use. Using simulated physics and motion capture to develop an interactive virtual reality environment, we capture natural human movements in response to controlled stimuli. This research then applies insights into the mathematics underlying physics simulation to adapt the physics solver to support many important tasks involved in analyzing and synthesizing humanoid movement. These tasks include fitting an articulated physical model to motion capture data, modifying the model pose to achieve a desired configuration (inverse kinematics), inferring internal torques consistent with changing pose data (inverse dynamics), and transferring a movement from one model to another model (retargeting). The result is a powerful and intuitive process for analyzing and synthesizing movement in a single unified framework.Computer Science

Virtuaalse proovikabiini 3D kehakujude ja roboti juhtimisalgoritmide uurimine

Väitekirja elektrooniline versioon ei sisalda publikatsiooneVirtuaalne riiete proovimine on üks põhilistest teenustest, mille pakkumine võib suurendada rõivapoodide edukust, sest tänu sellele lahendusele väheneb füüsilise töö vajadus proovimise faasis ning riiete proovimine muutub kasutaja jaoks mugavamaks. Samas pole enamikel varem välja pakutud masinnägemise ja graafika meetoditel õnnestunud inimkeha realistlik modelleerimine, eriti terve keha 3D modelleerimine, mis vajab suurt kogust andmeid ja palju arvutuslikku ressurssi. Varasemad katsed on ebaõnnestunud põhiliselt seetõttu, et ei ole suudetud korralikult arvesse võtta samaaegseid muutusi keha pinnal. Lisaks pole varasemad meetodid enamasti suutnud kujutiste liikumisi realistlikult reaalajas visualiseerida. Käesolev projekt kavatseb kõrvaldada eelmainitud puudused nii, et rahuldada virtuaalse proovikabiini vajadusi. Välja pakutud meetod seisneb nii kasutaja keha kui ka riiete skaneerimises, analüüsimises, modelleerimises, mõõtmete arvutamises, orientiiride paigutamises, mannekeenidelt võetud 3D visuaalsete andmete segmenteerimises ning riiete mudeli paigutamises ja visualiseerimises kasutaja kehal. Selle projekti käigus koguti visuaalseid andmeid kasutades 3D laserskannerit ja Kinecti optilist kaamerat ning koostati nendest andmebaas. Neid andmeid kasutati välja töötatud algoritmide testimiseks, mis peamiselt tegelevad riiete realistliku visuaalse kujutamisega inimkehal ja suuruse pakkumise süsteemi täiendamisega virtuaalse proovikabiini kontekstis.Virtual fitting constitutes a fundamental element of the developments expected to rise the commercial prosperity of online garment retailers to a new level, as it is expected to reduce the load of the manual labor and physical efforts required. Nevertheless, most of the previously proposed computer vision and graphics methods have failed to accurately and realistically model the human body, especially, when it comes to the 3D modeling of the whole human body. The failure is largely related to the huge data and calculations required, which in reality is caused mainly by inability to properly account for the simultaneous variations in the body surface. In addition, most of the foregoing techniques cannot render realistic movement representations in real-time. This project intends to overcome the aforementioned shortcomings so as to satisfy the requirements of a virtual fitting room. The proposed methodology consists in scanning and performing some specific analyses of both the user's body and the prospective garment to be virtually fitted, modeling, extracting measurements and assigning reference points on them, and segmenting the 3D visual data imported from the mannequins. Finally, superimposing, adopting and depicting the resulting garment model on the user's body. The project is intended to gather sufficient amounts of visual data using a 3D laser scanner and the Kinect optical camera, to manage it in form of a usable database, in order to experimentally implement the algorithms devised. The latter will provide a realistic visual representation of the garment on the body, and enhance the size-advisor system in the context of the virtual fitting room under study

