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.

La localisation précise d’un train sur la voie ferrée est une information vitale pour la gestion du trafic et la sécurité des passagers. Le système européen de contrôle des trains (ETCS) embarque ainsi un accéléromètre mono axe mesurant l’accélération longitudinale du train. Ce capteur est l’un des nombreux capteurs présents à bord permettant une odométrie précise. Cependant, sa mesure est faussée par la projection de la gravité sur l’axe sensible en fonction de l’inclinaison de la voie. L’objectif de ce mémoire est donc d’augmenter l’intérêt de ce capteur en développant une solution basée sur une centrale inertielle complète dans le but de fournir une accélération longitudinale fiable. Pour cela, un estimateur d’état a été développé à partir d’un filtre de Kalman étendu et de la prise en compte de contraintes sur le vecteur d’état. L’utilisation d’une équation de réactualisation du gain de Kalman force ainsi l’estimation d’état à évoluer dans un espace contraint. De plus, le vecteur d’observation du système a été augmenté par les informations fournies par un estimateur de vitesse et un estimateur d’attitude du train. L’estimateur de vitesse utilise une analyse fréquentielle des mesures accélérométriques et l’estimateur d’attitude exploite la complémentarité fréquentielle des mesures gyrométriques et accélérométriques pour estimer les angles de roulis et de tangage. Ces informations sont ensuite fusionnées avec les mesures de la centrale. Enfin, des expérimentations ont été réalisées en Turquie dans un train et les performances de l’estimateur ont été validées en comparant les résultats obtenus aux données fournies par une centrale de navigation haut de gamme. / The precise location of a train on the rail network is vital information for traffic management and passenger safety. The European Train Control System (ETCS) features a single-axis accelerometer which measures the longitudinal acceleration of the train. This sensor is one of many sensors onboard providing a precise odometry. However, its measurement is corrupted by the projection of the gravity on the sensitive axis as a function of the inclination of the track. The purpose of this work is to increase the value of this sensor by developing a solution based on a complete inertial system in order to provide a reliable longitudinal acceleration. For this, a state estimator was developed based on an extended Kalman filter and the consideration of constraints on the state vector. The use of updating equation of the Kalman gain forces the state estimation to evolve in a constrained space. In addition, the observation vector has been increased with the information provided by a velocity estimator and a train attitude estimator. The velocity estimator uses a frequency analysis of the accelerometer measurements and the attitude estimator operates the frequency complementarity of gyro and accelerometer measurements, to estimate the roll and pitch angles. This information is then merged with the measurements of the IMU. Finally, experiments were carried out in Turkey on a train and the estimator's performance was validated by comparing the results with data from a high-performance inertial navigation system.

