Soil moisture estimation of eucalyptus forests in Portugal with l-band SAR using polarimetric - Decompositions and machine learning

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial TechnologiesSoil moisture is a critical ecological parameter because it is a primary input for all processes that involve the complex interaction between land surface and the atmosphere. Remote sensing, especially using microwaves, has shown great promise in measuring soil moisturewith several operating satellites focused on its continuous estimation and monitoring on a global scale. Portugal is predominantly characterized by Mediterranean and semi-arid climates that feature low and sporadic precipitation. Over 10% of Portugal’s land area has been planted with Eucalyptus globulus- a non-native, fast-growing tree primarily planted for industrial use. Some studies have demonstrated that eucalyptus plantations adversely affect water availability, but overall results have been inconclusive as there are numerous other confounding variables. The goals of this study were to determine, using fully polarimetric L-band SAR and machine learning, if soil moisture could be accurately predicted in eucalyptus forests, and if there is a significant difference in soil moisture inside eucalyptus forests relative to other forests. Vegetated surfaces complicate the estimation of soil moisture because their structure and water content contribute significantly to backscatter of the radar signal. Thus, four polarimetric decompositions were compared to separate vegetative versus surface backscatter. The inputs from those decompositions, as well as several additional radar indices and polarizations from the microwave images, were used as feature inputs into two different machine learning models. After a feature selection process, the soil moisture estimations were retrieved and compared using cross-validation. The best overall soil moisture retrieval for Eucalyptus forests came from Random Forest with a RMSE of 0.021, a MAE of 0.017, and a MBE of 0.001. Through a statistical t-test, predicted soil moisture values in eucalyptus forests did not differ significantly as compared to other forest types in the study area

Empirical multi-band characterization of propagation with modelling aspects for communictions

Diese Arbeit präsentiert eine empirische Untersuchung der Wellenausbreitung für drahtlose Kommunikation im Millimeterwellen- und sub-THz-Band, wobei als Referenz das bereits bekannte und untersuchte sub-6-GHz-Band verwendet wird. Die großen verfügbaren Bandbreiten in diesen hohen Frequenzbändern erlauben die Verwendung hoher instantaner Bandbreiten zur Erfüllung der wesentlichen Anforderungen zukünftiger Mobilfunktechnologien (5G, “5G and beyond” und 6G). Aufgrund zunehmender Pfad- und Eindringverluste bei zunehmender Trägerfrequenz ist die resultierende Abdeckung dabei jedoch stark reduziert. Die entstehenden Pfadverluste können durch die Verwendung hochdirektiver Funkschnittstellen kompensiert werden, wodurch die resultierende Auflösung im Winkelbereich erhöht wird und die Notwendigkeit einer räumlichen Kenntnis der Systeme mit sich bringt: Woher kommt das Signal? Darüber hinaus erhöhen größere Anwendungsbandbreiten die Auflösung im Zeitbereich, reduzieren das small-scale Fading und ermöglichen die Untersuchung innerhalb von Clustern von Mehrwegekomponenten. Daraus ergibt sich für Kommunikationssysteme ein vorhersagbareres Bild im Winkel-, Zeit- und Polarisationsbereich, welches Eigenschaften sind, die in Kanalmodellen für diese Frequenzen widergespiegelt werden müssen. Aus diesem Grund wurde in der vorliegenden Arbeit eine umfassende Charakterisierung der Wellenausbreitung durch simultane Multibandmessungen in den sub-6 GHz-, Millimeterwellen- und sub-THz-Bändern vorgestellt. Zu Beginn wurde die Eignung des simultanen Multiband-Messverfahrens zur Charakterisierung der Ausbreitung von Grenzwert-Leistungsprofilen und large-scale Parametern bewertet. Anschließend wurden wichtige Wellenausbreitungsaspekte für die Ein- und Multibandkanalmodellierung innerhalb mehrerer Säulen der 5G-Technologie identifiziert und Erweiterungen zu verbreiteten räumlichen Kanalmodellen eingeführt und bewertet, welche die oben genannten Systemaspekte abdecken.This thesis presents an empirical characterization of propagation for wireless communications at mm-waves and sub-THz, taking as a reference the already well known and studied sub-6 GHz band. The large blocks of free spectrum available at these high frequency bands makes them particularly suitable to provide the necessary instantaneous bandwidths to meet the requirements of future wireless technologies (5G, 5G and beyond, and 6G). However, isotropic path-loss and penetration-loss are larger with increasing carrier frequency, hence, coverage is severely reduced. Path-loss can be compensated with the utilization of highly directive radio-interfaces, which increases the resolution in the angular domain. Nonetheless, this emphasizes the need of spatial awareness of systems, making more relevant the question “where does the signal come from?” In addition, larger application bandwidths increase the resolution in the time domain, reducing small-scale fading and allowing to observe inside of clusters of multi-path components (MPCs). Consequently, communication systems have a more deterministic picture of the environment in the angular, time, and polarization domain, characteristics that need to be reflected in channel models for these frequencies. Therefore, in the present work we introduce an extensive characterization of propagation by intensive simultaneous multi-band measurements in the sub-6 GHz, mm-waves, and sub-THz bands. Firstly, the suitability of the simultaneous multi-band measurement procedure to characterize propagation from marginal power profiles and large-scale parameters (LSPs) has been evaluated. Then, key propagation aspects for single and multi-band channel modelling in several verticals of 5G have been identified, and extensions to popular spatial channel models (SCMs) covering the aforementioned system aspects have been introduced and evaluated

