Previously, conventional state estimation techniques have been used for state estimation in power systems. These conventional methods are based on steady state models. As a result of this, power system dynamics during disturbances or transient conditions are not adequately captured. This makes it challenging for operators in control centers to perform visual tracking of the system, proper fault diagnosis and even take adequate preemtive control measures to ensure system stability during voltage dips. Another challenge is that power systems are nonlinear in nature. There are multiple power components in operation at any given time making the system highly dynamic in nature. Consequently, the need to study and implement better dynamic estimation tools that capture system dynamics during disturbances and transient conditions is necessary. For this thesis work, we present the Unscented Kalman Filter (UKF) which integrates Unscented Transformation (UT) to Kalman Filtering. Our algorithm takes as input the output of a synchronous machine modeled in MATLAB/Simulink as well as data from a PMU device assumed to be installed at the terminal bus of the synchronous machine, and estimate the dynamic states of the system using a Kalman Filter. We have presented a detailed and analytical study of our proposed algorithm in estimating two dynamic states of the synchronous machine, rotor angle and rotor speed. Our study and result shows that our proposed methodology has better efficiency when compared to the results of the Extended Kalman Filter (EKF) algorithm in estimating dynamic states of a power system.  Our results are presented and analyzed on the basis of how accurately the algorithm estimates the system states following various simulated transient and small-signal disturbances.

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.

Este trabalho tem a finalidade de apresentar e comparar técnicas de redução de ruído utilizando como critérios de avaliação a mínima distorção espectral e a redução de ruído, na reconstrução dos sinais de voz degradados por ruído. Para tanto, utilizou-se os filtros de Kalman de tempo discreto e de freqüência discreta em conjunto com a técnica de subtração espectral de potência. Os sinais utilizados foram contaminados por ruídos branco e colorido, e a avaliação do desempenho dos algoritmos foi realizada tendo-se como parâmetros a relação sinal/ruído segmentada (SNRseg) e a distância de Itakura-Saito (d(a,b)). Após o processamento, verificou-se que a técnica, proposta neste trabalho, de filtragem de Kalman no tempo em conjunto com a subtração espectral de potência, apresentou resultados um pouco melhores em relação à filtragem de Kalman na freqüência em conjunto com a subtração espectral de potência. / This work has as main objective to present and to compare techniques of noise reduction using as evaluation criterion the low spectral distortion and the noise reduction in the reconstruction of corrupted speech signals. For so much, it was used the Kalman\'s filters in the time and frequency domain together with the technique of power spectral subtraction. The used signals were corrupted by white and colored noises and the evaluation of effectiveness of the algorithms was accomplished using the segmental signal-to-noise ratio (SNRseg) and the Itakura-Saito distance (d(a,b)). After the processing, it was noticed that the Kalman filtering in the time together with power spectral subtraction presented better results than the Kalman filtering in the frequency together with power spectral subtraction.

Este trabalho apresenta um modelo matemático para a inferência do estado emocional de um usuário ou interlocutor com base em suas expressões faciais. O modelo apresentado consiste em dois estágios básicos, responsáveis pelo tratamento de sinais e sua integração, respectivamente. No primeiro estágio, filtros de Kalman independentes são utilizados para o processamento paralelo dos sinais relativos às expressões faciais emocionais. O estágio de integração, por sua vez, aplica os sinais filtrados a um sistema no qual uma partícula desliza sobre uma superfície a qual representa os estados e transições emocionais. O estado emocional do interlocutor é inferido, quadro a quadro, por meio da inspeção da posição instantânea da partícula. Uma heurística de simulação-otimização baseada em recozimento simulado (simulated annealing), é introduzida a fim de automatizar o processo de ajuste dos parâmetros do modelo em conformidade com o algoritmo de detecção de expressões faciais escolhido. O modelo proposto foi validado utilizando-se um corpus contendo 51 vídeos. Os resultados são comparados à classificação realizada por um grupo de voluntários, correspondendo a esta em 92% dos casos. / This work presents a mathematical model for emotional state inference based solely on facial expressions. The presented model consists of two basic steps, which are responsible for signal processing and its integration, respectively. During the former, independent Kalman filters are employed for parallel processing of emotional facial expression related signals. The later step, integration, applies those filtered signals to a system where a massless particle slides along a surface representing the emotional states of interest and its transitions. The subjects emotional state is inferred from the particles instantaneous position at each frame. A simulation-optimization heuristic based on simulated annealing is introduced as for fully automatic parameter tuning technique, which allows for easily coupling between the proposed model and different facial expression detection algorithms. The proposed model is validated against 51 multimodal emotional videos. The results are compared to human-based classification and a 92% agreement rate is observed.

