Nous traitons le sujet de l’estimation conjointe des signaux aléatoires dépendant de paramètres déterministes et inconnus. Premièrement, on aborde le sujet du côté applicatif en proposant deux algorithmes de séparation de la parole voisée mono-capteur. Dans le premier, nous utilisons le modèle autorégressif de la parole qui décrit les corrélations court et long termes (quasi-périodique) pour formuler un modèle d’état dépendant de paramètres inconnus. EM-Kalman est ainsi utilisé pour estimer conjointement les sources et les paramètres. Dans le deuxième, nous proposons une méthode fréquentielle pour le même modèle de la parole où les sources et les paramètres sont estimés séparément. Les observations sont découpées à l’aide d’un fenêtrage bien conçu pour assurer une reconstruction parfaite des sources après. Les paramètres (de l’enveloppe spectrale) sont estimés en maximisant le critère du GML exprimé avec la matrice de covariance paramétrée que nous modélisons plus correctement en tenant compte de l’effet du fenêtrage. Le filtre de Wiener est utilisé pour estimer les sources. Deuxièmement, on aborde l’estimation conjointe d’un point de vue plus théorique en s'interrogeant sur les performances relatives de l’estimation conjointe par rapport à l’estimation séparée d’une manière générale. Nous considérons le cas conjointement Gaussien (observations et variables cachées) et trois méthodes itératives d'estimation conjointe: MAP en alternance avec ML, biaisé même asymptotiquement pour les paramètres, EM qui converge asymptotiquement vers ML et VB que nous prouvons converger asymptotiquement vers la solution ML pour les paramètres déterministes. / The thesis is composed of two parts. In the first part, we deal with the monaural speech separation problem. We propose two algorithms. In the first algorithm, we exploit the joint autoregressive model that models short and long (periodic) correlations of Gaussian speech signals to formulate a state space model with unknown parameters. The EM-Kalman algorithm is then used to estimate jointly the sources (involved in the state vector) and the parameters of the model. In the second algorithm, we use the same speech model but this time in the frequency domain (quasi-periodic Gaussian sources with AR spectral envelope). Observation data is sliced using a well-designed window. Parameters are estimated separately from the sources by optimizing the Gaussian ML criterion expressed using the sample and parameterized covariance matrices. Classical frequency domain asymptotic methods replace linear convolution by circulant convolution leading to approximation errors. We show how the introduction of windows can lead to slightly more complex frequency domain techniques, replacing diagonal covariance matrices by banded covariance matrices, but with controlled approximation error. The sources are then estimated using the Wiener filtering. The second part is about the relative performance of joint vs. marginalized parameter estimation. We consider jointly Gaussian latent data and observations. We provide contributions to Cramer-Rao bounds, then, we investigate three iterative joint estimation approaches: Alternating MAP/ML which suffers from inconsistent parameter bias, EM which converges to ML and VB that we prove converges asymptotically to the ML solution for parameter estimation.

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[pt] A importância da estrutura a termo da taxa de juros dificilmente é exagerada. A estrutura a termo agrega de forma sucinta uma quantidade enorme de informação sobre o estado presente e sobre as expectativas futuras da economia de um país. Nesse trabalho, utilizando técnicas de estimação por filtro de Kalman, estimamos, com dados brasileiros, quatro modelos teóricos da ETTJ, todos casos particulares do modelo afim estudado por Duffie e Kan (1996). Analisamos o resultado de nossas estimações tendo em vista o comportamento histórico da ETTJ brasileira durante o período. Comparamos os modelos entre si, apontando para aqueles que melhor se ajustam aos dados observados. Avaliamos que nossos resultados suportam resultados anteriores de que a hipótese das expectativas não é verificada na ETTJ brasileira. / [en] The importance of the term structure of interest rates is hardly exaggerated. The term structure succinctly summarizes an enormous quantity of information about the actual state and about the future expectations of/ for the economy of a country. Within this work, using Kalman filter estimation techniques, we estimate, with Brazilian data, four different models of the term structure, all particular cases of the affine model studied by Duffie and Kan (1996). We analyze the parameter estimates relating it to the historical behavior of Brazilian data during the sample period. We compare the models among them, choosing the one most successful in fitting the data. Our results support a previous result regarding the non-validity of the expectation hypotheses in the Brazilian term structure.

