Uncertainty analysis is an important part of system design. The formula for error propagation through a system model that is most-often cited in literature is based on a first-order Taylor series. This formula makes several important assumptions and has several important limitations that are often ignored. This thesis explores these assumptions and addresses two of the major limitations. First, the results obtained from propagating error through nonlinear systems can be wrong by one or more orders of magnitude, due to the linearization inherent in a first-order Taylor series. This thesis presents a method for overcoming that inaccuracy that is capable of achieving fourth-order accuracy without significant additional computational cost. Second, system designers using a Taylor series to propagate error typically only propagate a mean and variance and ignore all higher-order statistics. Consequently, a Gaussian output distribution must be assumed, which often does not reflect reality. This thesis presents a proof that nonlinear systems do not produce Gaussian output distributions, even when inputs are Gaussian. A second-order Taylor series is then used to propagate both skewness and kurtosis through a system model. This allows the system designer to obtain a fully-described non-Gaussian output distribution. The benefits of having a fully-described output distribution are demonstrated using the examples of both a flat rolling metalworking process and the propeller component of a solar-powered unmanned aerial vehicle.

Historical topographic maps are valuable resources for studying past landscapes, but they are unsuitable for geospatial analysis. Cartographic map elements must be extracted and digitized for use in GIS. This can be accomplished by sophisticated image processing and pattern recognition techniques, and more recently, artificial intelligence. While these methods are generally effective, they require high levels of technical expertise. This study presents a straightforward method to digitally extract historical topographic map elements from within popular GIS software, using new and rapidly evolving toolsets. A convolutional neural network deep learning model was used to extract elevation contour lines from a 1940 United States Geological Survey (USGS) quadrangle in Sevier County, TN, ultimately producing a Digital Elevation Model (DEM). The topographically derived DEM (TOPO-DEM) is compared to a modern LiDAR-derived DEM to analyze its quality and utility. GIS-capable historians, archaeologists, geographers, and others can use this method in research and land management.

[pt] Colorimetria - Propagação de erros e cálculo da incerteza da medição nos resultados espectrofotométricos trata da medição da cor de objetos, baseada nas medições de irradiância espectral (objetos luminosos) ou de refletância ou transmitância espectral (objetos opacos ou transparentes), seguidas por cálculos colorimétricos conforme o sistema CIE. As medições são normalmente feitas em intervalos de 5nm (ou 10 nm) na faixa espectral de 360 a 780nm, e os três valores triestímulos (X, Y e Z) são calculados usando-se 42-84 pontos medidos por equações padrões. A distribuição dos valores medidos R(lambda) é, provavelmente, normal, com uma correlação entre os valores obtidos variável em posições diferentes do espectro. As distribuições dos valores e as correlações entre X, Y e Z são desconhecidas e dependem da forma da curva espectral da cor e do funcionamento dos instrumentos de medição. No controle instrumental das cores são usadas fórmulas muito complexas, baseadas nas transformações não lineares dos valores X, Y e Z em L*, a*, b*, C* e h°. A determinação da incerteza dos resultados dados em coordenadas CIELAB ou expressos em fórmulas de diferenças (delta)E*, (delta) ECMC ou CIE (delta) E2000 é fundamental no controle instrumental das cores em qualquer indústria. À base de um número elevado de medições repetidas de várias amostras têxteis e padrões cerâmicos, são analisadas a distribuição e outras características estatísticas dos valores R(lambda) diretamente medidos, e - usando o método de propagação de erros - são calculadas as incertezas das medições em termos colorimétricos. A pesquisa de mestrado objeto do presente trabalho desenvolve- se sob a égide de um convênio de cooperação que o Programa de Pós-Graduação em Metrologia da PUC-Rio está celebrando com o SENAI/CETIQT, viabilizado a inclusão dessa pesquisa dentre os dez projetos-piloto que participaram do Convênio FINEP/MCT número 22.01.0692.00, Referência 1974/01, que aportou recursos do Fundo Setorial Verde Amarelo para direcionar o esforço de pesquisa em metrologia para a solução de um problema de interesse do setor têxtil que fez uso de conhecimentos avançados de metrologia da cor. Relacionado à demanda de medições espectrofotométricas com elevado controle metrológico, o