Metodologia para Filtragem de Kalman Fuzzy Tipo-2 Intervalar Baseada em Modelagem Computacional das Componentes Espectrais Não-Observáveis de Dados Experimentais.

Abstract

In this dissertation, a methodology for design of Kalman filters, using interval type-2 fuzzy models, in discrete time domain, via spectral decomposition of experimental data, is proposed. The adopted methodology consists of recursive parametric estimation of local state space linear submodels of interval type-2 fuzzy Kalman filter for tracking and forecasting of the dynamics inherited to experimental data, using an interval type-2 fuzzy version of Observer/Kalman Filter Identification (OKID) algorithm. The partitioning of the experimental data is performed by interval type-2 fuzzy Gustafson-Kessel clustering algorithm. The interval Kalman gains in the consequent proposition of interval type-2 fuzzy Kalman filter are updated according to unobservable components computed by recursive spectral decomposition of experimental data. Computational results illustrate the efficiency of proposed methodology, as compared to approaches widely cited in the literature, for filtering and tracking the state variables of Lorenz’s chaotic attractor in a noisy environment, as well as filtering and tracking the reference trajectory through state variables of Chen’s chaotic attractor in noisy environment and time delays. Experimental results illustrate the applicability of proposed methodology for adaptive tracking and real time forecasting the dynamic spreading behavior of novel coronavirus 2019 (COVID-19) outbreak in state of Maranhão and Brazil.