Le modèle RiskMetrics développé par la Banque JP Morgan suite à l'amendement des accords de Bâle de 1988 a été érigé comme mesure de risque financier pour faire face aux importantes perturbations ayant affecté les marchés bancaires internationaux. Communément appelé Value at Risk, il a été admis par l'ensemble des organes et institutions financiers comme une mesure de risque cohérente. Malgré sa popularité, elle est le sujet de beaucoup de controverses. En effet, les paramètres d'estimation du système RiskMetrics sont supposés fixes au cours du temps ce qui est contraire aux caractéristiques des marchés financiers. Deux raisons valables permettent de justifier cette instabilité temporelle : * la présence d'agents hétérogènes fait qu'on n'analyse plus la VaR en se focalisant sur une seule dimension temporelle mais plutôt sur des fréquences de trading (nous recourons pour cela à la méthode Wavelet). * la structure des séries financières qui d'habitude est affectée par les phénomènes de crash, bulle etc. Ceux-ci peuvent être considérés comme des variables cachées qu'on doit prendre en compte dans l'évaluation du risque. Pour cela, nous recourons à la modélisation espace d'états et au filtre de Kalman. Nous savons d'emblée que les performances de la VaR s'évaluent en recourant au test de backtesting. Celui-ci repose sur la technique de régression roulante qui montre une faille évidente : Nous ne pouvons pas connaitre le processus gouvernant la variation des paramètres, il n'y a pas endogénéisation de la dynamique de ceux-ci. Pour apporter une solution à ce problème, nous proposons une application du filtre de Kalman sur les modèles VaR et WVaR. Ce filtre, par ses fonctions corrige de manière récursive les paramètres dans le temps. En ces termes nous définissons une mesure de risque dit SVaR qui en réalité est la VaR obtenue par une actualisation des paramètres d'estimation. Elle permet une estimation précise de la volatilité qui règne sur le marché financier. Elle donne ainsi la voie à toute institution financière de disposer de suffisamment de fonds propres pour affronter le risque de marché. / The RiskMetrics model developed by the bank JP Morgan following the amendment of Basel accords 1988 was erected as a measure of financial risk to deal with important disturbances affecting international banking markets. Commonly known as Value at Risk, it was accepted by all bodies and financial institutions to be a coherent risk measure. Despite its popularity, it is the subject of many controversies. Indeed, the estimation parameters of RiskMetrics are assumed to be fixed over time, which is contrary to the characteristics of financial markets. Two valid reasons are used to justify temporal instability : *Due to the presence of heterogenous agents the VaR is not analysed by focusing on a single temporal dimension but rather on trading frequencies (we use Wavelet method for it). *The structure of financial time series wich is usually affected by the crash bubble phenomenons and so on. These can be considered as hidden variables that we must take into account in the risk assessment. For this, we use state space modeling and kalman filter. We immediately know that performances of the VaR are evaluated using backtesting test. This is based on the technique of rolling regression wich shows an obvious break : We can not know the processes governing the variation of parameters; there is no endogeneisation dynamics thereof. To provide a solution to this problem, we propose an application of the kalman filter on VaR and WVaR models. This filter recursively corrects by its functions the parameters of time. In these terms we define a risk measure called SVaR wich in realitity is the VaR obtained by updating estimation parameters. It provides an accurate estimate of the volatility existing in the financial market. It thus gives way to any financial institution to have enough capital to face market risk.