Este trabalho tem a finalidade de apresentar e comparar técnicas de redução de ruído utilizando como critérios de avaliação a mínima distorção espectral e a redução de ruído, na reconstrução dos sinais de voz degradados por ruído. Para tanto, utilizou-se os filtros de Kalman de tempo discreto e de freqüência discreta em conjunto com a técnica de subtração espectral de potência. Os sinais utilizados foram contaminados por ruídos branco e colorido, e a avaliação do desempenho dos algoritmos foi realizada tendo-se como parâmetros a relação sinal/ruído segmentada (SNRseg) e a distância de Itakura-Saito (d(a,b)). Após o processamento, verificou-se que a técnica, proposta neste trabalho, de filtragem de Kalman no tempo em conjunto com a subtração espectral de potência, apresentou resultados um pouco melhores em relação à filtragem de Kalman na freqüência em conjunto com a subtração espectral de potência. / This work has as main objective to present and to compare techniques of noise reduction using as evaluation criterion the low spectral distortion and the noise reduction in the reconstruction of corrupted speech signals. For so much, it was used the Kalman\'s filters in the time and frequency domain together with the technique of power spectral subtraction. The used signals were corrupted by white and colored noises and the evaluation of effectiveness of the algorithms was accomplished using the segmental signal-to-noise ratio (SNRseg) and the Itakura-Saito distance (d(a,b)). After the processing, it was noticed that the Kalman filtering in the time together with power spectral subtraction presented better results than the Kalman filtering in the frequency together with power spectral subtraction.

No Brasil a exploração do petróleo está crescendo cada vez mais principalmente com as atividades offshore devido às constantes descobertas de novas jazidas em alto mar. Isto cria a necessidade de embarcações que garantam operações mais seguras o que pode ser obtido com aquelas dotadas de sistemas de posicionamento dinâmico. O projeto de um sistema de posicionamento dinâmico não é simples sob o ponto de vista de controle já que é um sistema não-linear multivariável sobreatuado; e não é barato devido aos elevados custos de implementação. Portanto, para se projetar adequadamente este tipo de sistema é imprescindível a elaboração de meios para ensaiar toda a estrutura real em desenvolvimento num tanque de provas utilizando modelos em escala. Neste trabalho é mostrado o projeto, construção e testes da eletrônica embarcada de um aparato experimental para ensaios de veículos oceânicos em tanque de provas, cujo projeto baseou-se em aspectos técnicos importantes para seu bom funcionamento como a descentralização dos processamentos necessários, a comunicação sem fio robusta com um console central responsável pelo processamento de todos os algoritmos do controlador superior e a preocupação com a compatibilidade eletromagnética do sistema. O console central consiste de uma interface de comunicação com o usuário e dos blocos de controle que são o filtro de Kalman, o controlador e o alocador de empuxos. Nos ensaios o desempenho da eletrônica é averiguado experimentalmente e os excelentes resultados obtidos mostram que o modelo responde de acordo com os comandos do controlador, principalmente com relação aos controles localizados para cada motor de propulsor contribuindo assim para o bom comportamento do conjunto. / In Brazil the exploration of oil is increasing mainly with the offshore activities due to the new found deposits. This situation requires more safety vessels which can be achieved using dynamic positioning systems. As a dynamic positioning system is a multivariable non linear and overactuated system, its design is not simple; and it is also not cheap due to high implementation costs. Therefore, the development of experimental environments to adequately study and design this type of system is essential. This work shows the embedded electronic project and assembly of an experimental setup in order to test floating vessel models. The project was developed based on important technical aspects to guarantee a good performance like processing decentralization, robust wireless communication with a central console responsible by the all control algorithms and the concern with electromagnetic compatibility of the system. The central console is composed by a human interface, control and Kalman filter structures and a thruster allocation algorithm. The performance of the electronic structure is verified experimentally during the tests and the excellent results show that the model works, in accordance to the controller commands, mainly related to local thruster control which contributes to the good system behavior