desenvolvimento e a orientação acadêmico-científica da presente dissertação de mestrado deu-se nas instalações do SENAI/CETIQT, que possui comprovada competência técnica e científica na área e uma adequada infra-estrutura laboratorial em metrologia da cor de suporte ao trabalho. / [en] Colorimetry - Propagation of Errors and Uncertainty Calculations in Spectrophotometric Measurements treats the measurement of the colour of objects, based on the measurement of spectral irradiance (self-luminous objects) or that of spectral reflectance or transmittance (opaque or transparent objects), followed by colorimetric calculations according to the CIE system. Measurements are generally made in 5nm (or 10 nm) intervals in the spectral range of 360 to 780nm, and the 3 tristimulus values (X, Y and Z) are calculated from the 42-84 measurement points by standard equations. The statistical distribution of the measured R (lambda) values is probably normal; the correlation between the values varies depending on their position in the spectrum. The distribution of and the correlation between the X, Y and Z values are not known and they depend on the form of the spectral curve of each colour and on the operation of the measuring instrument. Complex formulae are used in the instrumental control of colours based on non-linear transformations of the X, Y and Z values into L*a*b*C*h°. The determination of the uncertainty of the results given in CIELAB coordinates or expressed in one of the colour difference formulae (delta)E*, (delta)ECMC or CIE(delta) E2000 is fundamental in the instrumental control of colours in any industry. Based on a large number of repeated measurements of different textile samples and ceramic standards, the distribution and other statistical characteristics of the directly measured R(lambda) values are analysed and - using the propagation of errors method - the uncertainties are calculated in colorimetric terms. The present research, a M. Sc. Dissertation work, was developed under the auspices of a co-operation agreement celebrated between the Post-graduate Programme in Metrology of PUC-Rio and SENAI/CETIQT, allowing for the inclusion of this M.Sc. Dissertation among the ten pilot projects which benefited from the financial support received from the FINEP/MCT Agreement number 22.01.0692.00, Reference 1974/01 (Fundo Verde-Amarelo). The project aims at driving the research effort in metrology to the solution of industrial problems, in this case the solution of a problem identified within the textile sector which requires to its solution advanced knowledge of colour metrology. Related the spectrophotometer measurements under the highest level of metrological control, the development and academic-scientific supervision of this M. Sc. Dissertation was performed at the laboratory facility of SENAI/CETIQT, an institution with proven technical and scientific competence in the field having sophisticated and well equipped laboratories in colour metrology meeting the measurement requirements needed to support the development of this research.

Networks with hundreds of ad hoc nodes equipped with communication and position finding abilities are conceivable with recent advancements in technology. Methods are presented in this thesis to assess the communicative capabilities and node position estimation of mobile ad hoc networks. Specifically, we investigate techniques for providing communication and geolocation with specific characteristics in wireless ad hoc networks. The material presented in this thesis, communication and geolocation, may initially seem a collection of disconnected topics related only distantly under the banner of ad hoc networks. However, systems currently in development combining these techniques into single integrated systems. In this thesis first, we investigate the effect of multilayer interaction, including fading and path loss, on ad hoc routing protocol performance, and present a procedure for deploying an ad hoc network based on extensive simulations. Our first goal is to test the routing protocols with parameters that can be used to characterize the environment in which they might be deployed. Second, we analyze the location discovery problem in ad hoc networks and propose a fully distributed, infrastructure-free positioning algorithm that does not rely on the Global Positioning System (GPS). The algorithm uses the approximate distances between the nodes to build a relative coordinate system in which the node positions are computed in three-dimensions. However, in reconstructing three-dimensional positions from approximate distances, we need to consider error threshold, graph connectivity, and graph rigidity. We also statistically evaluate the location discovery procedure with respect to a number of parameters, such as error propagation and the relative positions of the nodes.

