A Tomografia por Impedância Elétrica (EIT) é um método que utiliza estimativas da distribuição de condutividade ou impedância de tecidos orgânicos na obtenção de imagens médicas. O procedimento de obtenção das imagens baseia-se em medições de correntes ou voltagens no contorno da região sob análise e na estimação de parâmetros de um modelo desta região. No caso de pacientes submetidos à respiração artificial, o conhecimento da distribuição absoluta ou das variações de condutividades nos pulmões auxilia na detecção de fenômenos como colapso alveolar ou pneumotórax e permite o ajuste e controle da vazão e pressão do ar fornecido, de modo a evitar a ocorrência de tais anomalias. Este trabalho apresenta algoritmos cujo objetivo é a solução do problema inverso e mal posto de estimar a distribuição absoluta e as variações de condutividades nos pulmões através da EIT para a geração de imagens em duas dimensões. O algoritmo para a estimação da distribuição absoluta de condutividade utiliza o filtro estendido de Kalman. As simulações numéricas mostram que, com medidas incorporando ruído cujo desvio padrão atinge até 12% da máxima voltagem, as estimativas de condutividades convergem para a distribuição esperada com um desvio inferior a 7% do valor da máxima condutividade. Quanto à detecção de variações de condutividades em relação a uma distribuição de condutividades tomada como referência, as simulações numéricas sugerem que a solução do problema depende da utilização de métodos de regularização. / Electrical Impedance Tomography (EIT) is a method that uses estimates of conductivity or impedance distribution in living tissues to generate medical images. The estimation procedure is based on measurements of electrical currents or voltages at the boundary of the region under analysis, and on the processing of these data through a proper algorithm. In patients under artificial ventilation, knowledge of absolute or relative conductivity distribution in the lungs helps detecting the presence of alveolar collapse or pneumothorax, and allows setting and controlling air volume and pressure of the ventilation device. This work presents algorithms that aim at solving the ill-posed inverse problem of estimating absolute and relative conductivity distribution in the lungs through EIT for cross-sectional image reconstruction. The algorithm for absolute conductivity distribution estimation uses the extended Kalman filter. Numerical simulations show that, when the standard deviation of the measurement noise level raises up to 12% of the maximal measured voltage, the conductivity estimates converge to the expected vector within 7% accuracy of the maximal conductivity value. Addressing the estimation of conductivity changes in relation to a conductivity distribution taken as reference, numerical simulations suggest that the problem may be properly solved using regularization methods.

Nesta dissertação é apresentada a comparação do desempenho de três estimadores - o Filtro de Kalman Estendido, o Filtro de Kalman Unscented e o Filtro de Partículas - aplicados para estimar a postura de um robô diferencial. Uma câmera foi fixa no teto para cobrir todo o campo operacional do robô durante os experimentos, a fim de extrair o mapa e gerar o ground truth. Isso permitiu realizar uma análise do erro de forma precisa a cada instante de tempo. O desempenho de cada um dos estimadores foi avaliado sistematicamente e numericamente para duas trajetórias. Os resultados desse primeiro experimento demonstram que os filtros proporcionam grandes melhorias em relação à odometria e que o modelo dos sensores é crítico para obter esse desempenho. O Filtro de Partículas mostrou um desempenho melhor em relação aos demais nos dois percursos. No entanto, seu elevado custo computacional dificulta sua implementação em uma aplicação de tempo real. O Filtro de Kalman Unscented, por sua vez, mostrou um desempenho semelhante ao Filtro de Kalman Estendido durante a primeira trajetória. Porém, na segunda trajetória, a qual possui uma quantidade maior de curvas, o Filtro de Kalman Unscented mostrou uma melhora significativa em relação ao Filtro de Kalman Estendido. Foi realizado um segundo experimento, em que o robô planeja e executa duas trajetórias. Os resultados obtidos mostraram que o robô consegue chegar a um determinado local com uma precisão da mesma ordem de grandeza do que a obtida durante a estimação de estados do robô. / In this dissertation, the performance of three nonlinear-model based estimators - the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter - applied to pose estimation of a differential drive robot is compared. A camera was placed above the operating field of the robot to record the experiments in order to extract the map and generate the ground truth so the evaluation of the error can be done at each time step with high accuracy. The performance of each estimator is assessed systematically and numerically for two robot trajectories. The first experimental results showed that all estimators provide large improvements with respect to odometry and that the sensor modeling is critical for their performance. The particle filter showed a better performance than the others on both experiments, however, its high computational cost makes it difficult to implement in a real-time application. The Unscented Kalman Filter showed a similar performance to the Extended Kalman Filter during the first trajectory. However, during the second one (a curvier path) the Unscented Kalman Filter showed a significant improvement over the Extended Kalman Filter. A second experiment was carried out where the robot plans and executes a trajectory. The results showed the robot can reach a predefined location with an accuracy of the same order of magnitude as the obtained during the robot pose estimation.