Simultaneous Source Localization and Polarization Estimation via Non-Orthogonal Joint Diagonalization with Vector-Sensors

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods

The Buckland Park MF radar: routine observation scheme and velocity comparisons

This paper describes the routine observations scheme implemented for the Buckland Park medium frequency (BPMF) radar. These observations are rare among current MF/HF radar observations in that they are made using a relatively narrow transmit polar diagram. The flexibility of the radar allows a number of analyses to be performed simultaneously. The analyses described include the full correlation analysis (FCA), spatial correlation analysis (SCA), hybrid Doppler interferometry (HDI) and imaging Doppler interferometry (IDI) for observations of mesospheric dynamics and the temporal and spatial characteristics of their scatterers, the differential absorption experiment (DAE) for the estimation of electron densities and collision frequencies, and meteor analysis for estimation of meteor height, time and angle of arrival (AOA) distributions. Intercomparisons between wind velocities estimated using the FCA with SCA, HDI and IDI techniques are presented. The FCA velocities exhibit the well-known "triangle size effect" (TSE), whereby the wind velocity is underestimated at smaller antenna spacings. Although the SCA, IDI and HDI techniques were not applied concurrently, comparisons using FCA as a reference suggest these techniques produce velocities in good agreement.D. A. Holdsworth and I. M. Rei

Information retrieval from spaceborne GNSS Reflectometry observations using physics- and learning-based techniques

This dissertation proposes a learning-based, physics-aware soil moisture (SM) retrieval algorithm for NASA’s Cyclone Global Navigation Satellite System (CYGNSS) mission. The proposed methodology has been built upon the literature review, analyses, and findings from a number of published studies throughout the dissertation research. Namely, a Sig- nals of Opportunity Coherent Bistatic scattering model (SCoBi) has been first developed at MSU and then its simulator has been open-sourced. Simulated GNSS-Reflectometry (GNSS-R) analyses have been conducted by using SCoBi. Significant findings have been noted such that (1) Although the dominance of either the coherent reflections or incoher- ent scattering over land is a debate, we demonstrated that coherent reflections are stronger for flat and smooth surfaces covered by low-to-moderate vegetation canopy; (2) The influ- ence of several land geophysical parameters such as SM, vegetation water content (VWC), and surface roughness on the bistatic reflectivity was quantified, the dynamic ranges of reflectivity changes due to SM and VWC are much higher than the changes due to the surface roughness. Such findings of these analyses, combined with a comprehensive lit- erature survey, have led to the present inversion algorithm: Physics- and learning-based retrieval of soil moisture information from space-borne GNSS-R measurements that are taken by NASA’s CYGNSS mission. The study is the first work that proposes a machine learning-based, non-parametric, and non-linear regression algorithm for CYGNSS-based soil moisture estimation. The results over point-scale soil moisture observations demon- strate promising performance for applicability to large scales. Potential future work will be extension of the methodology to global scales by training the model with larger and diverse data sets