O controle de plantas daninhas é uma importante preocupação para a agricultura tendo em vista as perdas de produtividade que estas causam ao competir com a cultura por água, luz e nutrientes. O uso de herbicida é a forma de manejo mais empregada em todo o mundo para o controle destas plantas. Entretanto, o uso frequente de um dado herbicida, além de causar diversos impactos ambientais, pode levar à diminuição da eficiência do próprio herbicida ao promover a seleção de plantas que são resistentes a este herbicida. Com o crescente número de novos casos de biótipos resistentes aos herbicidas, conter a evolução da resistência tornou-se uma necessidade para a agricultura convencional. Assim, grande esforço tem sido despendido para compreender este fenômeno e tentar contornar este problema. Neste sentido, os modelos computacionais se apresentam como importantes ferramentas para investigar os efeitos dos diversos fatores, em particular das estratégias de aplicação dos herbicidas, que influenciam na dinâmica da evolução da resistência. Com esta motivação, este trabalho tem como objetivo propor e estudar algumas estratégias de aplicação de herbicidas, ou ditos simplesmente controladores, que sejam implementáveis e que diminuam os impactos ambientais considerando a evolução da resistência. Para isto, assumimos que existe um herbicida, denominado neste trabalho por herbicida recomendado, que é o preferível dentre os disponíveis por produzir uma boa relação entre os benefícios produtivos e os malefícios aos ecossistemas. Para projetar os controladores, assumimos que é possível obter informações sobre a identificação visual da resistência em campo, feitas por um agente quando o número de indivíduos resistentes ultrapassa um certo limiar, assim como informações sobre a quantidade de plantas daninhas na área, feita possivelmente empregando técnicas de sensoriamento remoto. Então, para definir os controladores, empregamos diretamente a identificação visual da resistência e estimativas para o banco de sementes e para a fração dos genótipos do banco, geradas por um filtro de Kalman a partir de informações sobre a quantidade de plantas na área. Os controladores foram avaliados em relação à preservação da eficiência do herbicida recomendado, produtividade, impacto ambiental e propagação da resistência. Concluímos destes estudos que o controlador sugerido pode apresentar melhores resultados que os obtidos por controladores ditos convencionais, que se baseiam apenas na informação de identificação da resistência em campo. / Weed control is a major concern in agriculture as it causes significant loss of productivity by competition for water, sunlight and nutrients. The use of herbicides is the most common practice in the world to control them. However, the frequent use of a particular herbicide, besides causing many environmental impacts, may lead to loss of efficiency by promoting herbicide resistance via selection of resistant individuals. Considering the increasing number of herbicide resistant biotic, restraining resistance evolution is becoming a necessity for the conventional agriculture. This motivates a great deal of research effort to understand the involved phenomena and eventually to circumvent the problem. To this end, computational models are of great aid to understand the impact of many different aspects involved in this problem, in particular, to understand how different herbicide strategies usage lead to different resistance evolution dynamics. In this thesis we propose and study some strategies for herbicide application, which we refer to as controllers. We seek for controllers that can be implemented in real word crops growing, while decreasing environmental impacts and restrain resistance evolution. We assume that there exists one herbicide of choice for a given crop, meaning that it is preferred in terms of environmental impact and efficiency. To define the controllers, we assume that it is possible to obtain visual information on resistance, meaning that we observe when the proportion of resistant individuals is above a threshold. Also, we assume noisy observation of the number of adult weed individuals, possibly made by remote sensing. So, the controller directly employs the visual identification information and an estimate for the number of resistant seeds in the seed bank, generated by the Kalman filter using information on the number of adult weed. This strategy was evaluated in terms of herbicide efficiency preservation, crop production, environmental impact and resistance proliferation. We conclude that the proposed control strategies performed better than other strategies, called conventional strategies that are based only on the visual identification information.

