Parameter and ambiguity estimation in the temporal domain, for arcs of differential phase observations between two persistent scatterers (PS), is a critical part in Persistent Scatterer Interferometry (PSI). Deformation models, used as constraint in the parameter estimation, often do not capture the full extent of the deformation behaviour. This results in a poor separation of signal and noise, and rejection of arcs that do not behave conform the functional model. Previous work assumed that deformation behaviour is stationary and that a full time series can be described with a single set of deformation parameters. In order to develop a more broadly applicable deformation model, this study applies a temporal smoothness constraint during parameter estimation, by assuming that deformation rates are affected by a temporally correlated zero-mean random acceleration. This constraint is implemented using recursive least-squares, similar to Kalman filtering, which also enables efficient updating of arcs when new acquisitions are available.

Various kind of deformation types are simulated to create phase observations based on real TerraSAR-X, Radarsat2 and ERS stacks of interferograms. This simulated data is processed using the new recursive estimator and results are compared to that of a batch estimator using a steady-state assumption, to analyse the impact of adding a priori information about the smoothness of the physical signal. Furthermore, a case study on real data is performed on an area where non-linear subsidence has occurred, due to soil remediation. This study presents a mathematical framework for incorporating a priori knowledge about the smoothness of the deformation signal as constraint for parameter and ambiguity estimation. Especially non-linear deformation is better estimated using this method, resulting in a higher success-rate, better separation of signal and noise, and more PS passing quality thresholds. The framework moreover enables efficient updating of existing datasets when new acquisition are available.