Computational Approach For Real-Time Interval Type-2 Fuzzy Kalman Filtering and Forecasting via Unobservable Spectral Components of Experimental Data

Abstract

In this paper, a methodology for design of Kalman filter, using interval type-2 fuzzy systems, 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. Results illustrate the efficiency of proposed methodology, as compared to other approach widely cited in the literature, for filtering and tracking the state variables of Lorenz’s chaotic attractor in a noisy environment, and its applicability for adaptive and real-time forecasting the dynamic spread behavior of novel coronavirus 2019 (COVID-19) outbreak in state of Maranhão and Brazil.