Multichannel Blind Deconvolution of Circularly Polarized Imagery

Current methods can be used to recreate an expected Stokes polarization vector from measured light for characterization purposes. However, this only applies to three of the Stokes parameters, that is, the linear polarization components. Circular polarization is not currently being utilized for object characterization because the mathematical complexity is greater than for that of linear polarization. This research will analyze a way to expand existing algorithms to include circular polarization and enable the complete reconstruction of the Stokes vector from the measured light into a blind deconvolution algorithm for Stokes estimation and image reconstruction

Formation of ions and radicals from icy grains in comets

Ion and radical formation in comets are thought to occur primarily by photodissociation of gas phase molecules. Experimental evidence and theoretical calculations are presented that show that some of the radical and ions can come directly from ice grains. The experimental evidence suggest that if the frozen molecules on the surface of grains undergo direct dissociation then they may be able to release radicals directly in the gas phase. If the molecules undergo predissociation it is unlikely that they will release radicals in the gas phase since they should be quenched. Calculations of this direct photodissociation mechanism further indicate that even if the parent molecule undergoes direct dissociation, the yield will not be high enough to explain the rays structure in comets unless the radicals are stored in the grains and then released when the grain evaporates. Calculations were also performed to determine the maximum number of ions that can be stored in an icy grain's radius. This number is compared with the ratio of the ion to neutral molecular density. The comparison suggests that some of the ions observed near the nucleus of the comet could have originally been present in the cometary nucleus. It is also pointed out that the presence of these ions in icy grains could lead to radical formation via electron recombination. Finally, an avalanche process was evaluated as another means of producing ions in comets

An indoor variance-based localization technique utilizing the UWB estimation of geometrical propagation parameters

A novel localization framework is presented based on ultra-wideband (UWB) channel sounding, employing a triangulation method using the geometrical properties of propagation paths, such as time delay of arrival, angle of departure, angle of arrival, and their estimated variances. In order to extract these parameters from the UWB sounding data, an extension to the high-resolution RiMAX algorithm was developed, facilitating the analysis of these frequency-dependent multipath parameters. This framework was then tested by performing indoor measurements with a vector network analyzer and virtual antenna arrays. The estimated means and variances of these geometrical parameters were utilized to generate multiple sample sets of input values for our localization framework. Next to that, we consider the existence of multiple possible target locations, which were subsequently clustered using a Kim-Parks algorithm, resulting in a more robust estimation of each target node. Measurements reveal that our newly proposed technique achieves an average accuracy of 0.26, 0.28, and 0.90 m in line-of-sight (LoS), obstructed-LoS, and non-LoS scenarios, respectively, and this with only one single beacon node. Moreover, utilizing the estimated variances of the multipath parameters proved to enhance the location estimation significantly compared to only utilizing their estimated mean values