Ce mémoire de thèse vise à proposer de nouvelles méthodes robustes pour l'estimation de la fréquence respiratoire (FR) à partir des signaux physiologiques souvent utilisés dans la clinique comme l'électrocardiogramme (ECG) ou le photoplethysmogramme (PPG), tout en évitant de porter des capteurs encombrants et inconfortables. En effet, la respiration influence les signaux ECG et/ou PPG. Plusieurs modulations qui décrivent la respiration sont extraites basée principalement sur l'amplitude, la fréquence et la ligne de base. Il est toutefois difficile de déterminer la combinaison optimale des modulations pour obtenir une estimation précise de la FR en raison du bruit, la spécificité de chaque patient et de l'activité. Après une revue de la littérature, il ressort que peu de travaux ont étudié la qualité de ces modulations. Nous proposons donc de quantifier la qualité des modulations à l'aide d'indices de qualité respiratoire (IQR), un nouvel indice basé sur une modulation sinusoïdale est introduit. Puis, deux méthodes sont proposées: la première sélectionne automatiquement la modulation avec l'IQR le plus élevé pour une estimation de la FR, la seconde combine les deux meilleurs modulations avec le lisseur de Kalman (LK). Une nouvelle approche de fusion de modulations basée sur un modèle multimodale est également explorée. Ces méthodes sont évaluées sur trois bases de données de différents contextes cliniques: la surveillance dans les soins postopératoires (où les patients sont immobiles), le suivi pendant les activités physiques quotidiennes et la surveillance néonatale. Les résultats expérimentaux montrent que les IQRs associés à un algorithme de fusion augmentent la précision de l'estimation de la FR à partir des modulations dérivées et montrent des résultats supérieurs aux travaux issus de la littérature. / The presented work in this dissertation concerns the development of approaches to estimate the breathing rate (BR) accurately from the electrocardiogram (ECG) and photoplethysmogram (PPG), to avoid wearing cumbersome and uncomfortable sensors for direct measurements. In fact, the respiration influences ECG and PPG signals. Several modulations are extracted to describe breathing cycles based on amplitude, frequency and baseline. However, it is difficult to determine the optimal combination to estimate the BR due to the noise and patient-dependency. Since few works have studied the quality of these modulations, we propose to study the quality of modulations using respiratory quality indices (RQI). To do so, we present two methods: the first automatically selects the modulations with the highest RQI for BR estimation, the second tracks the respiration signal using Kalman smoother. The obtained results show superior performance comparing to the methods in the literature. In addition, an extension of fusion approach is presented based on a multi-mode model. These proposed methods are tested on several datasets with different clinical contexts: monitoring post-operative care (where patients are immobile), daily physical activities and neonatal monitoring. The experimental results show that the RQIs coupled with a fusion algorithm increase the accuracy of the BR estimation from the derived modulations.

This study compares independent use of two known algorithms (Kalmar filter with background subtraction and Particle Filter) that are commonly deployed in object tracking applications. Object tracking in general is very challenging; it presents numerous problems that need to be addressed by the application in order to facilitate its successful deployment. Such problems range from abrupt object motion, during tracking, to a change in appearance of the scene and the object, as well as object to scene occlusions, and camera motion among others. It is important to take into consideration some issues, such as, accounting for noise associated with the image in question, ability to predict to an acceptable statistical accuracy, the position of the object at a particular time given its current position. This study tackles some of the issues raised above prior to addressing how the use of either of the aforementioned algorithm, minimize or in some cases eliminate the negative effects

Space travelers in science fiction can drop out of hyperspace and make a pinpoint landing on any strange new world without stopping to get their bearings, but real-life space navigation is an art characterized by limited information and complex mathematics that yield no easy answers. This study investigates, for the first time ever, what position and velocity estimation errors can be expected by a starship arriving at a distant star - specifically, a miniature probe like those proposed by the Breakthrough Starshot initiative arriving at Proxima Centauri. Such a probe consists of nothing but a small optical camera and a small microprocessor, and must therefore rely on relatively simple methods to determine its position and velocity, such as observing the angles between its destination and certain guide stars and processing them in an algorithm known as an extended Kalman filter. However, this algorithm is designed for scenarios in which the position and velocity are already known to high accuracy. This study shows that the extended Kalman filter can reliably estimate the position and velocity of the Starshot probe at speeds characteristic of current space probes, but does not attempt to model the filter’s performance at speeds characteristic of Starshot-style proposals. The gravity of the target star is also estimated using the same methods.