As principais causas da redução da produtividade agrícola são os eventos climáticos, e a variável meteorológica de grande importância para a produção agrícola é a precipitação. Alguns dos problemas das bases de dados meteorológicos são a descontinuidade e dados faltantes. Nesse sentido, os dados de precipitação em ponto de grade (Gridpoint), são uma excelente fonte de informações em pesquisas climatológicas. Para superar os problemas de dados faltantes e construir um banco de dados completos é necessário um processo de imputação. Portanto, o objetivo do trabalho foi comparar metodologias de imputação, utilizou abordagens univariada e múltipla, e comparou o desempenho em termos de imputação em diferentes cenários de dados faltantes e utilizou a raiz do erro quadrático médio (RMSE) como métrica. Para séries de precipitação diária que tinham dados faltantes foi realizado a imputação pelo método imputação múltipla por equações encadeadas (MICE), utilizando a informação de mês, ano e precipitação em ponto de grade. Foram utilizados quatro modelos, nos quais a precipitação diária dependia de: mês; mês e ano; precipitação em ponto de grade; mês, ano e precipitação diária em ponto de grade. Utilizou-se a raiz do erro quadrático médio (RMSE) como métrica e para verificar as imputações, analisou-se a semelhança entre os dados observados e os dados imputados pelo Teste de Kolmogorov-Smirnov e pelos gráficos da média e variância das imputações. O modelo com o maior número de variáveis foi escolhido para imputar os dados faltantes das séries de precipitação diária. Nesse trabalho, o uso de dados de precipitação em ponto de grade mostrou ser na imputação de dados de séries de precipitação diária. Para uma série de precipitação diária completa, concentra-se na comparação e avaliação de métodos de imputação nas abordagens univariada e múltipla, para dados de precipitação diária. Na abordagem univariada, utilizou-se diferentes configurações filtro de Kalman, Média Móvel Ponderada e Decomposição Sazonal. Na abordagem múltipla, utilizou-se o método MICE, com diferentes modelos. Os dados faltantes foram estimados em uma série de precipitação diária, em que os dados faltantes foram gerados de maneira aleatória e em trechos e utilizou-se a raiz do erro quadrático médio (RMSE) como métrica. Os resultados identificaram que o método de Filtro de Kalman forneceu os menores valores de RMSE, para todos os cenários de dados faltantes. A aplicação do algoritmo Filtro de Kalman produziu melhores estimativas para os valores diários de precipitação. O Filtro de Kalman pode ser uma importante metodologia para imputação de dados de precipitação diária, garantido uma série temporal completa para análises de vários setores, dentre eles a agricultura. / The main causes of the reduction of agricultural productivity are the climatic events, and the meteorological variable of great importance for the agricultural production is precipitation. Some of the problems of meteorological databases are discontinuity and missing data. In this sense, grid point precipitation (Gridpoint) data is an excellent source of information in climatological research. To overcome missing data problems and build a continuous database, an imputation process is required. Therefore, this work has the objective of comparing two imputation methodologies, using the MICE method and the Kalman filter, and comparing the performance in terms of imputation in different scenarios of missing data, using root mean square error (RMSE) as metric. For series of daily precipitation that had missing data, imputation was carried out by the multiple imputation method by chain equations (MICE), using the information of month, year and precipitation in grid point. Four models were used, in which the daily precipitation depended on: month; month and year; precipitation in grid point; month, year and daily precipitation in grid point. The root mean squared error (RMSE) was used as a metric and to verify imputations, the similarity between the observed data and the data imputed by the Kolmogorov-Smirnov test and the mean and variance imputation graphs were analyzed. The model with the largest number of variables was chosen to impute missing data from the daily precipitation series. In this work, precipitation data in grid point showed the importance and advantages of their use as information in imputation of daily precipitation series data. For a complete daily precipitation series, it focuses on the comparison and evaluation of imputation methods in the univariate and multiple approaches for daily precipitation data. In the univariate approach, we used different Kalman filter configurations, Weighted Moving Average, and Seasonal Decomposition. In the multiple approach, the MICE method was used, with different models. The missing data were estimated in a series of daily precipitation, in which the missing data were generated randomly and in sections, and the root mean square error (RMSE) was used as a metric. The results identified that the Kalman Filter method provided the lowest RMSE values for all missing data scenarios. The application of the Kalman filter algorithm produced better estimates for the daily values of precipitation. The Kalman Filter can be an important methodology for imputation of daily precipitation data, ensuring a complete time series for analysis of several sectors, among them agriculture.

