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.

Interferometry SAR (InSAR) enables the estimation of displacements of (objects on) the Earth’s surface. To provide reliable estimates, both an independent stochastic and functional model are required. However, the intrinsic problem of InSAR is that both are unknown. Here, we propose an independent definition of the stochastic model, via an approximation scheme for 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. Detecting temporal partitions in the amplitude time series, we assign quality values to all phase observations within each partition. To reduce the impact of outliers, we introduce the normalized median absolute deviation (NMAD) of the vector of amplitudes to robustly estimate the variance of the phase observations. The method results in a scatterer-specific and time-variable stochastic model, which is independent of the phase observations itself and prior to parameter estimation. This differs from many conventional methods, where the quality is often determined a posteriori from the residuals between the model and the observations. This yields more realistic and reliable displacement estimates, as well as improved statements on the precision and reliability of the estimated parameters.

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.

The estimation of displacement vectors for (objects on) the Earth's surface using satellite InSAR requires geometric transformations of the observables based on orbital viewing geometries. Usually, there are insufficient viewing geometries available for full 3-D reconstruction, leading to nonunique solutions. Currently, there is no standardized approach to deal with this problem, resulting in products that are based on haphazard and/or oversimplified assumptions with biased estimates and reduced interpretability. Here, we show that a clear definition of - and subsequent adherence to - enabling conditions guarantees the validity and quality of displacement vector estimates leading to standardized interferometric products with improved interpretability. We introduce the concept of the null line as a key metric for InSAR geometry and bias estimation, assess its impact and orientation for all positions on Earth, and propose a novel reference system that is inherently unbiased. We evaluate current operational practice, leading to a taxonomy of frequently encountered misconceptions and to recommendations for InSAR product generation and interpretation. We also propose new subscript notation to uniquely distinguish different projection and decomposition products. Our propositions contribute to further standardization of InSAR product definition, improved map annotation, and robust interpretability.