名古屋大学博士学位論文 学位の種類:博士(工学) 学位授与年月日:平成19年9月28日

Este trabalho apresenta uma solução geral para a detecção de alinhamentos de dados em conjuntos multidimensionais não ordenados e ruidosos. Nesta abordagem, o tipo requerido de alinhamento de dados pode ser uma forma geométrica (e.g., linha reta, plano, círculo, esfera, seção cônica, entre outras) ou qualquer estrutura, com dimensionalidade arbitrária, que possa ser caracterizada por um subespaço linear. A detecção é realizada por meio de um procedimento composto por três etapas. Na etapa de inicialização, um espaço de parâmetros com p (n − p) dimensões é definido de modo que cada ponto neste espaço represente uma instância do alinhamento requerido, descrito por um subespaço p-dimensional em um domínio n-dimensional. Em seguida, uma grade de acumuladores é criada como sendo a representação discreta do espaço de parâmetros. Na segunda etapa do procedimento, cada elemento no conjunto de dados de entrada (também um subespaço no domínio n-dimensional) é mapeado para o espaço de parâmetros como os pontos (no espaço de parâmetros) representando os subespaços requeridos que contém ou que estão contidos no elemento de entrada. À medida que os elementos de entrada são mapeados, as células do acumulador relacionadas com o mapeamento são incrementadas pelo valor de importância do elemento mapeado. A etapa final do procedimento recupera os subespaços p-dimensionais que melhor se ajustam aos dados de entrada como sendo os máximos locais na grade de acumuladores. A parametrização proposta é independente das propriedades geométricas dos alinhamentos a serem detectados. Além disso, o procedimento de mapeamento é independente do tipo de dado de entrada e é capaz de se adaptar a elementos com dimensionalidades arbitrárias. Essas características permitem a utilização da técnica (sem a necessidade de modificações) como uma ferramenta para a detecção de padrões em uma grande quantidade de aplicações. Por conta de sua natureza geral, otimizações desenvolvidas para a abordagem proposta beneficiam, de forma imediata, todos os casos de detecção. Neste trabalho eu demonstro uma implementação em software da técnica proposta e mostro que ela pode ser aplicada tanto em casos simples de detecção, quanto na detecção concorrente de tipos diferentes de alinhamentos, com diferentes interpretações geométricas e em conjuntos de dados compostos por vários tipos de elementos. Esta dissertação também apresenta uma extensão do esquema de detecção para dados de entrada com distribuição Gaussiana de incerteza. A extensão proposta produz distribuições de valores mais suaves na grade de acumuladores e faz com que a técnica fique mais robusta à detecção de subespaços espúrios. / This dissertation presents a generalized closed-form framework for detecting data alignments in large unordered noisy multidimensional datasets. In this approach, the intended type of data alignment may be a geometric shape (e.g., straight line, plane, circle, sphere, conic section, among others) or any other structure, with arbitrary dimensionality that can be characterized by a linear subspace. The detection is performed using a three-step process. In the initialization, a p (n − p)-dimensional parameter space is defined in such a way that each point in this space represents an instance of the intended alignment described by a p-dimensional subspace in some n-dimensional domain. In turn, an accumulator array is created as the discrete representation of the parameter space. In the second step each input entry (also a subspace in the n-dimensional domain) is mapped to the parameter space as the set of points representing the intended p-dimensional subspaces that contain or are contained by the entry. As the input entries are mapped, the bins of the accumulator related to such a mapping are incremented by the importance value of the entry. The subsequent and final step retrieves the p-dimensional subspaces that best fit input data as the local maxima in the accumulator array. The proposed parameterization is independent of the geometric properties of the alignments to be detected. Also, the mapping procedure is independent of the type of input data and automatically adapts to entries of arbitrary dimensionality. This allows application of the proposed approach (without changes) in a broad range of applications as a pattern detection tool. Given its general nature, optimizations developed for the proposed framework immediately benefit all the detection cases. I demonstrate a software implementation of the proposed technique and show that it can be applied in simple detection cases as well as in concurrent detection of multiple kinds of alignments with different geometric interpretations, in datasets containing multiple types of data. This dissertation also presents an extension of the general detection scheme to data with Gaussian-distributed uncertainty. The proposed extension produces smoother distributions of values in the accumulator array and makes the framework more robust to the detection of spurious subspaces.