Markerless Kinematics of Pediatric Manual Wheelchair Mobility

Pediatric manual wheelchair users face substantial risk of orthopaedic injury to the upper extremities, particularly the shoulders, during transition to wheelchair use and during growth and development. Propulsion strategy can influence mobility efficiency, activity participation, and quality of life. The current forefront of wheelchair biomechanics research includes translating findings from adult to pediatric populations, improving the quality and efficiency of care under constrained clinical funding, and understanding injury mechanisms and risk factors. Typically, clinicians evaluate wheelchair mobility using marker-based motion capture and instrumentation systems that are precise and accurate but also time-consuming, inconvenient, and expensive for repeated assessments. There is a substantial need for technology that evaluates and improves wheelchair mobility outside of the laboratory to provide better outcomes for wheelchair users, enhancing clinical data. Advancement in this area gives physical therapists better tools and the supporting research necessary to improve treatment efficacy, mobility, and quality of life in pediatric wheelchair users. This dissertation reports on research studies that evaluate the effect of physiotherapeutic training on manual wheelchair mobility. In particular, these studies (1) develop and characterize a novel markerless motion capture-musculoskeletal model systems interface for kinematic assessment of manual wheelchair propulsion biomechanics, (2) conduct a longitudinal investigation of pediatric manual wheelchair users undergoing intensive community-based therapy to determine predictors of kinematic response, and (3) evaluate propulsion pattern-dependent training efficacy and musculoskeletal behavior using visual biofeedback.Results of the research studies show that taking a systems approach to the kinematic interface produces an effective and reliable system for kinematic assessment and training of manual wheelchair propulsion. The studies also show that the therapeutic outcomes and orthopaedic injury risk of pediatric manual wheelchair users are significantly related to the propulsion pattern employed. Further, these subjects can change their propulsion pattern in response to therapy even in the absence of wheelchair-based training, and have pattern-dependent differences in joint kinematics, musculotendon excursion, and training response. Further clinical research in this area is suggested, with a focus on refining physiotherapeutic training strategies for pediatric manual wheelchair users to develop safer and more effective propulsion patterns

Pushing the envelope for estimating poses and actions via full 3D reconstruction

Estimating poses and actions of human bodies and hands is an important task in the computer vision community due to its vast applications, including human computer interaction, virtual reality and augmented reality, medical image analysis. Challenges: There are many in-the-wild challenges in this task (see chapter 1). Among them, in this thesis, we focused on two challenges which could be relieved by incorporating the 3D geometry: (1) inherent 2D-to-3D ambiguity driven by the non-linear 2D projection process when capturing 3D objects. (2) lack of sufficient and quality annotated datasets due to the high-dimensionality of subjects' attribute space and inherent difficulty in annotating 3D coordinate values. Contributions: We first tried to jointly tackle the 2D-to-3D ambiguity and insufficient data issues by (1) explicitly reconstructing 2.5D and 3D samples and use them as new training data to train a pose estimator. Next, we tried to (2) encode 3D geometry in the training process of the action recognizer to reduce the 2D-to-3D ambiguity. In appendix, we proposed a (3) new hand pose synthetic dataset that can be used for more complete attribute changes and multi-modal experiments in the future. Experiments: Throughout experiments, we found interesting facts: (1) 2.5D depth map reconstruction and data augmentation can improve the accuracy of the depth-based hand pose estimation algorithm, (2) 3D mesh reconstruction can be used to generate a new RGB data and it improves the accuracy of RGB-based dense hand pose estimation algorithm, (3) 3D geometry from 3D poses and scene layouts could be successfully utilized to reduce the 2D-to-3D ambiguity in the action recognition problem.Open Acces

The fourier virtual fields method for the identification of material property distributions

The requirement of a fast and accurate modulus identification technique has arisen in many fields of research, such as solid mechanics, structural health monitoring, medical diagnosis, etc. An inverse technique based on an appropriate interpretation of the principle of virtual work, namely the Virtual Fields Method (VFM), has been proposed in the literature, which is able to return elastic modulus values after a single matrix inversion. An extension of the virtual fields method to the spatial frequency domain in order to determine modulus distributions of materials based on a sine/cosine parameterisation of the unknown modulus is developed in this thesis, and will be called the Fourier-series-based Virtual Fields Method (F-VFM). The technique accepts in-plane (two-dimensional) or volumetric (three-dimensional) deformation measurement data as its input. An efficient numerical algorithm of the F-VFM based on the fast Fourier transform is presented, which can return thousands of unknown Fourier coefficients within a minute thus reducing the computation time by several orders of magnitude compared to a direct implementation of the F-VFM for typical dataset sizes. The F-VFM technique is also adapted to cope with a common situation in experimental mechanics where the knowledge of the boundary conditions is limited. The three versions of the F-VFM in this situation are respectively the experimental traction , windowed traction and Fourier-series traction approaches. The technique is then validated with numerical data from different stiffness patterns. The performance is compared to that of an iterative updating technique based on a genetic algorithm for one of these patterns, and computational effort is demonstrated to be at least five orders of magnitude less for the new F-VFM than for this updating method. The sensitivity of the performance of the F-VFM to noise is also investigated. Finally, the technique is applied to experimental data in both 2-D and 3-D cases with promising results