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Master's Dissertation
DOI
10.11606/D.18.2016.tde-18022016-101220
Document
Author
Full name
Aline Fernanda Bianco
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2005
Supervisor
Committee
Terra, Marco Henrique (President)
Ishihara, João Yoshiyuki
Nascimento, Vitor Heloiz
Title in Portuguese
Filtros de Kalman para sistemas singulares em tempo discreto
Keywords in Portuguese
Equação de Riccati
Estimativa de estados
Filtragem de Kalman
Sistemas dinâmicos
Sistemas singulares
Tempo discreto
Abstract in Portuguese
Esta dissertação apresenta um estudo dos filtros de Kalman para sistemas singulares em tempo discreto. Novos algoritmos são formulados para as estimativas filtradas, preditoras e suavizadas com as correspondentes equações de Riccati para sistemas singulares variantes no tempo. Nesta dissertação considera-se também uma aproximação do problema de filtragem de Kalman como um problema determinístico de ajuste ótimo de trajetória. A formulação proposta permite considerar um atraso no sinal de medida, sendo permitida a correlação entre os estados e os ruídos da medida. Apresentam-se também as provas da estabilidade e da convergência destes filtros.
Title in English
Kalman filters for discrete time singular systems
Keywords in English
Discrete-time
Dynamic systems
Kalman filtering
Riccati equation
Singular systems
State estimation
Abstract in English
This dissertation presents a study of Kalman filters for singular systems in discrete time. New algorithms are developed for the Kalman filtered, predicted and smoothed estimate recursions with the corresponding Riccati equations for time-variant singular systems. This dissertation addresses the Kalman filtering problem as a deterministic optimal trajectory fitting problem. The problem is formulated taking into account one delay in the measured signals and correlations between state and measurement noises. In the final, this work presents the stability and convergence proofs of these filters.
 
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Publishing Date
2016-02-18
 
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