Structural Health Monitoring (SHM) allows tracking the structural behavior in time and support decisions regarding, for instance, the need for maintenance and repair activities. Most traditional SHM systems require sensors that are directly applied to the structure to get insights into the structural performance. Satellite technologies can provide an appealing alternative to traditional SHM. They allow to measure displacements at a large scale and to follow their evolution without the need of directly accessing the structure. Further to this, the possibility to monitor large areas opens new avenues for the development of automatic alert systems able to issue an alarm and early-flag damaged structures. However, displacements of civil structures might also be induced by sources other than damage such as thermal or periodic hydrogeological variations. These can hinder the onset and development of damage or lead to false alarms if such displacements are erroneously interpreted as damages. This paper aims to present a new method for damage detection based on DInSAR measurements, that tackles both aspects providing reliable information about the onset of damage under environmentally changing conditions in a period corresponding to about twice the revisit time of the satellite. A case study is presented to demonstrate the applicability of the proposed method, namely the Palatino bridge in Rome, Italy. The satellite data are acquired by COSMO-SkyMed of the Italian Space Agency and consist of displacements of the observed structure recorded during a period spanning between 2011 and 2019.