The advent of new satellite signals with Galileo L1/E5 and modernized GPS L5 is expected to significantly improve navigation performance both in terms of accuracy and integrity monitoring. On the one hand, dual frequency measurements will allow to remove most of the ionospheric error degrading the pseudoranges. On the other hand, the opportunity of using two constellations of satellites for positioning will significantly improve the fault detection and exclusion (FDE) function availability by increasing the redundancy among the measurement sources. This enhancement comes at the expense an increased computational complexity when applying the existing integrity monitoring schemes. This paper focuses on Aircraft-based Autonomous Integrity Monitoring (AAIM) techniques where the GPS and Galileo are integrated with an Inertial Reference System (IRS). In this framework, we present an alternative approach for fault detection and exclusion based on the Generalized Likelihood Ratio algorithm which is well-known in the Control community. A few adaptations to the classical formulation are proposed to make the algorithm compliant with civil aviation requirements.