Urban resilience and decision-making rely on continuous monitoring of key safety indicators. The increasing availability of interferometric synthetic aperture radar (InSAR) observations offers a valuable opportunity for near real-time stability monitoring, particularly in the built environment. Traditional InSAR time-series methods use batch processing of all available data at a particular moment in time to estimate static and global displacement parameters, describing the motion of the effective scatterer over the entire evaluated time period. This batch approach limits the agility of the method to adapt to a changing temporal behavior, early anomaly detection, computational efficiency, and the systematic inclusion of newly acquired SAR data. Here, we introduce a new method to capture the complex dynamic behavior of a scatterer by estimating its instantaneous state (IS) instead of using a time-invariant parametric description. The IS estimation and prediction model uses single new SAR acquisitions to provide time updates and measurement updates using a Kalman filter methodology. It imposes smoothness constraints on the displacement signal by modeling the velocity as an exponentially correlated, mean-reverting Ornstein-Uhlenbeck process, thereby enhancing the practicality of the method, and employs the normalized median amplitude dispersion as a proxy for phase quality. The results demonstrate that IS-InSAR matches the estimation quality of batch methods in non-dynamic circumstances while more effectively capturing dynamic behavior. Updating IS with single observations enables near real-time monitoring, and the explicit specification of smoothness parameters facilitates implicit phase unwrapping.

The growing availability of SAR data offers a real-time deformation monitoring opportunity, but data utilization can be inefficient. Our study introduces a mathematical framework using recursive least-squares and the wrapped phase, allowing efficient updates when new data arrives. This method also incorporates prior knowledge about signal smoothness for non-linear displacement estimation. Compared to the batch solution, our recursive approach achieves parameter estimation without storing past measurements while respecting signal smoothness constraints.

InSAR enables the estimation of displacements of (objects on) the earth's surface. To provide reliable estimates, both a stochastic and mathematical model are required. However, the intrinsic problem of InSAR is that both are unknown. Here we derive the Variance-Covariance Matrix (VCM) for double differenced phase observations for an arc, i.e., the phase difference between two points relative to a reference epoch. Using the Normalized Amplitude Dispersion we subdivide the time series in multiple partitions. The method results in a more realistic stochastic model, and consequently more realistic and reliable displacement parameters. The stochastic model also allows to make statements on the precision and reliability of the estimated parameters.