InSAR enables the estimation of spatio-temporal displacements, relative to a reference point and a reference epoch, here defined as the mother image. When dealing with time series, there are several options to treat the mother image in computing and plotting the temporal phase differences, producing distinctly different results, in terms of the estimated displacement parameters and their precision. Here we review the three approaches mostly encountered in literature, discuss the implications of the different approaches, and recommend the ‘embracing mother’ approach for standard InSAR analyses and visualizations.

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.

Parametric models are widely utilized for interferometric synthetic aperture radar (InSAR) time series analysis under the assumption that the parameterization is invariant over time. Yet, the complexity of InSAR scatterers makes the hypothesis of this consistent and uniform behavior less likely. Here, we propose a method for non-parametric time series analysis for arcs between point scatterers based on basic splines (B-splines), which has the potential of fitting the time series adequately due to its high flexibility. We implement B-spline modelling for the kinematic behavior of arcs, and we propose to apply it in the complex domain and optimize the B-spline settings by means of amplitude data. We find that B-splines in the complex domain show great potential for estimating InSAR time series behavior, due to its insensitivity to errors in the integer ambiguity estimation, and that multiple model solutions can be derived from different B-spline parameter combinations. Our approach does not aim to provide a solution of the InSAR non-uniqueness problem, but it emphasizes the contribution of smoothness constraints to limit the solution space.

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 3D reconstruction, leading to non-unique 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.

To retrieve the full displacement vector from InSAR, three line-of-sight (LoS) observations from different viewing geometries are required. However, often, at most two LoS observations are available. Within the literature, we encounter different approaches to address for this problem, unfortunately often with either mathematical or semantic flaws. Their impact reaches from quantitative errors in the reported studies, mismatches in comparative studies with other geodetic techniques, a lack of trust in the technology by end-users, to plain confusion. We propose both a uniform nomenclature and an alternative approach to the standard 3D decomposition problem using the concept of a strap-down reference system.