This paper deals with H∞ Filter (HF)-Fuzzy logic based mobile robot localization and mapping as an approach to prevent the Finite Escape Time (FET) problem in HF. The FET problem has been limiting the HF capabilities in estimation for decades and has been one of the important aspects to be considered to ensure HF performs well during mobile robot observations. The proposed technique focusses on the HF innovation stage by including very few Fuzzy Logic rules, and fuzzy sets. The design is generally divided into two stages; firstly, the analysis of HF innovation characteristics and then the implementation of Fuzzy Logic technique into the system. The analysis also presents the preliminary study on different membership functions to discover the best possible technique to combine with HF based mobile robot localization. The simulation results proved that Fuzzy Logic can be used to avoid the FET from occurred while at the same time improving the estimation of both mobile robot and landmarks.