What is Spectral Decomposition

This chapter presents a methodology for designing of fuzzy Kalman filter (FKF) via spectral decomposition of the experimental data. The adopted methodology consists in the parametric estimation of local state-space linear submodels of a fuzzy model of the dynamic system, by means of a fuzzy algorithm based on least squares, as well as in the estimation of FKF gains from the fuzzy model, using the parallel and distributed compensation (PDC) method. The partitioning of experimental data is performed by the fuzzy C-Means (FCM) clustering algorithm, for the definition of the rule base as well as the nonlinear FKF characteristic. Considering the PDC method, the Kalman gains in the consequent of each FKF rule are updated as a function of the unobservable components resulting from the spectral decomposition of noisy experimental data. Computational and experimental results illustrate the good performance of the methodology presented when compared to relevant approaches from the literature.