This paper describes a new approach to Persistent Scatterer Interferometry (PSI) data processing and analysis, which is implemented in the PSI chain of the Geomatics (PSIG) Division of CTTC. This approach includes three main processing blocks. In the first one, a set of correctly unwrapped and temporally ordered phases are derived, which are computed on Persistent Scatterers (PSs) that cover homogeneously the area of interest. The key element of this block is given by the so-called Cousin PSs (CPSs), which are PSs characterized by a moderate spatial phase variation that ensures a correct phase unwrapping. This block makes use of flexible tools to check the consistency of phase unwrapping and guarantee a uniform CPS coverage. In the second block, the above phases are used to estimate the atmospheric phase screen. The third block is used to derive the PS deformation velocity and time series. Its key tool is a new 2+1D phase unwrapping algorithm. The procedure offers different tools to globally control the quality of the processing steps. The PSIG procedure has been successfully tested over urban, rural and vegetated areas using X-band PSI data. Its performance is illustrated using 28 TerraSAR-X StripMap images over the metropolitan area of Barcelona.