Multi-Temporal Small Baseline Interferometric SAR Algorithms: Error Budget and Theoretical Performance

Abstract

Multi-temporal interferometric synthetic aperture radar (MT-InSAR) techniques are well recognized as useful tools for detecting and monitoring Earth’s surface temporal changes. In this work, the fundamentals of error noise propagation and perturbation theories are applied to derive the ground displacement products’ theoretical error bounds of the small baseline (SB) differential interferometric synthetic aperture radar algorithms. A general formulation of the least-squares (LS) optimization problem, representing the SB methods implementation’s core, was adopted in this research study. A particular emphasis was placed on the effects of time-uncorrelated phase unwrapping mistakes and time-inconsistent phase disturbances in sets of SB interferograms, leading to artefacts in the attainable InSAR products. Moreover, this study created the theoretical basis for further developments aimed at quantifying the error budget of the time-uncorrelated phase unwrapping mistakes and studying time-inconsistent phase artefacts for the generation of InSAR data products. Some experiments, performed by considering a sequence of synthetic aperture radar (SAR) images collected by the ASAR sensor onboard the ENVISAT satellite, supported the developed theoretical framework.

On the Phase Nonclosure of Multilook SAR Interferogram Triplets

“…In this work, we refer to a unified representation of the SB algorithms. Indeed, the different implementations of the SB methods proposed in the literature have individual peculiarities; however, they can almost be unified [47], [66] considering they solve a linear optimization problem that relates the vector of the (known) unwrapped ML SB interferograms, namely , to a model of unknown parameters of the ground deformation . The adopted unified representation of the SB linear transformation is as follows: (18) where is the design matrix of the considered linear transformation.…”

Integrated Analysis of the Combined Risk of Ground Subsidence, Sea Level Rise, and Natural Hazards in Coastal and Delta River Regions

“…It is calculated for each coherent DS target, the (unknown) displacement time-series [28]. A recent study [23] on the theoretical accuracy of the SB methods and the SBAS technique, in particular, showed how ground deformation error bounds are in general agreement with the result of quantitative analyses that showed that the accuracy of SBAS measurements is on the order of 1 mm yr −1 and 3-5 mm, for the ground deformation velocity and each data measurement, respectively. Additional recent advancements of the methods based on distributed target deformations can be found in [37,[39][40][41][42].…”

“…The principal results of the investigations performed within our Dragon IV project have been published in peer-reviewed journals over the last five years [14][15][16][17][18][19][20][21][22][23][24][25][26][27] and represent the starting point for future studies to be performed in the following years. We will summarize the main results of previous research related to this project in this article.…”

Analysis of Groundwater Depletion/Inflation and Freeze–Thaw Cycles in the Northern Urumqi Region with the SBAS Technique and an Adjusted Network of Interferograms

“…A recent work [44] comprehensively addressed, from the theoretical perspective, the problem of deriving some bounds for the relative errors of Mt-InSAR SB products. In particular, using the basic principles of perturbation and error propagation theory [45][46][47], it has been shown that the expected relative error ε v of the computed vector v (i.e., the solution of the least-squares problem of Equation ( 1)) is given by:…”

“…Toward that aim, the average spatial coherence of the chosen interferograms and the connectivity of their network were taken into account at the same time. Our work benefits from the primary outcomes of a recent investigation [44] that addressed the error budget analysis of SB Mt-InSAR techniques.…”