A Tomografia por Impedância Elétrica (EIT) é um método que utiliza estimativas da distribuição de condutividade ou impedância de tecidos orgânicos na obtenção de imagens médicas. O procedimento de obtenção das imagens baseia-se em medições de correntes ou voltagens no contorno da região sob análise e na estimação de parâmetros de um modelo desta região. No caso de pacientes submetidos à respiração artificial, o conhecimento da distribuição absoluta ou das variações de condutividades nos pulmões auxilia na detecção de fenômenos como colapso alveolar ou pneumotórax e permite o ajuste e controle da vazão e pressão do ar fornecido, de modo a evitar a ocorrência de tais anomalias. Este trabalho apresenta algoritmos cujo objetivo é a solução do problema inverso e mal posto de estimar a distribuição absoluta e as variações de condutividades nos pulmões através da EIT para a geração de imagens em duas dimensões. O algoritmo para a estimação da distribuição absoluta de condutividade utiliza o filtro estendido de Kalman. As simulações numéricas mostram que, com medidas incorporando ruído cujo desvio padrão atinge até 12% da máxima voltagem, as estimativas de condutividades convergem para a distribuição esperada com um desvio inferior a 7% do valor da máxima condutividade. Quanto à detecção de variações de condutividades em relação a uma distribuição de condutividades tomada como referência, as simulações numéricas sugerem que a solução do problema depende da utilização de métodos de regularização. / Electrical Impedance Tomography (EIT) is a method that uses estimates of conductivity or impedance distribution in living tissues to generate medical images. The estimation procedure is based on measurements of electrical currents or voltages at the boundary of the region under analysis, and on the processing of these data through a proper algorithm. In patients under artificial ventilation, knowledge of absolute or relative conductivity distribution in the lungs helps detecting the presence of alveolar collapse or pneumothorax, and allows setting and controlling air volume and pressure of the ventilation device. This work presents algorithms that aim at solving the ill-posed inverse problem of estimating absolute and relative conductivity distribution in the lungs through EIT for cross-sectional image reconstruction. The algorithm for absolute conductivity distribution estimation uses the extended Kalman filter. Numerical simulations show that, when the standard deviation of the measurement noise level raises up to 12% of the maximal measured voltage, the conductivity estimates converge to the expected vector within 7% accuracy of the maximal conductivity value. Addressing the estimation of conductivity changes in relation to a conductivity distribution taken as reference, numerical simulations suggest that the problem may be properly solved using regularization methods.

A filtragem, na sua forma mais geral, tem estado presente na vida do homem há muito tempo. Com o surgimento de novas tecnologias (surgimento da eletricidade e a sua evolução) e o desenvolvimento da computação, as técnicas de filtragem (separação) de sinais elétricos. Normalmente, os sistemas de comunicação (telefonia móvel e fixa, sinais recebidos de satélites e outros sistemas) contém sinais indesejáveis responsáveis pela degradação do sinal original. Dentro desse contexto, este projeto de pesquisa apresenta um estudo do algoritmo Filtro Duplo de Kalman Estendido, onde um filtro e Kalman e duas redes neurais são empregadas para a redução de ruídos em sinais de voz. O algoritmo estudado foi aplicado ao processamento de um sinal corrompido por dois tipos de ruídos diferentes: ruído branco e ruído gaussiano e ruído branco não estacionário, conseguindo-se bons resultados. Uma melhora sensível do sinal filtrado pode ser conseguida com técnicas de pré-filtragem do sinal. Neste trabalho foi utilizado o filtro de médias para a pré-filtragem, obtendo um sinal filtrado com ruído musical de baixa intensidade. / Filtering in it\'s most general kind has been present in men\'s life for a long time. With the appearance of new technologies (appearance of electricity and it\'s evolution) and the deyelopment of the computer science, the filtering techniques started to be widely used in engineering to the filtering (separation) of electric signals. Normally the communication systems (fixed and mobile telephony, signals sent from satellites and other systems) bring undesired results responsible for the degradation of the original signal. Within this context, this research project shows a study of the algorithm Dual Extended Kalman Filtering, in which a Kalman filter and two neural networks are used for the reduction of noise in speech signals. The algorithm studied was applied to the processing of a signal corrupted by two types of different noises: gaussian white noise and non stationary white noise obtaining good results. A significant improvement of the filtered noise can be obtained with techniques of pre-filtering of the signal. In this research the average filter for a pre-filtering was used, obtaining a filtered signal with musical noise oflow intensity.

