Satellite radar interferometry (InSAR) is a powerful technique for monitoring deformation phenomena. While deformation phenomena occur in a three-dimensional (3D) world, one of the limitations of the InSAR phase observations is that they are only sensitive to the projection of the 3D displacement vector onto the radar line-of-sight (LoS) direction. To uniquely estimate the three displacement components, we would require at least three sets of spatiotemporally coinciding independent (STCI) LoS observations, (i.e., scatterers on an object that is not subject to internal deformations, observed at the same time) available over the same Region of Uniform Motion (RUM). More importantly, the system of equations needs to have a full rank coefficient matrix. Unfortunately, in most practical situations at most two sets of STCI LoS observations are available, resulting in an underdetermined system with an infinite amount of possible solutions. Within the InSAR literature we encounter different approaches to address the underdeterminancy problem, unfortunately often with either mathematical or semantic flaws. We concluded that the InSAR community has no uniform way of addressing the underdeterminancy problem. We developed a taxonomy for the different fallacious approaches that can help by evaluating InSAR results and reviewing InSAR papers. Moreover, using the east-north-up (ENU) reference frame for decomposing the LoS observations provides results that are not tuned to the needs of the end-user of an InSAR product. Therefore, we developed an alternative solution to the underdetermined problem, in the form of a `strap-down' approach, which uses a local strap-down reference system that is fixed to the deformation phenomenon with transversal, longitudinal, and normal (TLN) components. For many practical cases, such as line-infrastructure, landslides, or subsidence bowls, analysis of the main driving forces supports the assumption that significant deformations in the longitudinal direction are unlikely. We found that using the strap-down approach gives physically more relevant estimates. Moreover, it results in more relevant estimates since it properly includes all uncertainties. We can further conclude that the conventional way of communicating (PS)-InSAR results by means of a `dot distribution map' is sub-optimal when considering the quality of the estimates. For many cases, `vector arrow maps', or traditional geodetic vector-based visualizations, including error ellipses are a viable and more optimal alternative.

Under urban sprawl the trend of new established complex structures has rapidly increased. In this context little importance has been given to maintenance, even if this represents an important step in combating and avoiding disasters and developing improved future structural designs. Over the last years low-cost Global Navigation Satellite System (GNSS) equipment has faced rapid and important development opening a new door to reliable and high accuracy positioning applications such as structural health monitoring (SHM). This study focuses on assessing, from a geodetic perspective, the capabilities of a pair of low-cost dual frequency GNSS receivers for capturing the kinematic response of structures to wind. An experiment has been carried out with a stainless steel cantilever beam, aiming to highlight the advantages of employing a differential GNSS system for monitoring low frequency changes in the structure’s body. Hence, in this context the nominal precision of the GNSS system in East, North and Up direction of 4, 5 and 10 millimeter (1σ), was further improved to 3, 4 and 8 miilimeters in the presence of a Global Positioning System (GPS) based multipath (MP) correction. However, it is safer to consider that the true displacement retention potential of the low-cost GNSS receivers corresponds to 3 times (3σ) the aforementioned standard deviation values, resulting in slightly larger than 1 centimeter detectable horizontal displacements, and up to 2.4 centimeters vertical displacements. To support this, wind-induced beam displacements of up to 1.9 centimeters were identified and attested based on a cross correlation analysis with meteorological information. Next, the architecture of a GNSS based SHM system is proposed that can detect structural displacements in real time and rise safety alarms. Therefore, with real time kinematic (RTK) differential positioning and a position outlier and slip statistical testing procedure, a clear strategy for the estimation and identification of uni- or tri-dimensional displacement quantities in real time is proposed, to rise alarms about the magnitude and the direction of identified displacements. Hence, there is no doubt that newly released low-cost dual frequency GNSS receivers represent an alternative to high-end geodetic equipment for SHM, by offering an optimal balance between precision and cost efficiency.