A Tomografia por Impedância Elétrica tem como objetivo estimar a distribuição de impedância elétrica dentro de uma região a partir de medidas de potencial elétrico coletadas apenas em seu contorno externo quando corrente elétrica é imposta neste mesmo contorno. Uma das aplicações para esta tecnologia é o monitoramento das condições pulmonares de pacientes em Unidades de Tratamento Intensivo. Dentre vários algoritmos, destacam-se os filtros de Kalman que abordam o problema de estimação sob o ponto de vista probabilístico, procurando encontrar a distribuição de probabilidade do estado condicionada à realização das medidas. Para que estes filtros possam ser utilizados, um modelo de evolução temporal do sistema sendo observado deve ser adotado. Esta tese propõe o uso de um modelo de evolução para a variação de volume de ar nos pulmões durante a respiração de um paciente sob ventilação artificial. Este modelo é utilizado no unscented Kalman filter, uma extensão não linear do filtro de Kalman. Tal modelo é ajustado em paralelo à estimação do estado, utilizando um esquema dual de estimação. Um algoritmo de segmentação de imagem é proposto para identificar as regiões pulmonares nas imagens estimadas e assim utilizar o modelo de evolução. Com o intuito de melhorar as estimativas, o método do erro de aproximação é utilizado no modelo de observação para mitigar os erros de modelagem e informação a priori é adicionada na solução do problema inverso mal-posto. O método é avaliado através de simulações numéricas e ensaio experimental coletado em um voluntário. Os resultados mostram que o método proposto melhora as estimativas feitas pelo filtro de Kalman, propiciando a visualização de imagens absolutas, dinâmicas e com bom nível de contraste entre os tecidos e órgãos internos. / Electrical impedance tomography estimates the electrical impedance distribution within a region given a set of electrical potential measurements acquired along its boundary at the same time that electrical currents are imposed on the same boundary. One of the applications of this technology is lung monitoring of patients in Intensive Care Units. One class of algorithms employed for the estimation are the Kalman filters which deal with the estimation problem in a probabilistic framework, looking for the probability density function of the state conditioned to the acquired measurements. In order to use such filters, an evolution models of the system must be employed. This thesis proposes an evolution model of the variation of air in the lungs of patients under artificial ventilation. This model is used on the Unscented Kalman Filter, a nonlinear extension of the Kalman filter. This model is adjusted in parallel to the state estimation, in a dual estimation scheme. An image segmentation algorithm is proposed for identifying the lungs in the images. In order to improve the estimate, the approximation error method is employed for mitigating the observation model errors and prior information is added for the solution of the ill-posed inverse problem. The method is evaluated with numerical simulations and with experimental data of a volunteer. The results show that the proposed method increases the quality of the estimates, allowing the visualization of absolute and dynamic images, with good level of contrast between the tissues and internal organs.

