Stuttgart, Univ., Diss., 2007.

University, Diss., 2004--Bremen. / Erscheinungsjahr an der Haupttitelstelle: 2003.

We introduce Simultaneous Localization and Tracking (SLAT), the problem of tracking a target in a sensor network while simultaneously localizing and calibrating the nodes of the network. Our proposed solution, LaSLAT, is a Bayesian filter providing on-line probabilistic estimates of sensor locations and target tracks. It does not require globally accessible beacon signals or accurate ranging between the nodes. When applied to a network of 27 sensor nodes, our algorithm can localize the nodes to within one or two centimeters.

Σε αυτήν την διπλωματική εργασία ασχολούμαστε με το φίλτρο Kalman σε ανομοιόμορφη δειγματοληψία. Τα προαναφερθέντα αντικείμενα της εργασίας είτε χρησιμοποιούνται ξεχωριστά το ένα από το άλλο είτε εάν συνδυάζονται αποτελούν πάρα πολύ σημαντικά εργαλεία για κάθε επιστήμη και τεχνολογία. Το φίλτρο Kalman χρησιμοποιείται με μεγάλη επιτυχία για εκτίμηση και ανάλυση δυναμικών συστημάτων. Οι εφαρμογές του καλύπτουν πολλά πεδία όπως την μηχανική, την επιστήμη των υλικών, τα οικονομικά, ακόμα και την ιατρική. Από την άλλη, η χρήση της ανομοιόμορφης δειγματοληψίας, δηλαδή η δειγματοληψία σημάτων σε ανομοιόμορφα χρονικά διαστήματα αυξάνει συνεχώς και διαθέτει πάρα πολλά πλεονεκτήματα. Σκοπός της διπλωματικής είναι η μελέτη και η ανάλυση αυτών των δύο στοιχείων και η εξαγωγή συμπερασμάτων όσον αφορά τον καλύτερο δυνατό αλγόριθμο επεξεργασίας σήματος. Έτσι στο 1ο Κεφάλαιο ασχολούμαστε με την γενικότερη έννοια της δειγματοληψίας, αλλά αναλύουμε και την ανομοιόμορφη. Στο 2ο Κεφάλαιο κάνουμε μια αρχική εισαγωγή για το πώς συνεργάζονται τα φίλτρα με την δειγματοληψία. Έπειτα, στο 3ο Κεφάλαιο αναφέρουμε λεπτομερειακά τις θεωρητικές και υπολογιστικές έννοιες γύρω από το φίλτρο Kalman. Το 4ο Κεφάλαιο περιλαμβάνει την υλοποίηση αλγορίθμων φίλτρου Kalman με ομοιόμορφη και ανομοιόμορφη δειγματοληψία. Στη συνέχεια, στο 5ο Κεφάλαιο παραθέτουμε την σύγκριση των αλγορίθμων και το συμπέρασμα για το οποιός είναι ο αποτελεσματικότερος και αναφέρουμε κάποιες εφαρμογές. Τέλος, το 6ο Κεφάλαιο εμφανίζεται το παράρτημα των κωδίκων που χρησιμοποιήθηκαν και στο 7ο Κεφάλαιο παραθέτουμε τις πηγές που αναλύσαμε. / In this thesis we deal with the Kalman filter to irregular sampling. The above subjects of the essay either they are used separately from one another or they are combined, they are very important tools for any science and technology. The Kalman filter is used with great success for observing and analyzing each dynamic system. Its applications cover several fields such as engineering, materials science, economics, and even medicine. On the other hand, the use of non-uniform sampling, which is the procedure of sampling some signals at uneven intervals, is growing continuously and has many advantages. The aim of this essay is the study and analysis of both subjects and the export of conclusions about the best possible signal processing algorithm. So in the first chapter we deal with the general concept of sampling, but we analyze the irregular too. In the second chapter we make an initial introduction to how the filters cooperate with the sampling. Then, in the third chapter we report in detail the theoretical and computational concepts around the filter Kalman. The fourth chapter includes the implementation of Kalman filter algorithms with uniform and non-uniform sampling. Then, in Chapter 5 we present a comparison of algorithms and the conclusion on which is the most effective and we mention some applications. Finally, in the 6th chapter the Appendix of the codes is appeared and in the seventh chapter we cited the bibliograpfy we have analyzed.

