Filtragem Adaptativa de Kalman Nebulosa Tipo-2 Intervalar Baseada em Critério de Máxima Verossimilhança

Abstract

This dissertation proposes a methodology for an interval type-2 fuzzy Kalman Filter project based on maximum likelihood criteria. The developed methodology consists of offline and online stages. In the first stage, an initial data set is used for training, while in the online stage, a model update is performed for each new available measurement. In the offline stage, an initial data set is pre-processed by the batch version of the singular spectral analysis. The resultant data set is then partitioned by the interval type-2 fuzzy version of the maximum likelihood estimation clustering algorithm based on principal component analysis. By the end of the offline stage, a Kalman filter sub model is estimated for each obtained partition. This estimation is performed by a fuzzy version of the Observer/Kalman Filter Identification algorithm, developed in a way that allows each rule or submodule to have its own order. This operation is based on the Akiake information criterion. During the online operation, the model is updated with each new measurement. For this, an adaptation for the recursive singular spectral analysis update is created in such a way that redundant operations are removed, reducing the time required to update the most significant components of the new measurement. The difference between the model estimate and the updated spectral components is used to update the submodels via the recursive and refined Observer/Kalman Filter Identification algorithm, which was designed to allow time change in each submodel order. Finally, a modeling of the data set uncertainty is developed and used to adapt the fuzzy weighting expoent used in the clustering algorithm, allowing the estimated interval to adapt to the data set. In order to test the proposed methodology with the intention of demonstrating its efficacy in different scenarios, computational and experimental tests were performed. As computational results, the multivariable forecast about the position and velocity of the PRISMA spacecrat formation stands out. As experimental results, the interval tracking of the helicopter with 2 degrees of freedom, and the interval forecasting of an intermediary training rocket (suborbital vehicle VS-30) of the Alcântara launch center stands out.