The Earth's surface is continuously deforming due to natural and anthropogenic processes, such as tectonics, landslides, oil and gas extraction, and groundwater level changes. Persistent Scatterer Interferometry is a technique that provides measurements of this surface motion based on satellite radar images. The technique uses the persistent radar reflection from certain objects on the Earth's surface to estimate their deformation time series. However, since the location of these objects is unknown, Persistent Scatterer Interferometry comprises both an estimation and a detection problem. In this contribution a Persistent Scatterer Interferometry algorithm is presented that resolves this estimation and detection problem based on geodetic estimation theory. The complete processing procedure, from the original radar images to the geolocated Persistent Scatterers, is described. Herein, the estimation of the unknown phase ambiguities, both in the time and space domain, forms a key component. The developed algorithm is characterized by a continuous update of the stochastic model of the phase observations after the estimation and removal of error sources, a direct testing of the estimated phase ambiguities, and the ability to apply local deformation models to improve the number of detected Persistent Scatterers and the reliability of the estimated time series.