Robust positioning and navigation of a mobile robot in an urban environment is implemented by fusing the Global Positioning System (GPS) and Inertial Navigation System (INS) data with the aid of a motion estimator. To select and isolate malicious satellite signals and guarantee the minimum number of GPS signals for the localization, an enhanced fault detection and isolation (FDI) algorithm with a short-term memory has been developed in this research. When there are sufficient satellite signals for positioning, the horizontal dilution of precision (HDOP) has been applied for selecting the best four satellite signals to localize the mobile robot. Then, the GPS data are fused with INS data by a Kalman filter (KF) for a straight path and a curved motion estimator (CME) for a curved path. That is, the INS data are properly fused to the GPS data through the KF or CME process. To verify the effectiveness of the proposed algorithm, experiments using a mobile robot have been carried out on a university campus.