[pt] Os satélites de um sistema de comunicações que opera numa determinada faixa de frequências utilizando satélites não-geoestacionários podem sofrer interferências indesejáveis provocadas por transmissores do Serviço Fixo Terrestre (SF) que operam nessa mesma faixa. Para o operador do sistema não geoestacionário é importante identificar quais as áreas da superfície da Terra que contêm os transmissores responsáveis por essas interferências indesejáveis, o que seria um primeiro passo na tentativa de resolver o problema através de negociações bilaterais com as estações transmissoras do SF envolvidas (coordenação). O presente trabalho apresenta a modelagem matemática do problema, e propõe que a identificação dessas áreas seja feita por meio da estimação das potências e apontamentos (ângulos de azimute e elevação) das antenas transmissoras do SF com base em medidas de potência tomadas nos diversos feixes de recepção de um satélite de teste. O trabalho analisa aspectos específicos do problema e propõe a utilização do Filtro de Kalman Estendido (EKF) para a estimação das potências e apontamentos das antenas transmissoras do SF. / [en] Satellites of a non-geostationary communication system may be victims of harmful interference produced by terrestrial fixed service (FS) transmitting stations operating in the same frequency band. It is important to the satellite system operator to identify the specific areas on Earth s surface containing the FS stations that are responsible for such interference. This would be a first step for solving the problem via bilateral coordination with each of the involved FS operators. This dissertation presents a mathematical model for the problem and proposes that the identification of these areas be made though the estimation of the transmitted power and the antenna pointing (azimuth and elevation angles) of the various FS stations, based on received power measurements taken on the beams of a test non-GSO satellite. This work also investigates the particular aspects of the problem and proposes the Extended Kalman Filter (EKF) as the algorithm for estimation.

Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues. The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of other commodities, have always raised the questions regarding their interactions. Moreover, if there is any interaction, then one would like to know the extent of influence on each other. In this work, we undertake the study to shed a light on the above highlighted processes and issues. The presented study systematically deals with the development of stochastic dynamic models and mathematical, statistical and computational analysis of energy commodity spot price and interaction processes. Below we list the main components of the research carried out in this dissertation. (1) Employing basic economic principles, interconnected deterministic and stochastic models of linear log-spot and expected log-spot price processes coupled with non-linear volatility process are initiated. (2) Closed form solutions of the models are analyzed. (3) Introducing a change of probability measure, a risk-neutral interconnected stochastic model is derived. (4) Furthermore, under the risk-neutral measure, expectation of the square of volatility is reduced to a continuous-time deterministic delay differential equation. (5) The by-product of this exhibits the hereditary effects on the mean-square volatility process. (6) Using a numerical scheme, a time-series model is developed and utilized to estimate the state and parameters of the dynamic model. In fact, the developed time-series model includes the extended GARCH model as special case. (7) Using the Henry Hub natural gas data set, the usefulness of the linear interconnected stochastic models is outlined. (8) Using natural and basic economic ideas, interconnected deterministic and stochastic models in (1) are extended to non-linear log-spot price, expected log-spot price and volatility processes. (9) The presented extended models are validated. (10) Closed form solution and risk-neutral models of (8) are outlined. (11) To exhibit the usefulness of the non-linear interconnected stochastic model, to increase the efficiency and to reduce the magnitude of error, it was essential to develop a modified version of extended Kalman filtering approach. The modified approach exhibits the reduction of magnitude of error. Furthermore, Henry Hub natural gas data set is used to show the advantages of the non-linear interconnected stochastic model. (12) Parameter and state estimation problems of continuous time non-linear stochastic dynamic process is motivated to initiate an alternative innovative approach. This led to introduce the concept of statistic processes, namely, local sample mean and sample variance. (13) Then it led to the development of an interconnected discrete-time dynamic system of local statistic processes and (14) its mathematical model. (15) This paved the way for developing an innovative approach referred as Local Lagged adapted Generalized Method of Moments (LLGMM). This approach exhibits the balance between model specification and model prescription of continuous time dynamic processes. (16) In addition, it motivated to initiate conceptual computational state and parameter estimation and simulation schemes that generates a mean square sub-optimal procedure. (17) The usefulness of this approach is illustrated by applying this technique to four energy commodity data sets, the U. S. Treasury Bill Yield Interest Rate and the U.S. Eurocurrency Exchange Rate data sets for state and parameter estimation problems. (18) Moreover, the forecasting and confidence-interval problems are also investigated. (19) The non-linear interconnected stochastic model (8) was further extended to multivariate interconnected energy commodities and sources with and without external random intervention processes. (20) Moreover, it was essential to extend the interconnected discrete-time dynamic system of local sample mean and variance processes to multivariate discrete-time dynamic system. (21) Extending the LLGMM approach in (15) to a multivariate interconnected stochastic dynamic model under intervention process, the parameters in the multivariate interconnected stochastic model are estimated. These estimated parameters help in analyzing the short term and long term relationship between the energy commodities. These developed results are applied to the Henry Hub natural gas, crude oil and coal data sets.

