The combination of Global Navigation Satellite Systems (GNSS) and Inertial Navigation System (INS) has become the baseline of many transportation applications. 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 different robust estimators (such as M-estimators). We analyze first a fault-free case and compare the capacity of the inertial calibration with respect to the classical EKF with minimum variance criteria. Then, we consider different faulty scenarios where the pseudoranges contain one or several non-modeled biases. The tightly-coupled GNSS/INS robust Kalman filter performance in the presence of biases 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 biases effect thanks to the direct redundancy of the inertial sensor within the robust estimator.