Contributions to the study of the filtering problem of Markov jump linear systems in the worst-case scenario

• Ano de defesa: 2022
• Autor(a) principal: Silva, Paulo Vitor da Mota
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Laboratório Nacional de Computação Científica; Coordenação de Pós-Graduação e Aperfeiçoamento (COPGA); Brasil; LNCC; Programa de Pós-Graduação em Modelagem Computacional
• Palavras-chave em Português: Markov, Processos de; Sistemas lineares de controle; Sistemas dinâmicos lineares; Filtros (Matemática); CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE
• Link de acesso: https://tede.lncc.br/handle/tede/350

Filtering problem of dynamical systems is of paramount importance, since in many situations found in practice it is quite difficult to have access to the state or the system parameters. In this work, we deal with the filtering problem of the so-called Markov Jumps Linear Systems (MJLS), an important class of dynamical systems within a wider structure of dynamic systems subject to sudden changes in its behavior. In this context, a salient feature of the MJLS is the fact that the partial observations may be associated with three different scenarios: (1) only the state variable is partially observable; (2) only the Markov chain (the mechanism that model the switching) is partially observable and (3) both, the state variable and the Markov parameter are partially observables, which is the worst-case scenario. In this work we will be particularly interested in the worst-case scenario (setting 3). In this case, it is a well-known fact that the optimal filter is nonlinear and infinite dimensional (not useful for applications). This, in turns, has given rise to the search of sub-optimal filter for this scenario where the so-called Interacting Multiple Model (IMM) is one of the most celebrated sub-optimal filters in this context and one which has been very popular in maneuvering targets tracking problems. A watershed in this worst-case scenario is the so-called best linear mean square filter (BLMS filter), which is an optimal linear filter that has the desirable properties of the Kalman filter. The aim of this work is to put forward a careful comparison between these filters. We present the characteristics of the filters, pointing out their similarities, differences and advantages. Then, we performed simulations of the filters for different situations to compare their respective performances. We conclude with an application, for the sake of comparison, in the context of maneuvering target tracking.