The combination of Global Navigation Satellite Systems (GNSS) and Inertial Navigation System (INS) has become the baseline of many vehicular applications. However, in challenging GNSS scenarios, classical GNSS/INS integration estimators are very sensitive to multiple measurement faults (e.g., due to multipath). In this work, we design a tightly-coupled integration between GNSS and INS where we modify the update step of a classical Extended Kalman Filter (EKF) to consider more robust estimators, like M-estimators. We consider different faulty scenarios where the pseudoranges contain one or several non-modeled biases and ramps. The tightly-coupled GNSS/INS robust Kalman filter performance in the presence of faults is compared with the classical EKF and with a loosely-coupled Robust-GNSS/INS approach. The robust tightly-coupled version is able to minimize more efficiently the faults effect thanks to the direct redundancy of the inertial sensor within the robust estimator.