Deformation phenomena on Earth are inherently three dimensional. With SAR interferometry (InSAR), in many practical situations the maximum number of observations is two (ascending and descending), resulting in an infinite number of possible displacement estimates. Here we propose a practical solution to this underdeterminancy problem in the form of the strapdown approach. With the strapdown approach, it is possible to obtain “3D-global/2D-local” solutions, by using minimal and largely undisputed contextual information, on the expected driving mechanisms and/or spatial geometry. It is a generic method that defines a local reference system with transversal, longitudinal, and normal (TLN) axes, with displacement occurring in the transversal-normal plane only. Since the orientation of the local frame is based on the physics of the problem at hand, the strapdown approach gives physically more relevant estimates compared to conventional approaches. Moreover, using an a-priori uncertainty approximation on the orientation of the local frame it is possible to assess the precision of the final estimates. As a result, appropriate cartographic visualization using a vector map with confidence ellipses enables an improved interpretation of the results.@en

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.

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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.

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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.

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