Este trabalho apresenta uma solução geral para a detecção de alinhamentos de dados em conjuntos multidimensionais não ordenados e ruidosos. Nesta abordagem, o tipo requerido de alinhamento de dados pode ser uma forma geométrica (e.g., linha reta, plano, círculo, esfera, seção cônica, entre outras) ou qualquer estrutura, com dimensionalidade arbitrária, que possa ser caracterizada por um subespaço linear. A detecção é realizada por meio de um procedimento composto por três etapas. Na etapa de inicialização, um espaço de parâmetros com p (n − p) dimensões é definido de modo que cada ponto neste espaço represente uma instância do alinhamento requerido, descrito por um subespaço p-dimensional em um domínio n-dimensional. Em seguida, uma grade de acumuladores é criada como sendo a representação discreta do espaço de parâmetros. Na segunda etapa do procedimento, cada elemento no conjunto de dados de entrada (também um subespaço no domínio n-dimensional) é mapeado para o espaço de parâmetros como os pontos (no espaço de parâmetros) representando os subespaços requeridos que contém ou que estão contidos no elemento de entrada. À medida que os elementos de entrada são mapeados, as células do acumulador relacionadas com o mapeamento são incrementadas pelo valor de importância do elemento mapeado. A etapa final do procedimento recupera os subespaços p-dimensionais que melhor se ajustam aos dados de entrada como sendo os máximos locais na grade de acumuladores. A parametrização proposta é independente das propriedades geométricas dos alinhamentos a serem detectados. Além disso, o procedimento de mapeamento é independente do tipo de dado de entrada e é capaz de se adaptar a elementos com dimensionalidades arbitrárias. Essas características permitem a utilização da técnica (sem a necessidade de modificações) como uma ferramenta para a detecção de padrões em uma grande quantidade de aplicações. Por conta de sua natureza geral, otimizações desenvolvidas para a abordagem proposta beneficiam, de forma imediata, todos os casos de detecção. Neste trabalho eu demonstro uma implementação em software da técnica proposta e mostro que ela pode ser aplicada tanto em casos simples de detecção, quanto na detecção concorrente de tipos diferentes de alinhamentos, com diferentes interpretações geométricas e em conjuntos de dados compostos por vários tipos de elementos. Esta dissertação também apresenta uma extensão do esquema de detecção para dados de entrada com distribuição Gaussiana de incerteza. A extensão proposta produz distribuições de valores mais suaves na grade de acumuladores e faz com que a técnica fique mais robusta à detecção de subespaços espúrios. / This dissertation presents a generalized closed-form framework for detecting data alignments in large unordered noisy multidimensional datasets. In this approach, the intended type of data alignment may be a geometric shape (e.g., straight line, plane, circle, sphere, conic section, among others) or any other structure, with arbitrary dimensionality that can be characterized by a linear subspace. The detection is performed using a three-step process. In the initialization, a p (n − p)-dimensional parameter space is defined in such a way that each point in this space represents an instance of the intended alignment described by a p-dimensional subspace in some n-dimensional domain. In turn, an accumulator array is created as the discrete representation of the parameter space. In the second step each input entry (also a subspace in the n-dimensional domain) is mapped to the parameter space as the set of points representing the intended p-dimensional subspaces that contain or are contained by the entry. As the input entries are mapped, the bins of the accumulator related to such a mapping are incremented by the importance value of the entry. The subsequent and final step retrieves the p-dimensional subspaces that best fit input data as the local maxima in the accumulator array. The proposed parameterization is independent of the geometric properties of the alignments to be detected. Also, the mapping procedure is independent of the type of input data and automatically adapts to entries of arbitrary dimensionality. This allows application of the proposed approach (without changes) in a broad range of applications as a pattern detection tool. Given its general nature, optimizations developed for the proposed framework immediately benefit all the detection cases. I demonstrate a software implementation of the proposed technique and show that it can be applied in simple detection cases as well as in concurrent detection of multiple kinds of alignments with different geometric interpretations, in datasets containing multiple types of data. This dissertation also presents an extension of the general detection scheme to data with Gaussian-distributed uncertainty. The proposed extension produces smoother distributions of values in the accumulator array and makes the framework more robust to the detection of spurious subspaces.

