Instantaneous State InSAR: Estimation and Prediction for Near Real-Time Displacement Monitoring

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 frame. This batch approach limits the agility of the method to adapt to a changing temporal behavior, as well as early anomaly detection, computational efficiency, and the systematic inclusion of newly acquired SAR data. Here we introduce a new method to capture complex dynamic behavior of a scatterer by estimating the instantaneous state instead of a time-invariant parametric description. The instantaneous state (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 while more effectively capturing dynamic behavior. Updating instantaneous parameters with single observations enables near real-time monitoring, and the explicit specification of smoothness parameters facilitates implicit phase unwrapping.