The fuzzy Kalman filter: State estimation using possibilistic techniques

A new method to implement fuzzy Kalman filters is introduced. The combination of possibilistic techniques and the extended Kalman filter has special application in fields where inaccurate information is involved. The novelty of this article comes from the fact that by using possibility distributions, instead of Gaussian distributions, a fuzzy description of the expected state and observation is sufficient to obtain a good estimation. Some characteristics of this approach are that uncertainty does not need to be symmetric, and that a wide region of possible values for the expectations is allowed. To implement the algorithm, this approach also contributes a method to propagate uncertainty through the process model and the observation model, based on trapezoidal possibility distributions. Finally, several examples of a real mobile robot moving through a localization process, while using qualitative landmarks, are shown.