Este trabalho apresenta uma solução geral para a detecção de alinhamentos de dados em conjuntos multidimensionais não ordenados e ruidosos. Nesta abordagem, o tipo requerido de alinhamento de dados pode ser uma forma geométrica (e.g., linha reta, plano, círculo, esfera, seção cônica, entre outras) ou qualquer estrutura, com dimensionalidade arbitrária, que possa ser caracterizada por um subespaço linear. A detecção é realizada por meio de um procedimento composto por três etapas. Na etapa de inicialização, um espaço de parâmetros com p (n − p) dimensões é definido de modo que cada ponto neste espaço represente uma instância do alinhamento requerido, descrito por um subespaço p-dimensional em um domínio n-dimensional. Em seguida, uma grade de acumuladores é criada como sendo a representação discreta do espaço de parâmetros. Na segunda etapa do procedimento, cada elemento no conjunto de dados de entrada (também um subespaço no domínio n-dimensional) é mapeado para o espaço de parâmetros como os pontos (no espaço de parâmetros) representando os subespaços requeridos que contém ou que estão contidos no elemento de entrada. À medida que os elementos de entrada são mapeados, as células do acumulador relacionadas com o mapeamento são incrementadas pelo valor de importância do elemento mapeado. A etapa final do procedimento recupera os subespaços p-dimensionais que melhor se ajustam aos dados de entrada como sendo os máximos locais na grade de acumuladores. A parametrização proposta é independente das propriedades geométricas dos alinhamentos a serem detectados. Além disso, o procedimento de mapeamento é independente do tipo de dado de entrada e é capaz de se adaptar a elementos com dimensionalidades arbitrárias. Essas características permitem a utilização da técnica (sem a necessidade de modificações) como uma ferramenta para a detecção de padrões em uma grande quantidade de aplicações. Por conta de sua natureza geral, otimizações desenvolvidas para a abordagem proposta beneficiam, de forma imediata, todos os casos de detecção. Neste trabalho eu demonstro uma implementação em software da técnica proposta e mostro que ela pode ser aplicada tanto em casos simples de detecção, quanto na detecção concorrente de tipos diferentes de alinhamentos, com diferentes interpretações geométricas e em conjuntos de dados compostos por vários tipos de elementos. Esta dissertação também apresenta uma extensão do esquema de detecção para dados de entrada com distribuição Gaussiana de incerteza. A extensão proposta produz distribuições de valores mais suaves na grade de acumuladores e faz com que a técnica fique mais robusta à detecção de subespaços espúrios. / This dissertation presents a generalized closed-form framework for detecting data alignments in large unordered noisy multidimensional datasets. In this approach, the intended type of data alignment may be a geometric shape (e.g., straight line, plane, circle, sphere, conic section, among others) or any other structure, with arbitrary dimensionality that can be characterized by a linear subspace. The detection is performed using a three-step process. In the initialization, a p (n − p)-dimensional parameter space is defined in such a way that each point in this space represents an instance of the intended alignment described by a p-dimensional subspace in some n-dimensional domain. In turn, an accumulator array is created as the discrete representation of the parameter space. In the second step each input entry (also a subspace in the n-dimensional domain) is mapped to the parameter space as the set of points representing the intended p-dimensional subspaces that contain or are contained by the entry. As the input entries are mapped, the bins of the accumulator related to such a mapping are incremented by the importance value of the entry. The subsequent and final step retrieves the p-dimensional subspaces that best fit input data as the local maxima in the accumulator array. The proposed parameterization is independent of the geometric properties of the alignments to be detected. Also, the mapping procedure is independent of the type of input data and automatically adapts to entries of arbitrary dimensionality. This allows application of the proposed approach (without changes) in a broad range of applications as a pattern detection tool. Given its general nature, optimizations developed for the proposed framework immediately benefit all the detection cases. I demonstrate a software implementation of the proposed technique and show that it can be applied in simple detection cases as well as in concurrent detection of multiple kinds of alignments with different geometric interpretations, in datasets containing multiple types of data. This dissertation also presents an extension of the general detection scheme to data with Gaussian-distributed uncertainty. The proposed extension produces smoother distributions of values in the accumulator array and makes the framework more robust to the detection of spurious subspaces.

