The fuzzy Kalman filter: Improving its implementation by reformulating uncertainty representation

Abstract

The fuzzy Kalman filter (FKF), introduced some years ago, is revisited. In the initial version, trapezoidal possibility distributions functions instead of gaussian probability distributions were proposed, and trapezius were modeled by four representative points. Nevertheless, and although the algorithm works properly, an implementation problem occurs when propagating uncertainty through a non-linear function in multi-variable systems, something that was solved by linearization. In this work we propose an alternative method to represent uncertainty, still using trapezoidal distributions, which avoids the previous inconvenience and eases the Kalman filter steps computation. We reformulate the FKF algorithm, presenting a new theoretical approach as well as validation tests in both simulation and a real mobile robot.