<p>The market for unmanned aerial vehicles (UAVs) is growing rapidly. In order to meet the demand for marine applications CybAero AB has recently started a project named Mobile Automatic Launch and Landing Station (MALLS). MALLS enables the uav to land on moving targets such as ships. This thesis studies a system that estimates the pose of a helicopter in order to land on a moving target.</p><p>The main focus has been on developing a pose estimation system using computer vision. Two different methods for estimating the pose have been studied, one using homography and one using an Extended Kalman Filter (ekf). Both methods have been tested on real flight data from a camera mounted on a RC-helicopter. The accuracy of the pose estimation system has been verified with data from a test with the camera mounted on an industrial robot. The test results show that the ekf-based system is less sensitive to noise than the homography-based system. The ekf-based system however requires initial values which the homography-based system does not. The accuracy of both systems is found to be good enough for the purpose.</p><p>A novel control system with control rules for performing an autonomous landing on a moving target has been developed. The control system has not been tested during flight.</p> / <p>Marknaden for obemannade autonoma luftburna farkoster (UAV:er) växer snabbt. För att möta behovet av marina tillämpningar har CybAero AB nyligen startat ett projekt som kallas Mobil Automatisk Start- och Landningsstation (MALLS). Syftet med malls är att möjliggöra autonom start och landning på objekt i rörelse, som till exempel ett fartyg. I det här examensarbetet studeras ett system för att bestämma position och attityd för en helikopter relativt en helikopterplatta, för att möjliggöra landning på ett ojekt i rörelse.</p><p>Fokus har främst legat på att utveckla ett positionerings- och attitydbestämningssystem. Ett datorseende positionerings- och attitydbestämningssystem har utvecklats. Två olika metoder har undersökts, ett system som bygger på homografi och ett annat som bygger på Extended Kalman Filter (EKF). Båda metoderna har testats med verklig data från en kamera monterad på en RC helikopter. Noggrannheten i positionsbestämmelsen har undersökts med hjälp av data från en industrirobot. Testresultaten visar att det EKF-baserade systemet är mindre bruskänsligt än det homografibaserade systemet. En nackdel med det ekf-baserade systemet är däremot att det kräver initialvillkor vilket det homografibaserade systemet inte gör. Noggrannheten på båda systemen finner vi tillfredsställande för syftet.</p><p>Ett enkelt styrsystem med styrlagar för att genomföra landningar på ett rörligtobjekt har utvecklats. Styrsystemet har dock inte testats under verklig flygning.</p>

