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Abstract(s)
A estimação em tempo real é um dos tópicos mais importantes na engenharia,
principalmente em sistemas não-lineares, presentes em praticamente todas as aplicações
aeroespaciais. Na indústria aeroespacial, há cada vez mais a tendência de utilizar
instrumentos, sensores e métodos de estimação que sejam precisos, leves e com baixos
custos computacional e financeiro.
O termo filtragem ou estimação é utilizado para o conjunto de técnicas e algoritmo que
permitem obter uma redução de ruídos ou erros de medição além de estimar estados não
mensuráveis diretamente. A grande dificuldade encontra-se justamente na complexidade
dos sistemas observados, que podem apresentar dinâmica altamente não-linear, além de
ruídos e baixa disponibilidade de dados, o que torna a seleção do método de filtragem um
fator muito importante para que haja o máximo de redução do erro de estimação.
Um dos métodos mais importantes desenvolvidos foi o filtro de Kalman linear, considerado
filtro ótimo para sistemas lineares. Mas, visto que a maioria dos sistemas reais envolve
dinâmica não-linear, outros métodos foram desenvolvidos com vista a superar este impasse.
Métodos como o famoso filtro de Kalman Estendido (EKF – Extended Kalman Filter), o
filtro de Kalman Unscented (UKF – Unscented Kalman Filter) e o filtro de Kalman Pseudolinear (PSELIKA – Pseudo Linear Kalman Filter) foram algumas das soluções
implementadas que tiveram sucesso em aplicações reais, apresentando vantagens e
limitações particulares.
Para o filtro EKF, a sua principal limitação é o seu comportamento errático e possivelmente
divergente em sistemas altamente não-lineares, ou com estimações iniciais imprecisas. Já
para o UKF, a dimensão do estado pode aumentar significativamente a complexidade
temporal do algoritmo, o que pode torná-la uma solução inviável para tempo real. O filtro
PSELIKA apresenta limitação parecida onde a complexidade das operações efetuadas é a
principal causa do custo computacional elevado.
Destes métodos, o PSELIKA chama atenção pelo facto de ser aplicável em praticamente
qualquer sistema não-linear, dentro das condições necessárias, mas sendo possível utilizar
os métodos de filtragem linear ao modelar a dinâmica do sistema numa estrutura pseudolinear. A limitação é dada pela necessidade de resolver a equação Algébrica de Riccati
associada e realizar inversões matriciais para o cálculo da matriz de ganho do sistema,
necessitando bastantes recursos computacionais. Assim, com o objetivo de reduzir o custo computacional e melhorar o desempenho, as redes
neuronais têm sido integradas aos métodos de filtragem. Estas são ferramentas
extraordinárias que atuam como funções não-lineares capazes de obter conhecimento
experimental, e neste caso, podem atuar para prever os cálculos efetuados durante o método
de filtragem PSELIKA.
De forma a reduzir a principal limitação do método de estimação PSELIKA, aproveitando
do facto de apresentar uma estrutura pseudo-linear, esta dissertação propôs a integração de
uma rede neuronal do tipo Perceptron de Múltiplas Camadas (MLP- Multilayer
Perceptron) ao algoritmo PSELIKA, tendo como principal objetivo a redução do custo
computacional original, implementando, por fim, um algoritmo denominado PSELIKAMLP.
Com vista a validar a utilização do algoritmo, nesta dissertação são abordados dois casos de
estudo: a estimação da taxa angular e atitude de um veículo aeroespacial, além da estimação
da órbita de um satélite artificial. Nestes, são comparados a exatidão, complexidade
temporal e espacial entre o algoritmo implementado, o filtro EKF e o filtro PSELIKA.
Os resultados demonstram que o algoritmo implementado foi capaz de reduzir
significativamente o tempo computacional do método PSELIKA, sem um grande
detrimento da exatidão da estimação, mas apresentando complexidade espacial superior.
Assim, é uma possível aplicação para a redução do custo computacional servindo de
complemento para o algoritmo original.
