Integrity is an important index for GNSS-based navigation and positioning, and the receiver autonomous integrity monitoring ( RAIM) algorithm has been presented for integrity applications. In the integrated navigation systems of a global navigation satellite system ( GNSS) and inertial navigation system ( INS) ,the conventional RAIM algorithm has been developed to extended receiver autonomous integrity monitoring (ERAIM). However, the ERAIM algorithm may fail and a false alarm may generate once the measurements are contaminated by significant outliers, and this problem is rarely discussed in the existing literatures. In this paper, a robust fault detection and the corresponding data processing algorithm are proposed based on the ERAIM algorithm and the robust estimation. In the proposed algorithm, weights of the measurements are adjusted with the equivalent weight function, and the efficiency of the outlier detection and identification is improved, therefore, the estimates become more reliable, and the probability of the false alarm is decreased. Experiments with the data collected under actual environments are implemented, and results indicate that the proposed algorithm is more efficient than the conventional ERAIM algorithm for multiple outliers and a better filtering performance is achieved.