O eletrocardiograma transMITe informações com relação à passagem do pulso elétrico pelo coração e, conseqüentemente, do funcionamento deste. Desde o início da sua utilização, possibilitada pelo trabalho de Willem Einthoven criando a primeira máquina capaz de medir o pulso elétrico de forma não invasiva e com sensibilidade forte o bastante para ser capaz de produzir um gráfico proveitoso, o eletrocardiograma é muito utilizado para avaliação clínica de pacientes. Entretanto a evolução das máquinas que o descrevem não foi muito além do que o elaborado por Einthoven no início do século 20. As máquinas capazes de captar o eletrocardiograma se tornaram menores (até portáteis para algumas aplicações), gráficos passaram a ser disponibilizados em telas de vídeo (ao invés das fitas de papel) e, como maior evolução, as máquinas que observam o eletrocardiograma passaram a conseguir captar a ocorrência de um ciclo cardíaco com alta confiabilidade e, atualmente, passaram a medir também o parâmetro ST com precisão deliMITada (necessitando ajuda do operador para ajuste em alguns casos). É baseado nestes fatos que esta dissertação procura estudar algoritmos matemáticos, de forma mais focada nos modelos do impulso elétrico durante os ciclos cardíacos, e avaliar suas capacidades de interpretar parâmetros do ciclo de ECG de forma precisa e rápida para que o médico tenha prontamente os dados necessários para realizar a avaliação clínica do paciente. Em primeira análise foram estudados os algoritmos para detecção do pulso de eletrocardiograma (detecção da onda R), em seguida feito o janelamento da curva de ECG a fim de separar os ciclos cardíacos. A partir deste ponto foram analisados os modelos matemáticos gerados por equações polinomiais, Transformada de Fourier e Transformada wavelet. E, com o intuito de filtrar ruídos e gerar derivações não medidas, foi implementado um filtro de kalman em um modelo vetorial do eletrocardiograma. Para avaliar os resultados obtidos foram utilizados requisitos de desempenho declarados pelo FDA norte americano e pela norma européia IEC60601-2-51. Essas análises foram feitas através da utilização dos algoritmos gerados nas curvas provindas do banco de dados do PhisioNet. O método polinomial não foi considerado interessante na medida em que não possibilita gerar uma equação para um ciclo cardíaco, mas sim várias equações (uma para cada ponto do ciclo). Os demais métodos apresentaram melhor eficiência na medida em que foram capazes de gerar parâmetros com significado físico e possibilitando melhor caracterização de pontos importantes da curva do eletrocardiograma. / The electrocardiogram gives information related to the passage of an electric pulse through the heart and, therefore, to his state function. Since the beginning of electrocardiogram utilization, thanks to the work of Willem Einthoven building the first machine capable of measuring the electric pulse non-invasively and with sensitivity enough to be able to provide a profitable graph, it is widely used for clinical evaluation of patients. However the evolution of the machines that describes the electrocardiogram hadn´t much more advances since the elaborated by Einthoven in the beginning of the 20th century. They become smaller (even portable for some applications), the graphs are now displayed in video screens (instead of the paper strip) and, taking place as the biggest evolutions, machines that observes the electrocardiogram became able to recognize a cardiac cycle with high reliability and, more recently, became able to measure the ST parameter with liMITed precision (it needs the help of the operator to set specific measuring points in some cases). It is based in these facts that this dissertation looks for analyzing mathematic algorithms, more specifically the mathematic models of the electric impulse during the cardiac cycles, and evaluate their capacities to expound ECG parameters in a fast and reliable way in order to the physician receive promptly the data needed for his clinical evaluation of the patient. For the first step were analyzed some algorithms for electrocardiogram pulse detection (detection of R wave), in the following step were done the windowing of the ECG wave in order to separate the cardiac cycles. In this step were analyzed the mathematic models generated by polynomial equations, Fourier Transform and Wavelet Transform. And, in order to filter noises and generate leads not measure, it was implemented a kalman´s filter at a vector model. To evaluate the obtained results were used the requirements of performance given by north-american FDA and by the European rule IEC60601-2-51. These evaluations were done by executing the generated algorithms in the waves supplied by the databank PhisioNet. The polynomial method weren´t considered interesting because it weren´t able to generate an equation for the cardiac cycle, but many equations (one for each point of the cycle). The other methods showed a better efficiency since they were capable of generate parameters with physical meaning and being able to do a better characterization of the important points of the electrocardiogram wave.