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In this paper we study continuous tracking of airplanes using object detection models, namely YOLOv7, combined with a Kalman filter. The tracking should be able to be done in real-time. The idea of combining Kalman filters with an object detection model comes from the lack of time-dependent context in models such as YOLOv7. The model analyzes each frame independently and outputs airplane detections for the analyzed frame. Therefore, if an airplane flies behind a tree or a cloud, the object detection model will say that there is no object there. The Kalman filter is used to construct an object with a state consisting of position and velocity for every airplane. As such if an airplane flies behind a tree, it is possible to extrapolate the trajectory and resume tracking once the airplane is visible again, much like a human would extrapolate the trajectory naturally. In the report I describe the implementation and training of a YOLOv7 model, I further describe the construction and implementation of a Kalman filter as well as how observations are mapped on to objects in the Kalman filter. During this I introduce a parameter called cumulative confidence. This describes how long something is being tracked after observations cease. After losing sight of an object, the cumulative confidence starts to drop. When it reaches zero and the object is removed. This can take anywhere between 100 ms to 6 seconds depending on how much confidence the object has accumulated. Objects accumulate confidence by being observed and detected by the object detection model. In the results section I describe how the performance of the program changed when using a Kalman filter or when not using a Kalman filter. The results showed that continuous tracking of airborne airplanes was superior when using a Kalman filter as opposed to only using the YOLOv7 model. Continuous tracking was never lost in these 2 airborne cases when using the integrated Kalman filter. Continuous tracking was lost 5 respectively 11 times on the same cases when not using the Kalman filter. The last case in the results section, an airplane on a runway, showed the same performance with and without the Kalman filter. I go into detail why this is in both the results section and in Section 5.1 (Interpreting the results). / I detta pappret studeras kontinuerlig spårning av flygplan med hjälp av objektdetekterings-modeller, mer specifikt YOLOv7 modellen i kombination med Kalman filter. Spårningen ska kunna göras i realtid. Idén att kombinera Kalman filter med modeller för objektdetektering kommer från avsaknaden på tidsberoende kontext i modeller som YOLOv7. Modellen analyserar varje bild i en dataström oberoende och ger en utmatning med positioner av flygplan i den analyserade bilden. Därmed, om ett flygplan flyger in bakom ett träd eller ett moln så kommer modellen konstatera att det inte är ett objekt där. Kalman filtret används för att konstruera ett objekt med ett tillstånd som består av position och hastigheten av varje flygplan. På så vis om ett flygplan flyger in bakom ett träd är det möjligt att extrapolera vägen planet kommer flyga samt återuppta spårning när flygplanet blir synligt igen, på samma vis som en människa extrapolerar planets bana naturligt. I rapporten beskriver jag en implementering och träning av en YOLOv7 modell. Vidare beskriver jag konstruktionen och implementationen av ett Kalman filter, samt hur observationer mappas till objekt i Kalman filtret. Jag introducerar även en parameter som kallas “kumulativt förtroende”. Denna beskriver hur länge något spåras även efter att observationer upphör. När ett objekt ej får observationer längre så börjar det kumulativa förtroendet minska. När det når noll så tas objektet bort. Detta kan ta mellan 100 ms och sex sekunder, beroende på hur mycket förtroende objektet har ackumulerat. Objekt ackumulerar förtroende genom att bli observerade och detekterade av YOLOv7 modellen. I resultatdelen beskriver jag hur prestandan skiljer sig om programmet använder ett Kalman filter eller inte ett Kalman filter. Resultaten visar att kontinuerlig spårning av flygplan i luften var bättre när man använder ett Kalman filter. Spårningen av flygplan upphörde aldrig i de 2 fallen då flygplan var i luften. På dessa fallen så tappade modellen spårningen 5 respektive 11 gånger när den inte använde Kalman filtret. Det tredje och sista fallet i resultatdelen, ett flygplan på banan, visade samma prestanda med eller utan Kalman filtret. Jag går in i detalj kring varför det var så i resultatdelen och i diskussionen.