Conventional snapshot Receiver Autonomous Integrity Monitoring (RAIM) algorithms, which use a single set of measurements collected simultaneously, have limited performances to check the integrity of GNSS in safetycritical civil aviation applications when vertical guidance requirements are applied. In this context, snapshot and sequential RAIM FDE algorithms based on the constrained Generalized Likelihood Ratio (GLR) test have been proposed. These techniques, described in this paper, are based on a formalized definition of a horizontal or vertical error that must be considered as a positioning failure and consist in computing for each epoch and for each satellite channel a minimal additional pseudo range bias that leads to such situations. Proceeding like this allows partially compensating the lack of availability of conventional methods. As such, sequential technique is particularly attractive. Indeed this algorithm takes into account history of measurements to make its decision and moreover the pseudo range correlation is directly integrated through an autoregressive (AR) model. The purpose of our study is to benefit fully from these improvements by targeting more complex fault profiles. A sequential constrained GLR is designed to detect combined step ramp pseudo range errors. Our goal is to protect ourselves from faults that only depend on two parameters: initial position (amplitude of the step) and speed (rate of the slope) and that tend to lead to a positioning failure within an observation window ?t . A first evaluation of this advanced RAIM performances is presented in this paper. The robustness of this method is assessed for several profiles of additional error through a comparison of detection rates. The impact of the constellation geometry on our RAIM availability targeting at APV (APproach with Vertical guidance) requirements is also studied. The results obtained show that the robustness of the existing techniques has been improved by our method. For a combined constellation GPS + Galileo, this first performance evaluation is quite encouraging, before a complete study on a world wide case.