O filtro de Kalman estendido tem sido a mais popular ferramenta de filtragem não linear das últimas quatro décadas. É de fácil implementação e apresenta baixo custo computacional. Nos casos nos quais as não linearidades do sistema dinâmico são significativas, porém, o filtro de Kalman estendido pode apresentar resultados insatisfatórios. Nessas situações, o filtro de Kalman unscented substitui com vantagens o filtro de Kalman estendido, pois pode apresentar melhores estimativas de estado, embora ambos os filtros exibam complexidade computacional de mesma ordem. A qualidade das estimativas de estado do filtro unscented está intimamente ligada à sintonia dos parâmetros que controlam a transformada unscented. A versão escalada dessa transformada exibe três parâmetros escalares que determinam o posicionamento dos pontos sigma e, consequentemente, afetam diretamente a qualidade das estimativas produzidas pelo filtro. Apesar da importância do filtro de Kalman unscented, a sintonia ótima desses parâmetros é um problema para o qual ainda não há solução definitiva. Não há nem mesmo recomendações heurísticas que garantam o bom funcionamento do filtro unscented na maior parte dos problemas tratáveis por meio de filtros Gaussianos. Essa carência e a importância desse filtro para a área de filtragem não linear fazem da busca por mecanismos de sintonia automática do filtro unscented área de pesquisa ativa. Assim, este trabalho propõe técnicas para sintonia automática dos parâmetros da transformada unscented escalada. Além da sintonia desses parâmetros, também é abordado o problema de sintonizar as matrizes de covariância dos ruídos de processo e de medida demandadas pelo modelo do sistema dinâmico usado pelo filtro unscented. As técnicas propostas cobrem então a sintonia automática de todos os parâmetros do filtro. / The extended Kalman filter has been the most popular nonlinear filter of the last four decades. It is easy to implement and exhibits low computational cost. When nonlinearities are significant, though, the extended Kalman filter can display poor state estimation performance. In such situations, the unscented Kalman filter can yield better state estimates, while displaying the same order of computational complexity as the extended Kalman filter. The quality of the state estimates produced by the unscented Kalman filter is directly influenced by the tuning of the scalar parameters that govern the unscented transform. The scaled version of the unscented transform features three scalar parameters that determine the positioning of the sigma points, thus directly affecting the filter state estimation performance. Despite the importance of the unscented Kalman filter, the optimal tuning of the scaled unscented transform parameters is still an open problem. This work hence discusses algorithms for the automatic tuning of the unscented transform parameters. The discussion includes the tuning of the needed noise covariance matrices, thus covering the automatic tuning of all parameters of the unscented Kalman filter.

Este trabalho apresenta um sistema de rastreamento de obstáculos, utilizando sensor laser 2D e filtro de Kalman. Este filtro não é muito eficiente em situações em que ocorrem severas perturbações na posição medida do obstáculo, como, por exemplo, um objeto rastreado passando por trás de uma barreira, interrompendo o feixe de laser por alguns instantes, tornando impossível receber do sensor as informações sobre sua posição. Este trabalho sugere um método de minimizar esse problema com o uso de um algoritmo denominado Corretor de Discrepâncias. / An obstacle detection and tracking system using a 2D laser sensor and the Kalman filter is presented. This filter is not very efficient in case of severe disturbances in the measured position of the obstacle, as for instance, when an object being tracked is behind a barrier, thus interrupting the laser beam, making it impossible to receive the sensor information about its position. This work suggests a method to minimize this problem by using an algorithm called Corrector of Discrepancies.

[pt] Este trabalho examina uma nova estratégia para detenção de Sinais TCM em presença de desvanecimento não-seletivo em freqüência. Esta estratégia faz uso de um conjunto de estimativas da distorção do canal, cada uma associada a um estado da treliça de decodificação, que são utilizadas simultaneamente no processo de decodificação. No método proposto, a cada intervalo de símbolo calcula-se uma estimativa de canal para cada percurso sobrevivente, usando os sinais associados a este percurso como decisões dos sinais transmitidos até então, juntamente com um algoritmo do tipo Filtro de Kalman. O método é descrito inicialmente para uso em sistemas sem intercalação- desintercalação. Uma versão modificada é proposta para permitir o uso da nova estratégia em associação com esquemas de intercalação-desintercalação. Resultados de desempenho obtidos, via simulação, com os métodos propostos são comparados com os resultados obtidos supondo- se o conhecimento ideal das distorções introduzidas pelo canal bem como os resultados apresentados na literatura, referentes a outros métodos de deteção. / [en] We look into a new strategy for detecting trellis-code modulated signal in the presence of frequency non- selective fading which makes simultaneous use in the decoding procedure of a set of channel distortion estimates, each one associated to a trellis state. During each symbol interval, based on a Kalman Filter-type algorithm, a distinct channel estimate is recursively generated for each survivor path using this path symbols as the truly transmitted symbols. A method is first proposed for use in non-interleaved systems. A modified version for interleaved systems. A modified version for interleaved systens is then presented. Performances are evaluated by computer simulations and comparisons mede to curves pertaining to other methods in the literature and to curves obteined under ideal channel state information assumption.

