A novel interval type-2 fuzzy Kalman filtering and tracking of experimental data

In this paper, a methodology for design of fuzzy Kalman filter, 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 for filtering and tracking the time delayed state variables of Chen's chaotic attractor in a noisy environment, and experimental results illustrate its applicability for adaptive and real time forecasting the dynamic spread behavior of novel Coronavirus 2019 (COVID-19) outbreak in Brazil.