Um componente fundamental no sistema de um robô móvel consiste na habilidade de localizar-se acuradamente, o que envolve estimar sua postura em relação a uma representação global do espaço. A especificação geral de uma abordagem de localização baseada em dados sensoriais possui uma estimativa inicial da postura do robô e usa os dados coletados pelos sensores, em conjunto com um mapa do ambiente, para produzir uma estimativa mais precisa da postura, que oferece um valor de maior confiança em relação à postura real do robô. Uma dificuldade é que os dados sensoriais são corrompidos por erros de medidas derivados de diversas fontes, como ruídos, quantização, dispositivos de digitalização, deslizamentos do robô, entre outras. Sensores distintos medem diferentes propriedades físicas, corrompidas por diversos erros de medida. O uso de dados oriundos de vários sensores fornece informação redundante e complementar, que pode ser processada para derivar uma estimativa combinada com o objetivo de aumentar a confiança na estimativa final da postura. Nesta dissertação é proposto ELViS, um sistema que estima a localização de um robô móvel equipado com odômetros, uma câmera de vídeo e um semi-anel frontal de 8 sonares, o qual opera, com sucesso, em um ambiente interno, estruturado e estático. Assume-se que o robô navega sobre uma superfície plana e que diversos segmentos de retas possam ser identificados nas imagens do ambiente. Para aumentar a seletividade dos marcos visuais e diminuir a complexidade computacional no processamento e correspondência dos dados com os modelos, elementos do ambiente são representados por modelos minimalistas, possibilitando o uso do ELViS em um grande número de aplicações onde o custo ou tempo de execução sejam fatores limitantes. ELViS foi implementado e testado utilizando dois estimadores baseados em Filtro de Kalman. Os resultados, obtidos com robôs reais e em simulações, indicam direções bastante promissoras. / A key component of a mobile robot system is the ability to localize itself accurately, which involves estimating its pose with respect to some global representation of space. The general specification of a sensor-based localization approach starts with an initial estimate of the robot\'s pose and uses sensor data in conjunction with a map to produce a refined pose estimate that has an increased confidence about the true pose of the robot. One of the main difficulties is that sensor data is corrupted by measurement errors. These errors can arise from noise, quantization, digitalization artifacts, wheel slippage, and other such sources. Different sensors measure different physical properties, which are corrupted by different sources of measurement errors. The use of data from multiple sensors provides redundant and complementary information that can be processed to obtain a combined estimate aiming at an increase in the confidence of the final pose estimate. In this work we propose ELViS, a system that estimates the localization of a mobile robot equipped with odometers, a video camera and a frontal semi-ring of 8 sonar sensors, and that operates successfully in stationary and structured indoor environments. It is assumed that the robot navigates on flat surfaces and that straight lines can be identified in the environment image acquired by the camera. To increase selectivity of the landmarks and reduce computational complexity in data processing and matching to the map, environment features are represented using minimalist models in the map. This allows the use of ELViS in a large number of applications where tight budget or execution time constraints exist. ELViS has been implemented and tested using two estimators based on the Kalman Filter. The results, obtained with the real robots and in series of simulation runs, indicate promising directions.

Um componente fundamental no sistema de um robô móvel consiste na habilidade de localizar-se acuradamente, o que envolve estimar sua postura em relação a uma representação global do espaço. A especificação geral de uma abordagem de localização baseada em dados sensoriais possui uma estimativa inicial da postura do robô e usa os dados coletados pelos sensores, em conjunto com um mapa do ambiente, para produzir uma estimativa mais precisa da postura, que oferece um valor de maior confiança em relação à postura real do robô. Uma dificuldade é que os dados sensoriais são corrompidos por erros de medidas derivados de diversas fontes, como ruídos, quantização, dispositivos de digitalização, deslizamentos do robô, entre outras. Sensores distintos medem diferentes propriedades físicas, corrompidas por diversos erros de medida. O uso de dados oriundos de vários sensores fornece informação redundante e complementar, que pode ser processada para derivar uma estimativa combinada com o objetivo de aumentar a confiança na estimativa final da postura. Nesta dissertação é proposto ELViS, um sistema que estima a localização de um robô móvel equipado com odômetros, uma câmera de vídeo e um semi-anel frontal de 8 sonares, o qual opera, com sucesso, em um ambiente interno, estruturado e estático. Assume-se que o robô navega sobre uma superfície plana e que diversos segmentos de retas possam ser identificados nas imagens do ambiente. Para aumentar a seletividade dos marcos visuais e diminuir a complexidade computacional no processamento e correspondência dos dados com os modelos, elementos do ambiente são representados por modelos minimalistas, possibilitando o uso do ELViS em um grande número de aplicações onde o custo ou tempo de execução sejam fatores limitantes. ELViS foi implementado e testado utilizando dois estimadores baseados em Filtro de Kalman. Os resultados, obtidos com robôs reais e em simulações, indicam direções bastante promissoras. / A key component of a mobile robot system is the ability to localize itself accurately, which involves estimating its pose with respect to some global representation of space. The general specification of a sensor-based localization approach starts with an initial estimate of the robot\'s pose and uses sensor data in conjunction with a map to produce a refined pose estimate that has an increased confidence about the true pose of the robot. One of the main difficulties is that sensor data is corrupted by measurement errors. These errors can arise from noise, quantization, digitalization artifacts, wheel slippage, and other such sources. Different sensors measure different physical properties, which are corrupted by different sources of measurement errors. The use of data from multiple sensors provides redundant and complementary information that can be processed to obtain a combined estimate aiming at an increase in the confidence of the final pose estimate. In this work we propose ELViS, a system that estimates the localization of a mobile robot equipped with odometers, a video camera and a frontal semi-ring of 8 sonar sensors, and that operates successfully in stationary and structured indoor environments. It is assumed that the robot navigates on flat surfaces and that straight lines can be identified in the environment image acquired by the camera. To increase selectivity of the landmarks and reduce computational complexity in data processing and matching to the map, environment features are represented using minimalist models in the map. This allows the use of ELViS in a large number of applications where tight budget or execution time constraints exist. ELViS has been implemented and tested using two estimators based on the Kalman Filter. The results, obtained with the real robots and in series of simulation runs, indicate promising directions.

