A Novel Fuzzy Kalman Filter for Mobile Robots Localization Fernando Matia Universidad Politecnica de Madrid Departamento de Automatica matia@etsii.upm.es Agustin Jimenez Universidad Politecnica de Madrid Departamento de Automatica ajimenez@etsii.upm.es Diego Rodriguez-Losada Universidad Politecnica de Madrid Departamento de Automatica drodri@etsii.upm.es Basil M. Al-Hadithi Universidad Alfonso X El Sabio Departamento de Electronica y Sistemas basil@uax.es Abstract A new method to implement fuzzy Kalman filters is introduced in this pa- per. This has special application in fields where inaccurate models or sen- sors are involved, such as in mobile robotics. The innovation consists in us- ing possibility distributions, instead of gaussian distributions. The main ad- vantage of this approach is that un- certainty is not needed to be symmet- ric, while a region of possible solutions is allowed. The contribution of this work also includes a method to prop- agate uncertainty through both the pro- cess and the observation models. This one is based on quantifying uncertainty as trapezoidal possibility distributions. Finally, the way to reduce the EKF in- consistence when large number of iter- ations are carried out is shown. Keywords: State Estimation, Kalman Filter, Fuzzy Logic, Mobile Robotics. 1 Introduction Mobile robots localization is traditionally car- ried out using probabilistic techniques. The well known Extended Kalman Filter (EKF) provides an accurate solution to mobile robots localization. Apparently, the only condition is to initiate appro- priately uncertainty matrices of the initial state es- timation P(0|0), the process model Q(k + 1) and the measurement model R(k + 1). Nevertheless, localization is done by combining incoming measures with an accurate map of the environment. This implies three main inherent problems to the EKF. First, initial maps of the environment are usually fuzzy. Second, mea- sure uncertainty is not gaussian and, indeed, is not symmetric. Third, uncertainty propagation through non-linear equations produce accumula- tive errors, which have demonstrated to become important when the robot moves hundreds of me- ters. At least the two first problems suggest the idea of representing uncertainty by using fuzzy logic. A novel Fuzzy Kalman filter (FKF) is presented in this paper. Many authors propose to combine fuzzy logic and the Kalman estimation process. [4] and [5] present a probabilistic EKF for mobile robots, where fuzzy rules are used to adapt uncertainty matrices Q(k) and R(k + 1). [7] applies fuzzy rules combined with a Kalman filter for mobile robots localization, but fuzzy logic is only used for sensor fusion outside the state estimation pro- cess. [6] goes further and uses fuzzy relations to represent both the observation model and the system model. Nevertheless, noise is white. [9] presents a fuzzy filter for a glucoregulatory sys- tem that has better performance that a conven- tional EKF, but still includes probability. Finally, [10] presents the unscented Kalman filter as a method to minimize the inconsistency problem of the EKF. This method does not use fuzzy logic, and proposes the use of higher order probabilistic measures. While existent works on FKF focus on using fuzzy rules and fuzzy relations, we propose to in-