A Tomografia por Impedância Elétrica tem como objetivo estimar a distribuição de impedância elétrica dentro de uma região a partir de medidas de potencial elétrico coletadas apenas em seu contorno externo quando corrente elétrica é imposta neste mesmo contorno. Uma das aplicações para esta tecnologia é o monitoramento das condições pulmonares de pacientes em Unidades de Tratamento Intensivo. Dentre vários algoritmos, destacam-se os filtros de Kalman que abordam o problema de estimação sob o ponto de vista probabilístico, procurando encontrar a distribuição de probabilidade do estado condicionada à realização das medidas. Para que estes filtros possam ser utilizados, um modelo de evolução temporal do sistema sendo observado deve ser adotado. Esta tese propõe o uso de um modelo de evolução para a variação de volume de ar nos pulmões durante a respiração de um paciente sob ventilação artificial. Este modelo é utilizado no unscented Kalman filter, uma extensão não linear do filtro de Kalman. Tal modelo é ajustado em paralelo à estimação do estado, utilizando um esquema dual de estimação. Um algoritmo de segmentação de imagem é proposto para identificar as regiões pulmonares nas imagens estimadas e assim utilizar o modelo de evolução. Com o intuito de melhorar as estimativas, o método do erro de aproximação é utilizado no modelo de observação para mitigar os erros de modelagem e informação a priori é adicionada na solução do problema inverso mal-posto. O método é avaliado através de simulações numéricas e ensaio experimental coletado em um voluntário. Os resultados mostram que o método proposto melhora as estimativas feitas pelo filtro de Kalman, propiciando a visualização de imagens absolutas, dinâmicas e com bom nível de contraste entre os tecidos e órgãos internos. / Electrical impedance tomography estimates the electrical impedance distribution within a region given a set of electrical potential measurements acquired along its boundary at the same time that electrical currents are imposed on the same boundary. One of the applications of this technology is lung monitoring of patients in Intensive Care Units. One class of algorithms employed for the estimation are the Kalman filters which deal with the estimation problem in a probabilistic framework, looking for the probability density function of the state conditioned to the acquired measurements. In order to use such filters, an evolution models of the system must be employed. This thesis proposes an evolution model of the variation of air in the lungs of patients under artificial ventilation. This model is used on the Unscented Kalman Filter, a nonlinear extension of the Kalman filter. This model is adjusted in parallel to the state estimation, in a dual estimation scheme. An image segmentation algorithm is proposed for identifying the lungs in the images. In order to improve the estimate, the approximation error method is employed for mitigating the observation model errors and prior information is added for the solution of the ill-posed inverse problem. The method is evaluated with numerical simulations and with experimental data of a volunteer. The results show that the proposed method increases the quality of the estimates, allowing the visualization of absolute and dynamic images, with good level of contrast between the tissues and internal organs.

Le travail effectué au cours de cette thèse tente d’apporter une solution algorithmique à la problématique de l’estimation de l’état d’un mini-drone en vol qui soit compatible avec les exigences d’embarquabilité inhérentes au système. Il a été orienté vers les méthodes d’estimation non linéaire à base de modèles. Les algorithmes d’estimation, d’état ou de paramètres, et de contrôle apparaissent primordiaux, lorsque la technologie des capteurs et des actionneurs, pour des raisons de coût et d’encombrement essentiellement, ne permet pas de disposer de capacités illimitées. Ceci est particulièrement vrai dans le cas des micro- et des mini-drones. L’estimation permet de fusionner en temps réel les informations imparfaites provenant des différents capteurs et de fournir une estimation, par exemple de l’état du drone (orientation, vitesse, position) au calculateur embarqué où sont implémentés les algorithmes de commande de l’engin. Ce contrôle de l’appareil doit garantir sa stabilité en boucle fermée quelque soit l’ordre de consigne fourni directement par l’opérateur ou par tout système automatique de gestion du vol et assurer que celle-ci soit correctement recopiée. Estimation et commande participent donc grandement au succès de toute mission. Une dimension extrêmement importante qui a conditionné les travaux entrepris tout au long de cette thèse concerne la capacité d’emport des mini-drones que nous considérons. En effet, celle-ci, relativement limitée, et couplée à la volonté de ne pas grever les budgets de développement de tout mini-drone, autorise uniquement l’intégration de matériels dits bas-coûts. Malgré les progrès significatifs de la miniaturisation et l’augmentation continuelle des capacités de calcul embarqué (loi de Moore), les mini-drones d’intérêt considérés ici n’embarquent donc que des capteurs aux performances limitées dans un contexte où cette catégorie d’engins autonomes