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.

In marine environments, acoustic wave propagation is determined by sound-speed variations in the water column (related to salinity, temperature and pressure) , and seafloor properties in shallow environments. The refraction index variations and the boundary conditions guide the wave propagation so that an important amount of acoustic energy can propagate over long distances. Measurements of acoustic transmissions coupled with propagation models can be inverted to infer the water column properties (tomography) and the seafloor and subseafloor properties (geoacoustics). In this thesis a new method for shallow water inversion based on the sequential assimilation of acoustic measurements in Kalman filters is developed. Filtering algorithms for nonlinear systems, as the ensemble Kalman filter (EnKF), enable the integration of complex acoustic propagation models in the measurement model. The inverse problem is here reformulated into a state-space model to track sequentially the parameters (temperature, receiver positions, etc.) and their uncertainty by filtering regularly new acoustic data. Different applications are proposed to demonstrate the sequential acoustic filtering approach. First, the problem of characterizing horizontal inhomogeneities in the sound-speed field between an acoustic source and a vertical array of receivers is addressed. Starting from a range-averaged sound-speed profile, the filtering of complex multifrequency data enables the estimate and tracking of the range-dependence of the sound-speed field. The second application deals with the geoacoustic inversion problem based on a mobile source-receiver setup. The filtering approach is shown to provide more stable results than conventional inversion methods with a reduced computational burden. The last application is dedicated to the tracking of specific oceanic structures affecting the sound-speed field, here thermal fronts. An original parameterization scheme which is specific to the tracked feature is developed and enables to monitor the principal characteristics of the sound-speed field by filtering multifrequency acoustic data. This work shows that the sequential filtering approach of transmitted acoustic data can lead to environmental estimates on spatial and temporal scale of interest for regional or coastal oceanographic models and can supplement the dataset assimilated nowadays for forecasting purposes./Dans les environnements marins, la propagation des ondes acoustiques est directement conditionnée par les variations de vitesse de propagation dans l'eau (liée à la température, la salinité et la pression hydrostatique), ainsi que les propriétés du fond, lorsque le milieu est peu profond. La propagation de ces ondes, typiquement guidée par les variations d'indice de réfraction et les conditions aux limites, permet de transmettre une quantité d'énergie acoustique importante sur de longues distances. Associées à des modèles de propagation, des mesures de transmission acoustique peuvent être inversées afin de déterminer les propriétés de l'environnement sondé, que ce soit de la colonne d'eau (tomographie) ou du fond marin (géoacoustique). Dans cette thèse, une nouvelle méthode d'inversion en milieu peu profond, basée sur l'assimilation séquentielle de mesures acoustiques dans des filtres de Kalman, est développée. Les algorithmes de filtrage développés pour les systèmes non linéaires, tel que l'ensemble Kalman filter (EnKF), permettent d'intégrer des modèles de propagation acoustique complexes au sein du modèle de mesure. Le problème inverse est reformulé de façon séquentielle, en un modèle d'espace d'états, de sorte que l'évolution des paramètres (température, positions des récepteurs, etc.) et de leur incertitude est suivie au fur et à mesure de l'assimilation de nouvelles mesures. Différentes applications sont proposées pour démontrer les performances du filtrage séquentiel. Le premier problème abordé est celui de l'inversion et du suivi des inhomogénéités horizontales du champ de vitesse entre une source acoustique et une antenne verticale de récepteurs. A partir d'un profil de vitesse moyen sur la distance source-récepteurs, le filtrage de mesures complexes multi-fréquences permet d'estimer la dépendance horizontale du champ de vitesse et son évolution au cours du temps. La nature séquentielle de l'algorithme de filtrage motive la seconde application, dédiée à l'estimation des paramètres géoacoustiques d'un environnement à partir d'une configuration source-récepteur mobile. Les résultats démontrent que l'approche par filtrage permet d'obtenir des estimations géoacoustiques plus stables que celles obtenues par les méthodes d'inversion conventionnelles avec un coût de calcul réduit. La troisième et dernière application est dédiée au suivi de structures océaniques marquées, tels que les fronts thermiques. Une paramétrisation originale spécifique à la structure inversée est proposée et permet d'estimer et de suivre les caractéristiques principales du champ de température par filtrage de données acoustiques multi-fréquences. Ce travail montre que l'approche séquentielle de l'inversion des données acoustiques peut mener à des estimations environnementales sur des échelles spatiales et temporelles d'intérêt pour les modèles océanographiques côtiers et régionaux, de façon à compléter les données assimilées quotidiennement pour les prédictions.

