Interval type-2 evolving fuzzy Kalman filter for processing of unobservable spectral components from uncertain experimental data

Abstract

In this paper, an interval type-2 evolving fuzzy Kalman filter (IT2EFKF) is designed for processing unobservable spectral components of uncertain experimental data. The primary objective of the methodology proposed in the present research is to provide a novel mathematical tool for interval and spectral processing of uncertain experimental data in order to deal with real-world filtering, tracking, and forecasting problems. The adopted methodology consider the following steps: an initial model of the interval type-2 fuzzy Kalman filter, which is off-line identified from an initial window of the experimental data; the updating of antecedent proposition of interval type-2 fuzzy Kalman filter by using an interval type-2 formulation of evolving Takagi–Sugeno (eTS) clustering algorithm and the updating of consequent proposition by using a type-2 fuzzy formulation of Observer/Kalman Filter Identification (OKID) algorithm, taking into account the multivariable recursive Singular Spectral Analysis of the experimental data. Computational results for tracking the Mackey-Glass chaotic time series demonstrate the effectiveness of the proposed approach when compared to related methodologies from the literature, with superior results for RMSE of 0.0026. Experimental results for tracking a 2DoF helicopter illustrate its applicability, with superior results for RMSE and VAF of 0.00156 and 99.9874% for yaw angle, and of 0.00702 and 99.8863% for pitch angle, respectively.