est amenée à être de plus en plus fréquemment exploitée pour remplir des missions elles-mêmes toujours plus nombreuses. Celles-ci requièrent notamment que de tels drones puissent de manière sûre s’insérer et partager l’espace aérien civil moyennant le passage d’une certification de leur vol au même titre que pour les avions de transport des différentes compagnies aériennes. Dès lors, face à cet enjeu de sécurisation des vols de mini-drones, la consolidation de la connaissance de l’état de l’aéronef par des techniques d’estimation devient un tâche essentielle pour en assurer le contrôle, y compris en situations dégradées (pannes capteurs, perte occasionnelle de signaux, bruit et perturbations environnantes, imperfections des moyens de mesure, etc). Tenter de répondre à cet enjeu conduit naturellement le chercheur à s’attaquer à des problèmes relativement nouveaux, en tout cas pas forcément aussi proches de ceux qui se posent dans le secteur de l’aéronautique civile ou militaire, où le système avionique est sans commune mesure avec celui sur lequel nous avons travaillé dans cette thèse. Ce travail à tout d’abord consisté à définir une modélisation dynamique descriptive du vol des mini-drones étudiés, suffisamment générique pour être appliquée à différents types de minidrones (voilure fixe, multirotor, etc). Par la suite, deux algorithmes d’estimation originaux, dénommés IUKF et -IUKF, exploitant ce modèle, ont été développés avant d’être testés en simulation puis sur données réelles pour la version -IUKF. Ces deux méthodes transposent le cadre générique des observateurs invariants au cas de l’estimation non linéaire de l’état d’un système dynamique par une technique de type Unscented Kalman Filter (UKF) qui appartient à la classe plus générale des algorithmes de filtrage non linéaire de type Sigma Point (SP). La solution proposée garantit un plus grand domaine de convergence de l’estimé que les techniques plus traditionnelles. / This thesis presents the study of an algorithmic solution for state estimation problem of unmanned aerial vehicles, or UAVs. The necessary resort to multiple miniaturized low-cost and low-performance sensors integrated into mini-RPAS, which are obviously subjected to hardspace requirements or electrical power consumption constraints, has led to an important interest to design nonlinear observers for data fusion, unmeasured systems state estimation and/or flight path reconstruction. Exploiting the capabilities of nonlinear observers allows, by generating consolidated signals, to extend the way mini-RPAS can be controlled while enhancing their intrinsic flight handling qualities.That is why numerous recent research works related to RPAS certification and integration into civil airspace deal with the interest of highly robust estimation algorithm. Therefore, the development of reliable and performant aided-INS for many nonlinear dynamic systems is an important research topic and a major concern in the aerospace engineering community. First, we have proposed a novel approach for nonlinear state estimation, named pi-IUKF (Invariant Unscented Kalman Filter), which is based on both invariant filter estimation and UKF theoretical principles. Several research works on nonlinear invariant observers have been led and provide a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical properties and systems symmetries. The general invariant observer guarantees a straightforward form of the nonlinear estimation error dynamics whose properties are remarkable. The developed pi-IUKF estimator suggests a systematic approach to determine all the symmetry-preserving correction terms, associated with a nonlinear state-space representation used for prediction, without requiring any linearization of the differential equations. The exploitation of the UKF principles within the invariant framework has required the definition of a compatibility condition on the observation equations. As a first result, the estimated covariance matrices of the pi-IUKF converge to constant values due to the symmetry-preserving property provided by the nonlinear invariant estimation theory. The designed pi-IUKF method has been successfully applied to some relevant practical problems such as the estimation of Attitude and Heading for aerial vehicles using low-cost AH reference systems (i.e., inertial/magnetic sensors characterized by low performances). In a second part, the developed methodology is used in the case of a mini-RPAS equipped with an aided Inertial Navigation System (INS) which leads to augment the nonlinear state space representation with both velocity and position differential equations. All the measurements are provided on board by a set of low-cost and low-performance sensors (accelerometers, gyrometers, magnetometers, barometer and even Global Positioning System (GPS)). Our designed pi-IUKF estimation algorithm is described and its performances are evaluated by exploiting successfully real flight test data. Indeed, the whole approach has been implemented onboard using a data logger based on the well-known Paparazzi system. The results show promising perspectives and demonstrate that nonlinear state estimation converges on a much bigger set of trajectories than for more traditional approaches.