GNSS reflectometry for land remote sensing applications

Soil moisture and vegetation biomass are two essential parameters from a scienti c and economical point of view. On one hand, they are key for the understanding of the hydrological and carbon cycle. On the other hand, soil moisture is essential for agricultural applications and water management, and vegetation biomass is crucial for regional development programs. Several remote sensing techniques have been used to measure these two parameters. However, retrieving soil moisture and vegetation biomass with the required accuracy, and the appropriate spatial and temporal resolutions still remains a major challenge. The use of Global Navigation Satellite Systems (GNSS) reflected signals as sources of opportunity for measuring soil moisture and vegetation biomass is assessed in this PhD Thesis. This technique, commonly known as GNSS-Reflectometry (GNSS-R), has gained increasing interest among the scienti c community during the last two decades due to its unique characteristics. Previous experimental works have already shown the capabilities of GNSS-R to sense small reflectivity changes on the surface. The use of the co- and cross-polarized reflected signals was also proposed to mitigate nuisance parameters, such as soil surface roughness, in the determination of soil moisture. However, experimental evidence of the suitability of that technique could not be demonstrated. This work analyses from a theoretical and an experimental point of view the capabilities of polarimetric observations of GNSS reflected signals for monitoring soil moisture and vegetation biomass. The Thesis is structured in four main parts. The fi rst part examines the fundamental aspects of the technique and provides a detailed review of the GNSS-R state of the art for soil moisture and vegetation monitoring. The second part deals with the scattering models from land surfaces. A comprehensive description of the formation of scattered signals from rough surfaces is provided. Simulations with current state of the art models for bare and vegetated soils were performed in order to analyze the scattering components of GNSS reflected signals. A simpli ed scattering model was also developed in order to relate in a straightforward way experimental measurements to soil bio-geophysical parameters. The third part reviews the experimental work performed within this research. The development of a GNSS-R instrument for land applications is described, together with the three experimental campaigns carried out in the frame of this PhD Thesis. The analysis of the GNSS-R and ground truth data is also discussed within this part. As predicted by models, it was observed that GNSS scattered signals from natural surfaces are a combination of a coherent and an incoherent scattering components. A data analysis technique was proposed to separate both scattering contributions. The use of polarimetric observations for the determination of soil moisture was demonstrated to be useful under most soil conditions. It was also observed that forests with high levels of biomass could be observed with GNSS reflected signals. The fourth and last part of the Thesis provides an analysis of the technology perspectives. A GNSS-R End-to-End simulator was used to determine the capabilities of the technique to observe di erent soil reflectivity conditions from a low Earth orbiting satellite. It was determined that high accuracy in the estimation of reflectivity could be achieved within reasonable on-ground resolution, as the coherent scattering component is expected to be the predominant one in a spaceborne scenario. The results obtained in this PhD Thesis show the promising potential of GNSS-R measurements for land remote sensing applications, which could represent an excellent complementary observation for a wide range of Earth Observation missions such as SMOS, SMAP, and the recently approved ESA Earth Explorer Mission Biomass.La humedad del suelo y la biomasa de la vegetaci on son dos parametros clave desde un punto de vista tanto cient co como econ omico. Por una parte son esenciales para el estudio del ciclo del agua y del carbono. Por otra parte, la humedad del suelo es esencial para la gesti on de las cosechas y los recursos h dricos, mientras que la biomasa es un par ametro fundamental para ciertos programas de desarrollo. Varias formas de teledetección se han utilizado para la observaci on remota de estos par ametros, sin embargo, su monitorizaci on con la precisi on y resoluci on necesarias es todav a un importante reto tecnol ogico. Esta Tesis evalua la capacidad de medir humedad del suelo y biomasa de la vegetaci on con señales de Sistemas Satelitales de Posicionamiento Global (GNSS, en sus siglas en ingl es) reflejadas sobre la Tierra. La t ecnica se conoce como Reflectometr í a GNSS (GNSS-R), la cual ha ganado un creciente inter es dentro de la comunidad científ ca durante las dos ultimas d ecadas. Experimentos previos a este trabajo ya demostraron la capacidad de observar cambios en la reflectividad del terreno con GNSS-R. El uso de la componente copolar y contrapolar de la señal reflejada fue propuesto para independizar la medida de humedad del suelo de otros par ametros como la rugosidad del terreno. Sin embargo, no se pudo demostrar una evidencia experimental de la viabilidad de la t ecnica. En este trabajo se analiza desde un punto de vista te orico y experimental el uso de la informaci on polarim etrica de la señales GNSS reflejadas sobre el suelo para la determinaci on de humedad y biomasa de la vegetaci on. La Tesis se estructura en cuatro partes principales. En la primera parte se eval uan los aspectos fundamentales de la t ecnica y se da una revisi on detallada del estado del arte para la observaci on de humedad y vegetaci on. En la segunda parte se discuten los modelos de dispersi on electromagn etica sobre el suelo. Simulaciones con estos modelos fueron realizadas para analizar las componentes coherente e incoherente de la dispersi on de la señal reflejada sobre distintos tipos de terreno. Durante este trabajo se desarroll o un modelo de reflexi on simpli cado para poder relacionar de forma directa las observaciones con los par ametros geof sicos del suelo. La tercera parte describe las campañas experimentales realizadas durante este trabajo y discute el an alisis y la comparaci on de los datos GNSS-R con las mediciones in-situ. Como se predice por los modelos, se comprob o experimentalmente que la señal reflejada est a formada por una componente coherente y otra incoherente. Una t ecnica de an alisis de datos se propuso para la separacióon de estas dos contribuciones. Con los datos de las campañas experimentales se demonstr o el bene cio del uso de la informaci on polarim etrica en las señales GNSS reflejadas para la medici on de humedad del suelo, para la mayor a de las condiciones de rugosidad observadas. Tambi en se demostr o la capacidad de este tipo de observaciones para medir zonas boscosas densamente pobladas. La cuarta parte de la tesis analiza la capacidad de la t ecnica para observar cambios en la reflectividad del suelo desde un sat elite en orbita baja. Los resultados obtenidos muestran que la reflectividad del terreno podr a medirse con gran precisi on ya que la componente coherente del scattering ser a la predominante en ese tipo de escenarios. En este trabajo de doctorado se muestran la potencialidades de la t ecnica GNSS-R para observar remotamente par ametros del suelo tan importantes como la humedad del suelo y la biomasa de la vegetaci on. Este tipo de medidas pueden complementar un amplio rango de misiones de observaci on de la Tierra como SMOS, SMAP, y Biomass, esta ultima recientemente aprobada para la siguiente misi on Earth Explorer de la ESA