Design of nonlinear observers has received considerable attention since the early development of methods for linear state estimation. The most popular approach is the extended Kalman filter (EKF), that goes through significant degradation in the presence of nonlinearities, particularly if unmodeled dynamics are coupled to the process and the measurement. For uncertain nonlinear systems, adaptive observers have been introduced to estimate the unknown state variables where no priori information about the unknown parameters is available. While establishing global results, these approaches are applicable only to systems transformable to output feedback form. Over the recent years, neural network (NN) based identification and estimation schemes have been proposed that relax the assumptions on the system at the price of sacrificing on the global nature of the results. However, most of the NN based adaptive observer approaches in the literature require knowledge of the full dimension of the system, therefore may not be suitable for systems with unmodeled dynamics. We first propose a novel approach to nonlinear state estimation from the perspective of augmenting a linear time invariant observer with an adaptive element. The class of nonlinear systems treated here are finite but of otherwise unknown dimension. The objective is to improve the performance of the linear observer when applied to a nonlinear system. The approach relies on the ability of the NNs to approximate the unknown dynamics from finite time histories of available measurements. Next we investigate nonlinear state estimation from the perspective of adaptively augmenting an existing time varying observer, such as an EKF. EKFs find their applications mostly in target tracking problems. The proposed approaches are robust to unmodeled dynamics, including unmodeled disturbances. Lastly, we consider the problem of adaptive estimation in the presence of feedback control for a class of uncertain nonlinear systems with unmodeled dynamics and disturbances coupled to the process. The states from the adaptive EKF are used as inputs to the control law, which in target tracking usually takes the form of a guidance law. The applications of this approach lie in the areas of missile-target tracking, formation flight control and obstacle avoidance.

Vehicle motion and tire forces have been estimated using extended Kalman filters for many years. The use of extended Kalman filters is primarily motivated by the simultaneous presence of nonlinear dynamics and sensor noise. Two versions of extended Kalman filters are employed in this thesis: one using a deterministic tire-force model and the other using a stochastic tire-force model. Previous literature has focused on linear stochastic tire-force models and on linear deterministic tire-force models. However, it is well known that there exists a nonlinear relationship between slip variables and tire-force variables. For this reason, it is suitable to use a nonlinear deterministic tire-force model for the extended Kalman filter, and this is the novel aspect at this work. The objective of this research is to show the improvement of the extended Kalman filter using a nonlinear deterministic tire-force model in comparison to linear stochastic tire-force model. The simulation model is a seven degree-of-freedom bicycle model that includes vertical suspension dynamics but neglects the roll motion. A comparison between the linear stochastic tire-force model and the nonlinear deterministic tire-force model confirms the expected results. Simulation studies are performed on some illustrative examples obtaining good tracking performance.

A system for vessel characterization aimed at detecting deep vein thrombosis (DVT) in the lower limbs has been developed and evaluated using ultrasound image processing, location and force sensors measurements, blood flow information and a protocol based on the current clinical standard, compression ultrasound. The goal is to provide an objective and repeatable system to measure DVT in a rapid and standardized manner, as this has been suggested in the literature as an approach to improve overall detection of the disease. The system uses a spatial Kalman filter-based algorithm with an elliptical model in the measurement equation to detect vessel contours in transverse ultrasound images and estimate ellipse parameters, and temporal constant velocity Kalman filters for tracking vessel location in real-time. The vessel characterization also comprises building a 3-D vessel model and performing compression and blood flow assessments to calculate measures that indicate the possibility of DVT in a vessel. A user interface designed for assessing a vessel for DVT was also developed. The system and components were implemented and tested in simulations, laboratory settings, and clinical settings. Contour detection results are good, with mean and rms errors ranging from 1.47-3.64 and 3.69-9.67 pixels, respectively, in simulated and patient images, and parameter estimation errors of 5%. Experiments showed errors of 3-5 pixels for the tracking approaches. The measures for DVT were evaluated, independently and integrated in the system. The complete system was evaluated, with sensitivity of 67-100% and specificity of 50-89.5%. System learnability and memorability were evaluated in a separate user study, with good results. Contributions include a segmentation approach using a full parameter ellipse model in an extended Kalman filter, incorporating multiple measurements, an alternate sampling method for faster parameter convergence and application-specific initialization, and a tracking approach that includes a sub-sampled sum of absolutes similarity calculation and a method to detect vessel bifurcations using flow data. Further contributions include an integrated system for DVT detection that can combine ultrasound B-mode, colour flow and elastography images for vessel characterization, a system interface design focusing on usability that was evaluated with medical professionals, and system evaluations through multiple patient studies.