Optical testing in adverse environments, ophthalmology and applications where characterization by curvature is leveraged all have a common goal: accurately estimate wavefront shape. This dissertation investigates wavefront sensing techniques as applied to optical testing based on gradient and curvature measurements. Wavefront sensing involves the ability to accurately estimate shape over any aperture geometry, which requires establishing a sampling grid and estimation scheme, quantifying estimation errors caused by measurement noise propagation, and designing an instrument with sufficient accuracy and sensitivity for the application. Starting with gradient-based wavefront sensing, a zonal least-squares wavefront estimation algorithm for any irregular pupil shape and size is presented, for which the normal matrix equation sets share a pre-defined matrix. A Gerchberg–Saxton iterative method is employed to reduce the deviation errors in the estimated wavefront caused by the pre-defined matrix across discontinuous boundary. The results show that the RMS deviation error of the estimated wavefront from the original wavefront can be less than λ/130~ λ/150 (for λ equals 632.8nm) after about twelve iterations and less than λ/100 after as few as four iterations. The presented approach to handling irregular pupil shapes applies equally well to wavefront estimation from curvature data. A defining characteristic for a wavefront estimation algorithm is its error propagation behavior. The error propagation coefficient can be formulated as a function of the eigenvalues of the wavefront estimation-related matrices, and such functions are established for each of the basic estimation geometries (i.e. Fried, Hudgin and Southwell) with a serial numbering scheme, where a square sampling grid array is sequentially indexed row by row. The results show that with the wavefront piston-value fixed, the odd-number grid sizes yield lower error propagation than the even-number grid sizes for all geometries. The Fried geometry either allows sub-sized wavefront estimations within the testing domain or yields a two-rank deficient estimation matrix over the full aperture; but the latter usually suffers from high error propagation and the waffle mode problem. Hudgin geometry offers an error propagator between those of the Southwell and the Fried geometries. For both wavefront gradient-based and wavefront difference-based estimations, the Southwell geometry is shown to offer the lowest error propagation with the minimum-norm least-squares solution. Noll’s theoretical result, which was extensively used as a reference in the previous literature for error propagation estimate, corresponds to the Southwell geometry with an odd-number grid size. For curvature-based wavefront sensing, a concept for a differential Shack-Hartmann (DSH) curvature sensor is proposed. This curvature sensor is derived from the basic Shack-Hartmann sensor with the collimated beam split into three output channels, along each of which a lenslet array is located. Three Hartmann grid arrays are generated by three lenslet arrays. Two of the lenslets shear in two perpendicular directions relative to the third one. By quantitatively comparing the Shack-Hartmann grid coordinates of the three channels, the differentials of the wavefront slope at each Shack-Hartmann grid point can be obtained, so the Laplacian curvatures and twist terms will be available. The acquisition of the twist terms using a Hartmann-based sensor allows us to uniquely determine the principal curvatures and directions more accurately than prior methods. Measurement of local curvatures as opposed to slopes is unique because curvature is intrinsic to the wavefront under test, and it is an absolute as opposed to a relative measurement. A zonal least-squares-based wavefront estimation algorithm was developed to estimate the wavefront shape from the Laplacian curvature data, and validated. An implementation of the DSH curvature sensor is proposed and an experimental system for this implementation was initiated. The DSH curvature sensor shares the important features of both the Shack-Hartmann slope sensor and Roddier’s curvature sensor. It is a two-dimensional parallel curvature sensor. Because it is a curvature sensor, it provides absolute measurements which are thus insensitive to vibrations, tip/tilts, and whole body movements. Because it is a two-dimensional sensor, it does not suffer from other sources of errors, such as scanning noise. Combined with sufficient sampling and a zonal wavefront estimation algorithm, both low and mid frequencies of the wavefront may be recovered. Notice that the DSH curvature sensor operates at the pupil of the system under test, therefore the difficulty associated with operation close to the caustic zone is avoided. Finally, the DSH-curvature-sensor-based wavefront estimation does not suffer from the 2π-ambiguity problem, so potentially both small and large aberrations may be measured.