Bridge load rating is a procedure to determine the live load carrying capacity of a bridge. This rating is generally given out on a two-year period, which leaves the structural capacity unknown for this time interval. Conventional bridge load rating is obtained according to the bridge inspection results and commercial bridge rating software. However, this approach cannot effectively reflect actual live load carrying performance of the bridge, due to intrinsic limitation of visual inspection. Structural sensing has been utilized for measuring realistic structural behaviors to reflect the live load carrying capacity. However, this expensive and time-consuming process requires a known-weight vehicle and a substantial number of sensors under controlled full-scale field test conditions. In this research, a continuous live load performance index (LLPI) is proposed to monitor the live load capacity that the bridge can withstand without knowing the vehicle weight while also using a limited number of sensors. The LLPI uses existing bridge load rating methodology, in conjunction with experimental data and numerical simulations, to generate a value that describes the performance of the bridge due directly to the live load applied. Furthermore, the LLPI procedure utilizes an advanced state estimation algorithm, known as the Kalman Filter, to estimate the strain responses of the bridge at various locations while using a limited number of sensors. This procedure allows for an efficient structural health monitoring approach to determine the live load carrying capacity that the bridge can withstand. This research uses a lab-scaled truss structure with known properties for numerical and experimental validation. Because of this, this paper proposes a framework as to which the live load carrying performance can be monitored in real time. Future updates include testing on a real-life bridge structure while also determining optimal sensor placement for obtaining the LLPI. This research looks to develop a new live load performance index (LPPI) by considering: (1) the benefits and limitations of conventional bridge load rating approach, (2) the system identification and multi-metric data acquisition for the bridge structure, (3) numerical modeling and updating to best reflect the current dynamic properties of the bridge, (4) augmented Kalman Filter to estimate structural responses at various unknown locations, (5) LLPI formulation using experimental data, current bridge load rating methodology, and model-response estimations. The results obtained from this research provide a progressive live load capacity performance template to promote the advancement in civil infrastructure smart monitoring.

This thesis is about a robust filtering method known as the interval Kalman filter (IKF), an extension of the Kalman filter (KF) to the domain of interval mathematics. The key limitation of the KF is that it requires precise knowledge of the system dynamics and associated stochastic processes. In many cases however, system models are at best, only approximately known. To overcome this limitation, the idea is to describe the uncertain model coefficients in terms of bounded intervals, and operate the filter within the framework of interval arithmetic. In trying to do so, practical difficulties arise, such as the large overestimation of the resulting set estimates owing to the over conservatism of interval arithmetic. This thesis proposes and demonstrates a novel and effective way to limit such overestimation for the IKF, making it feasible and practical to implement. The theory developed is of general application, but is applied in this work to the heading estimation of the Springer unmanned surface vehicle, which up to now relied solely on the estimates from a traditional KF. However, the IKF itself simply provides the range of possible vehicle headings. In practice, the autonomous steering system requires a single, point-valued estimate of the heading. In order to address this requirement, an innovative approach based on the use of machine learning methods to select an adequate point-valued estimate has been developed. In doing so, the so called weighted IKF (wIKF) estimate provides a single heading estimate that is robust to bounded model uncertainty. In addition, in order to exploit low-cost sensor redundancy, a multi-sensor data fusion algorithm compatible with the wIKF estimates and which additionally provides sensor fault tolerance has been developed. All these techniques have been implemented on the Springer platform and verified experimentally in a series of full-scale trials, presented in the last chapter of the thesis. The outcomes demonstrate that the methods are both feasible and practicable, and that they are far more effective in providing accurate estimates of the vehicle’s heading than the conventional KF when there is uncertainty in the system model and/or sensor failure occurs.