Auditory brainstem response (ABR) evaluation has been one of the most reliable methods for evaluating hearing loss. Clinically available methods for ABR tests require averaging for a large number of sweeps (~1000-2000) in order to obtain a meaningful ABR signal, which is time consuming.  This study proposes a faster new method for ABR filtering based on wavelet-Kalman filter that is able to produce a meaningful ABR signal with less than 500 sweeps. The method is validated against ABR data acquired from 7 normal hearing subjects with different stimulus intensity levels, the lowest being 30 dB NHL. The proposed method was able to filter and produce a readable ABR signal using 400 sweeps; other ABR signal criteria were also presented to validate the performance of the proposed method.

Multiple Hypothesis Tracking (MHT) is generally the preferred data association technique for tracking targets in clutter and with missed detections due to its increased accuracy over conventional single-scan techniques such as Nearest Neighbor (NN) and Probabilistic Data Association (PDA). However, this improved accuracy comes at the price of greater complexity. Sequential K-best MHT is a simple implementation of MHT that attempts to achieve the accuracy of multiple hypothesis tracking with some of the simplicity of single-frame methods. Our first major objective is to determine under what general conditions Sequential K-best data association is preferable to Probabilistic Data Association. Both methods are implemented for a single-target, single-sensor scenario in two spatial dimensions. Using the track loss ratio as our primary performance metric, we compare the two methods under varying false alarm densities and missed-detection probabilities. Upon implementing a single-target Sequential K-best MHT tracker, a fundamental problem was observed in which the tracks coalesce. The second major thrust of this research is to compare different approaches to resolve this issue. Several methods to detect track coalescence, mostly based on the Mahalanobis and Kullback-Leibler distances, are presented and compared.

This thesis provides a novel approach to the problem of state estimation for discrete-time nonlinear systems in the presence of large model uncertainties. Though classical nonlinear Kalman filters such as the extended Kalman filter (EKF) can handle uncertainties by increasing the value of noise covariances, this is only applicable to systems with small uncertainties. To this end, a discretetime robust extended Kalman filter (REKF) is formulated and applied to examples from the fields of aerospace engineering and signal processing with an emphasis on attitude estimation for small unmanned aerial vehicles (UAVs) and image processing under the influence of atmospheric turbulence. The robust filter is an approximate set-valued state estimator where the Riccati and filter equations are obtained as an approximate solution to a reverse-time optimal control problem defining the set-valued state estimator. The advantages of the REKF over the classical EKF are investigated for examples from the fields aerospace engineering and signal processing where large model uncertainties are introduced. In the case of small UAVs, an alternative attitude estimation algorithm based on the REKF is proposed in the event of gyroscopic failure and the inability of the vehicle to carry redundant sensors due to limited payload capabilities. In the case of image reconstruction under atmospheric turbulence, a robust pixel-wandering (random shifts) scheme is proposed to aid the process of image reconstruction. Also, problems pertaining to platform vibration analysis for aerospace vehicles and a frequency demodulation process in the presence of channel-induced uncertainties is also discussed.

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.