Inertial Navigation Systems (INS) and Global Navigation Satellite Systems (GNSS) are often combined in vehicle navigation systems to ensure high accuracy navigation. The last generation of Inertial Measurement Unit (IMU) referred to as Micro-Electro-Mechanical Systems (MEMS) might be used in a lot of new applications thanks to their relatively low cost. Unfortunately, the information given by the MEMS are less accurate than with classical INS. This paper studies a two-step inversion procedure which improves the performance of an integrated GNSS/MEMS navigation system. This inversion is based on a good knowledge of the non linear model of the sensor output. After describing the MEMS models considered in this paper, we present the two steps of the proposed inversion procedure. The goal of the first step (referred to as calibration) is to estimate the model parameters that are related to sensor perturbations. This calibration is performed using the classical least square algorithm which uses the model inputs and outputs. The second step (referred to as model inversion) estimates the model inputs (i.e. acceleration and angular rate) by using an appropriate extended Kalman filter (EKF). Note that the observation equation required for the EKF depends on the estimated parameters resulting from the first step. The performance of the proposed INS/GPS hybridization is evaluated via several simulations which outline the relevance of the proposed calibration/inversion strategy. These simulations have allowed to conclude on the accuracy of each step detailed in this paper.