This paper deals with the Simultaneous Localization and Map building (SLAM) problem using an implementation of the Polynomial Extended Kalman Filter (PEKF). The proposed PEKF implementation is a filtering algorithm which is a polynomial transformation of state evolution and measurement equations. The performances of the algorithm have been evaluated through simulations. The comparison with the standard Extended Kalman Filter shows that the PEKF provides more consistent estimates in a SLAM framework. Experiments on real data are presented too.