<p>A control system for autonomous landing of an unmanned aerial vehicle (UAV)with high precision has been developed. The UAV is a medium sized model he-licopter. Measurements from a GPS, a camera and a compass are fused with anextended Kalman filter for state estimation of the helicopter. Four PID-controllers,one for each control signal of the helicopter, are used for the helicopter control.During the final test flights fifteen landings were performed with an average land-ing accuracy of 35 cm.    A bias in the GPS measurements makes it impossible to land the helicopter withhigh precision using only the GPS. Therefore, a vision system using a camera anda pattern provided landing platform has been developed. The vision system givesaccurate measurement of the 6-DOF pose of the helicopter relative the platform.These measurements are used to guide the helicopter to the landing target. Inorder to use the vision system in real time, fast image processing algorithms havebeen developed. The vision system can easily match up the with the camera framerate of 30 Hz.</p> / <p>Ett kontrolsystem för att autonomt landa en modellhelikopter har utvecklats.Mätdata från en GPS, en kamera samt en kompass fusioneras med ett Extend-ed Kalman Filter för tillståndsestimering av helikoptern. Fyra PID-regulatorer,en för varje kontrolsignal på helikoptern, har används för regleringen. Under densista provflygningen gjordes tre landingar av vilken den minst lyckade slutade35 cm från målet.    På grund av en drift i GPS-mätningarna är det omöjligt att landa helikopternmed hög precision med bara en GPS. Därför har ett bildbehandlingssystem som an-vänder en kamera samt ett mönster på platformen utvecklats. Bidbehandlingssys-temet mäter positionen och orienteringen av helikoptern relativt platformen. Dessamätningar används kompensera för GPS-mätningarnas drift. Snabba bildbehan-dlingsalgoritmer har utvecklats för att kunna använda bildbehandlingssystemet irealtid. Systemet är mycket snabbare än 30 bilder per sekund vilket är kameranshastighet.</p>

<p>The purpose of this report is to evaluate different methods for identifying states in robot models. Both linear and non-linear filters exist among these methods and are compared to each other. Advantages, disadvantages and problems that can occur during tuning and running are presented. Additional measurements from accelerometers are added and their use with above mentioned methods for state estimation is evaluated. The evaluation of methods in this report is mainly based on simulations in Matlab, even though some experiments have been performed on laboratory equipment. </p><p>The conclusion indicates that simple non-linear models with few states can be more accurately estimated with a Kalman filter than with an extended Kalman filter, as long as only linear measurements are used. When non-linear measurements are used an extended Kalman filteris more accurate than a Kalman filter. Non-linear measurements are introduced through accelerometers with non-linear measurement equations. Using accelerometers generally leads to better state estimation when the measure equations have a simple relation to the model.</p>

One of Saab Space’s products is the S19 guidance system for sounding rockets.Today this system is based on an inertial navigation system that blindly calculatesthe position of the rocket by integrating sensor readings with unknown bias. Thepurpose of this thesis is to integrate a Global Positioning System (GPS) receiverinto the guidance system to increase precision and robustness. There are mainlytwo problems involved in this integration. One is to integrate the GPS with sensorfusion into the existing guidance system. The seconds is to get the GPS satellitetracking to work under extremely high dynamics. The first of the two problems issolved by using an Extended Kalman filter (EKF) with two different linearizations.One of them is uses Euler angles and the other is done with quaternions. Theintegration technique implemented in this thesis is a loose integration between theGPS receiver and the inertial navigation system. The main task of the EKF isto estimate the bias of the inertial navigation system sensors and correct it toeliminate drift in the position. The solution is verified by computing the positionof a car using a GPS and an inertial measurement unit. Different solutions to theGPS tracking problem are proposed in a pre-study. / En av Saab Space produkter är navigationssystemet S19 som styr sondraketer.Fram till idag har systemet varit baserat på ett tröghetsnavigeringssystem somblint räknar ut position genom att integrera tröghetsnavigerinssystemets sensorermed okända biaser. Syftet med detta exjobb är att integrera en GPS med tröghetsnavigeringsystemetför att öka robusthet och precision. Det kan i huvudsak delasupp i två problem; att integrera en GPS-mottagare med det befintliga navigationsystemetmed användning utav sensorfusion, och att få satellitföljningen attfungera under extremt höga dynamiska förhållanden. Det första av de två problemenlöses genom ett Extended Kalman filter (EKF) med två olika linjäriseringar.Den första linjäriseringen är med Eulervinklar och är välbeprövad. Den andra ärmed kvaternioner. Integrationstekniken som implementeras i detta Examensarbeteär en lös integration mellan GPS-mottagaren och tröghetsnavigeringssystemet. Huvudsyftetmed EKF:en är att estimera bias i tröghetsnavigeringsystemets sensoreroch korrigera dem för att eliminera drifter i position. Lösningen verifieras genomatt räkna ut positionen för en bil med GPS och en inertiell mätenhet. Olika lösningartill satellitföljningen föreslås i en förstudie.