Die vorliegende Arbeit beschreibt ein generisches Verfahren zur wahrscheinlichkeitsbasierten Erkennung von Fahrsituationen und Fahrmanövern für sicherheitsrelevante Fahrerassistenzsysteme. Fahrsituationen und Manöver unterliegen einer gewissen Unsicherheit basierend auf der unterschiedlichen Situationswahrnehmung bzw. Manöverdurchführung der Fahrzeugführer. Diese Unsicherheitskomponente wird in den Ansatz zur Situations- und Manövererkennung mit einbezogen. Ein weiterer Unsicherheitsaspekt beruht auf den ungenauen Umgebungsinformationen auf denen die Situations- und Manövererkennung basiert. Beide Unsicherheitsursachen sind völlig unabhängig voneinander und werden aus diesem Grund separat betrachtet und modelliert. Zur Modellierung dieser beiden Unsicherheitsaspekte bedient sich der vorgestellte Ansatz der Fuzzy-Theorie, der Theorie der probabilistischen Netzen sowie Verfahren zur Fehlerfortpflanzung und Sensitivitätsanalyse. Nach der theoretischen Vorstellung dieser Methodiken wird in der Arbeit detailliert auf den Einsatz und das Zusammenspiel der einzelnen Verfahren zur Erkennung der Fahrsituationen und Fahrmanöver eingegangen. Die Umsetzbarkeit des vorgestellten Verfahrens wird am Beispiel der Notbremssituation gezeigt. Die Notbremssituation setzt sich aus unterschiedlichen Teilsituationen und Manövern zusammen. Die Erkennung der einzelnen Situationen und Manöver sowie die Zusammenführung zur übergeordneten Notbremssituation wurden mit Hilfe des vorgestellten Verfahrens realisiert. Zur Evaluierung der Erkennungsgüte wurden sowohl Messdaten aus dem Straßenverkehr als auch realitätsnahe Daten, aufgezeichnet auf Versuchsstrecken, herangezogen. / The present work describes a generic method for the probabilistic identification of driving situations and driving manoeuvres for safety relevant driver assistance systems. Driving situations and driving manoeuvres underlie a certain uncertainty based on the different situation perception and manoeuvre execution of the driver. This uncertainty component is considered in the approach for the situation and manoeuvre identification. An additional uncertainty aspect is based on the inaccurate environment information, the identification of driving situations and manoeuvres depend on. Both uncertainty aspects are completely independent and are considered and modelled separately for this reason. For modelling both of these uncertainty aspects the present approach is using the fuzzy theory, probabilistic networks, as well as methods for error propagation and sensitivity analysis. After introducing these techniques theoretically, the application and the interaction of the single methods to identify the driving situations and manoeuvres is described in detail. The practicability of the introduced proceeding is shown exemplarily on the emergency brake situation. The emergency brake situation consists of several situation and manoeuvre components. The identification of the single situations and manoeuvres as well as the combination to the higher emergency brake situation is realised with the introduced proceeding. Measuring data gathered on road traffic and close to reality data measured on a test track were used to evaluate the identification quality.