Limitations of experimental channel characterisation

KURZFASSUNG In dieser Dissertation wird die Experimentelle Kanalcharakterisierung und deren Grenzen in realenAusbreitungsumgebungen untersucht. Dies beinhaltet die Aufzeichnung der mehrdimensionalenbreitbandigen Kanalmatrix mit einem Multiple-Input Multiple-Output (MIMO) Channel-Sounderunter Verwendung von Antennenarrays auf der Sende- und Empfangsseite. Um den Funkkanalmit Hilfe der Parameter Sendewinkel (DoD), Empfangswinkel (DoA), Laufzeit (TDoA) und denkomplexen polarimetrischen Pfadgewichten zu charakterisieren, werden hochauflösende Parameterschätzverfahrenverwendet. Die Genauigkeit dieser Parameterschätzergebnisse in ”realen“ Messumgebungenwird durch eine Vielzahl von Fehlerquellen begrenzt. Diese Genauigkeitsgrenzen derParameterschätzung werden anhand zahlreicher Simulationen und Messungen analysiert. Fehlerquellenim gesamten Verarbeitungsablauf werden untersucht. Dazu gehören die Einschränkungendurch das Messsystem, systematische Fehler bei der Kalibrierung praktischer Antennenarrays sowieUnzulänglichkeiten des Funkkanalmodells des hochauflösenden Parameterschätzers. Darüber hinauswerden die Auswirkungen der Parametrierung bzw. Ableitung geometrisch basierter Kanalmodelleauf der Grundlage von Parameterschätzergebnissen mit begrenzter Genauigkeit aufgezeigt.Mit Messungen in typischen Ausbreitungsumgebungen kann der Funkkanal immer nur in Abhängigkeitder Messantennen beschrieben werden. Als Ziel wird jedoch eine antennenunabhängige Beschreibungdes Funkkanals angestrebt. Daher ist es notwendig, die Sende- und Empfangswinkel derspekularen Ausbreitungspfade mittels hochauflösender Parameterschätzverfahren zu bestimmen.Der gradientenbasierte Maximum Likelihood (ML) Parameterschätzer RIMAX, auf dem diese Arbeitaufbaut, verwendet ein Datenmodell, das den Funkkanal und das Messsystem inklusive derAntennenarrays beschreibt. Im Gegensatz zu anderen ML-Parameterschätzern wird ein Funkanalmodellangewendet, welches spekulare Reflektionen und verteilte diffuse Streuungen berücksichtigt.Für die Modellierung des Messsystems wird ein effizientes und exaktes Modell der gemessenenpolarimetrischen Richtcharakteristika benötigt. Das hier vorgeschlagene Modell, die so genannteEffective Aperture Distribution Function (EADF), beschreibt die Antennenrichtcharakteristikaanalytisch und basiert im Wesentlichen auf der zweidimensionalen (2D) Fouriertransformation derperiodischen Richtcharakteristika. Im Gegensatz zu anderen Verfahren können auf der Grundlageder EADF die Antennencharakteristika und ihre Ableitungen mit geringem Aufwand und hoherGenauigkeit berechnet werden. Für eine exakte Messung der Richtcharakteristika eines Antennenarrayswird ein vollpolarimetrisches 2D-Kalibrierverfahren vorgeschlagen. Mit diesem Verfahrenwird der komplette Messaufbau kalibriert. Dazu gehören der MIMO Channel-Sounder, die dualpolarisierte Referenzhornantenne und alle Hochfrequenzkomponenten außer dem zu untersuchendenAntennenarray. Im Zusammenhang mit der