The Possibilistic Kalman Filter: Definition and Comparison With the Available Methods

The Kalman filter (KF) is a commonly used algorithm for predicting the state variables of a system. It is based on the model of the system and some measurements (observed over time) that are characterized by their own uncertainty. This article defines a possibilistic KF whose main feature is to predict the values of the state variables and the associated uncertainty when uncertainty contributions of nonrandom nature are present. This possibilistic KF is defined in the mathematical framework of the possibility theory and employs random-fuzzy variables and the related mathematics since these variables can properly represent measurement results together with the associated uncertainty. A comparison with the available methods is provided, as well as the final validation.