Real-time estimation is one of the most important topics in engineering, especially in nonlinear systems, present in practically all aerospace applications. In the aerospace industry, there is an increasing tendency to use instruments, sensors and estimation methods that are precise, lightweight and with low computational and financial costs. The term filtering or estimation is used for the set of techniques and algorithms that allow reducing noise or measurement errors in addition to estimating states that cannot be measured directly. The great difficulty lies precisely in the complexity of the observed systems, which can present very non-linear dynamics in addition to noise and low data availability, which makes the selection of the filtering method a very important factor for maximum reduction of the estimation error. One of the most important methods developed was the linear Kalman filter, considered an optimal filter for linear systems. But since most real systems involve non-linear dynamics, other methods have been developed to overcome this impasse. Methods such as the famous Extended Kalman filter (EKF), the Unscented Kalman filter (UKF) and the Pseudo-linear Kalman filter (PSELIKA) were some of the solutions implemented that have been successful in real applications, presenting advantages and limitations. For the EKF filter, its main limitation is its erratic and possibly divergent behavior in highly non-linear systems, or with imprecise initial estimations. As for UKF, the dimension of the state can significantly increase the temporal complexity of the algorithm, which can make it an unfeasible solution for real time. The PSELIKA filter presents a similar limitation where the complexity of the operations performed is the main cause of the high computational cost. Of these methods, PSELIKA draws attention because it is applicable to practically any nonlinear system, within the necessary conditions, but it is possible to use linear filtering methods when modeling the system dynamics in a pseudo-linear structure. The limitation is given by the need to solve the associated Algebraic Riccati equation and perform matrix inversions to calculate the system's gain matrix, requiring considerable computational resources. Thus, with the aim of reducing computational cost and improving performance, neural networks have been integrated into filtering methods. These are extraordinary tools that act as non-linear functions capable of obtaining experimental knowledge, and in this case, can act to predict the calculations carried out during the PSELIKA filtering method. To reduce the main limitation of the PSELIKA estimation method, taking advantage of the fact that it presents a pseudo-linear structure, this dissertation proposed the integration of a Multilayer Perceptron (MLP- Multilayer Perceptron) neural network into the PSELIKA algorithm, with the main objective of reducing the original computational cost, finally implementing an algorithm called PSELIKA-MLP. With a view to validate the use of the algorithm, this dissertation addresses two case studies: the estimation of the angular rate and attitude of an aerospace vehicle, in addition to the estimation of the orbit of an artificial satellite. In these, the accuracy, temporal and spatial complexity between the implemented algorithm, the EKF filter and the PSELIKA filter are compared. The results demonstrate that the implemented algorithm was able to significantly reduce the computational time of the PSELIKA method, without a major detriment to estimation accuracy, but presenting superior spatial complexity. Thus, it is a possible application to reduce computational cost by serving as a complement to the original algorithm.
Real-time estimation is one of the most important topics in engineering, especially in nonlinear systems, present in practically all aerospace applications. In the aerospace industry, there is an increasing tendency to use instruments, sensors and estimation methods that are precise, lightweight and with low computational and financial costs. The term filtering or estimation is used for the set of techniques and algorithms that allow reducing noise or measurement errors in addition to estimating states that cannot be measured directly. The great difficulty lies precisely in the complexity of the observed systems, which can present very non-linear dynamics in addition to noise and low data availability, which makes the selection of the filtering method a very important factor for maximum reduction of the estimation error. One of the most important methods developed was the linear Kalman filter, considered an optimal filter for linear systems. But since most real systems involve non-linear dynamics, other methods have been developed to overcome this impasse. Methods such as the famous Extended Kalman filter (EKF), the Unscented Kalman filter (UKF) and the Pseudo-linear Kalman filter (PSELIKA) were some of the solutions implemented that have been successful in real applications, presenting advantages and limitations. For the EKF filter, its main limitation is its erratic and possibly divergent behavior in highly non-linear systems, or with imprecise initial estimations. As for UKF, the dimension of the state can significantly increase the temporal complexity of the algorithm, which can make it an unfeasible solution for real time. The PSELIKA filter presents a similar limitation where the complexity of the operations performed is the main cause of the high computational cost. Of these methods, PSELIKA draws attention because it is applicable to practically any nonlinear system, within the necessary conditions, but it is possible to use linear filtering methods when modeling the system dynamics in a pseudo-linear structure. The limitation is given by the need to solve the associated Algebraic Riccati equation and perform matrix inversions to calculate the system's gain matrix, requiring considerable computational resources. Thus, with the aim of reducing computational cost and improving performance, neural networks have been integrated into filtering methods. These are extraordinary tools that act as non-linear functions capable of obtaining experimental knowledge, and in this case, can act to predict the calculations carried out during the PSELIKA filtering method. To reduce the main limitation of the PSELIKA estimation method, taking advantage of the fact that it presents a pseudo-linear structure, this dissertation proposed the integration of a Multilayer Perceptron (MLP- Multilayer Perceptron) neural network into the PSELIKA algorithm, with the main objective of reducing the original computational cost, finally implementing an algorithm called PSELIKA-MLP. With a view to validate the use of the algorithm, this dissertation addresses two case studies: the estimation of the angular rate and attitude of an aerospace vehicle, in addition to the estimation of the orbit of an artificial satellite. In these, the accuracy, temporal and spatial complexity between the implemented algorithm, the EKF filter and the PSELIKA filter are compared. The results demonstrate that the implemented algorithm was able to significantly reduce the computational time of the PSELIKA method, without a major detriment to estimation accuracy, but presenting superior spatial complexity. Thus, it is a possible application to reduce computational cost by serving as a complement to the original algorithm.
Description
Keywords
Aplicações Aeroespaciais. Filtragem Não-Linear Filtro de Kalman Pseudo-Linear Redes Neuronais Artificiais Redução do Custo Computacional