Arraykalibrierung wird ein gradientenbasierterML-Parameterschätzer entwickelt, mit dem eine bei der Kalibriermessung auftretende Phasenabweichungkorrigiert wird. DesWeiteren wird ein leistungsstarkes Verfahren zur Bewertung praktischer Antennenarrays auf derBasis der EADFs gemessener Richtcharakteristika vorgeschlagen. Die Cram´er-Rao-Schranken derWinkelparameter in Abhängigkeit des Signal-Rausch-Verhältnisses werden mit dem EADF-Modellanalytisch berechnet. Der Vorteil des EADF-Modells besteht darin, dass die Richtcharakteristikaeines realen Antennenarrays unter Einbeziehung aller störenden Einflussgrößen beschrieben werden.Das vorgeschlagene Bewertungsverfahren wird anhand von Messungen im Antennenmessraum verifiziert.Das Modell des Messsystems inklusive der Antennenarrays, welches für die Parameterschätzungverwendet wird, kann das reale System nur begrenzt beschreiben. Es wurden Schätzergebnisse vonzahlreichen Messungen analysiert. Hierbei musste festgestellt werden, dass Fehler bei der Modellierungzu teilweise unglaubwürdigen Schätzergebnissen führen. Genauer untersucht werden Fehlerin Bezug auf die Antennenarrays und das Messsystem. Erstere werden hervorgerufen durchsystematische Fehler bei der Arraykalibrierung und durch die Verwendung unvollständiger Datenmodelle(z.B. Nichtberücksichtigung der polarimetrischen Eigenschaften der Antennen). Letztereentstehen einerseits durch Phasenrauschen und andererseits durch ungeeignete Kalibrierung. Eswird nachgewiesen, dass die Verwendung ungenauer Modelle zur Schätzung von Artefakten führt.Diese Schätzfehler äußern sich in Abweichungen und/oder in einer künstlichen Aufspreizung derWinkelschätzungen der spekularen Anteile. Es werden geeignete Methoden vorgeschlagen, um dieAuswirkungen von Modellfehlern weitestgehend zu vermeiden bzw. zu korrigieren. Betont werdenmuss jedoch, dass einige Fehler unvermeidbar sind. Die Auswirkungen aller unvermeidbaren Fehler auf die Experimentelle Kanalcharakterisierung inkomplexen Ausbreitungsumgebungen werden im letzten Teil dieser Arbeit dargestellt. Es wird gezeigt,unter welchen Bedingungen die geschätzten spekularen Anteile sowie die geschätzten verteiltendiffusen Streuanteile glaubwürdig und physikalisch relevant sind. Die Untersuchungen basierenauf ”realistischen“ Simulationen des Funkkanals (Ray-Tracing) und auf Messungen. Diese Synthesegarantiert Glaubwürdigkeit und Aussagefähigkeit der in der Arbeit gewonnenen Ergebnisse.Die Resultate dieser Dissertation sind speziell für Wissenschaftler auf dem Gebiet der Parameterschätzungsowie Funkkanalmodellierung von Interesse und können wie folgt zusammengefasstwerden: • die Entwicklung eines Modells zur exakten und effizienten Beschreibung der Richtcharakteristikavon Antennenarrays,• ein Verfahren zur Bewertung praktischer Antennenarrays,• die Sensibilisierung für Modellfehler und deren Auswirkungen auf die Parameterschätzergebnisseund• die Bestimmung der Grenzen Experimenteller Kanalcharakterisierung unter Berücksichtigungaller unvermeidbarer Fehlerquellen