In this study, we present a data processing framework to apply measurements of the Global Navigation Satellite System (GNSS) technique for analyzing and predicting the movements of civil structures such as bridges. The proposed approach reduces the noise level of GNSS measurements using the Kalman Filter (KF) approach and enables the estimation of static, semi-static, and dynamic components of the bridge’s movements using a series of analyses such as the temporal filtering and the Least Squares Harmonic Estimation (LS-HE). The numerical results indicate that by using a RTK-GNSS system the semi-static component is extracted with a Standard Deviation (STD) of 0.032, 0.048, and 0.06 m in the North, East, and Up (NEU) directions, while that of the dynamic component is 0.004, 0.003, and 0.01 m, respectively. Comparing the dominant frequencies of the bridge movements from LS-HE with those of the permanent stations provides information about the bridge’s stability. To predict its deflection, the Neural Network (NN) technique is tested to simulate the time-varying components, which are then compared with the safety limits, known by its design, to assess the structural health under usual load.