We present the preliminary results of an InSAR analysis of peatland surface motion covering a large spatial and temporal extent. This work is the first large scale analysis of the Dutch Green Heart region, and is made possible using a novel distributed scatter (DS) InSAR processing method. This method is designed to handle breakages in the observed interferometric phase time series which occur due to temporal decorrelation, which we designate with the term loss-of-lock.

We introduce SARXarray and STMtools, two python libraries designed to support the exploitation of modern Interferometric Synthetic Aperture Radar (InSAR) data by enabling handling of larger-than memory datasets and the incorporation and fusion with relevant contextual information. The libraries are developed upon two innovative and well-established open-source Python libraries: Xarray [5] and Dask [6]. They are implemented as Xarray extensions. SARXarray is designed to manipulate and operate on larger-than-memory coregistered raster stacks such as Single-look Complex images (SLC) or interferograms, performing scatterer selection and producing STM objects. STMtools leverage the Space-Time Matrix (STM) concept [3], [4] and provides functionalities to process STM and perform enrichment/data fusion with other data sources. Both libraries are built on the Xarray library, providing support for a wide range of data formats, and utilize Dask for parallel computation, making them scalable for distributed computation infrastructures. By enabling InSAR data analysis incorporating contextual information, the two libraries enhance the potential to uncover underlying mechanisms driving deformation phenomena.

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.

We present a methodology which enables InSAR observations of ground motion in regions of low coherence and periodic decorrelation events which makes use of spatial and temporal contextual data to increase the information available to the processing algorithms. While this study is focused on observations of cultivated peatlands, the approach is generic and can be applied to other types of regions where coherence loss may be a concern. Neighbouring regions are grouped together by their contextual attributes such that when one region decorrelates, other observations from similarly behaving regions can still be used to derive a kinematic displacement model, thereby spanning the incoherent gap.

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.

We introduce the termloss-of-lockto describe a specific form of coherence loss which results in the breakage of an InSAR time series. Loss-of-lock creates a specific pattern in the coherence matrix of a multilooked distributed scatterer (DS) by which it may be detected. Along with identification, we introduce a new DS processing methodology which is designed to mitigate the effects of loss-of-lock by introducing contextual data to assist in the time series processing. This methodology is of particular relevance to regions which suffer from severe temporal decorrelation, such as northern peatlands.We apply our new method to two subsiding cultivated peatland regions in The Netherlands which previously proved impossible to monitor using DS InSAR techniques. Our results show a very good agreement with in-situ validation data as well as spatial correlation between regions and the natural terrain.

The observed phase in time series of Interferometric Synthetic Aperture Radar (InSAR) products is a superposition of various components. Differential topography, line-of-sight displacements, and differential atmospheric delays are the main contributions, and need to be disentangled to derive accurate DEM, deformation or atmospherical products from InSAR. However, isolating the atmospheric component has been proven difficult as it is spatiotemporally highly dynamic and a superposition of two atmospheric states. Here we propose an approach to parameterize the stochastic properties of the single-epoch atmospheric delay field as a way to define the atmospheric signal. We found that the atmospheric signal of a time-series of interferograms can be characterized by structure functions, which can be used to isolate the single-epoch structure functions. Due to the scaling properties of the atmospheric signal, it is then possible to construct a parametric function per SAR acquisition, using two isotropic and three anisotropic parameters. Especially, the isotropic parameters for the short-distance and long-distance variation in atmospheric delay, can be used to characterize the atmospheric signal. For a test set of 151 Sentinel-1 acquisitions, this results in an atmospheric energy range of about 10 for short-distance and about 50 for long-distance scales. Our parametrization demonstrates that we can describe the spatiotemporal variability of InSAR atmospheric delays, which provides a measure for atmospheric noise for individual epochs in deformation time-series based on distance and azimuth.

We present a novel InSAR processing scheme which combines point scatterer (PS) and distributed scatter (DS) approaches in a hybrid framework along with contextual information about the environment under study. Data such as land parcel divisions, precipitation and temperature are integrated into the processing pipeline in order to produce accurate deformation time series estimates of the Dutch peatlands. In addition to these steps, a segmented processing scheme is introduced to manage irreversible losses of coherence in the interferogram stack. Initial results show a promising agreement with in-situ ground truth measurements gathered by extensometer readings of shallow surface deformation.

The estimation of Signal-to-Clutter Ratio (SCR) of a radar point target, such as a corner reflector, is an essential step for synthetic aperture radar (SAR) interferometry and positioning, as it influences the phase measurement variance as well as the absolute positioning precision. The standard method to estimate the SCR of a point target relies on the debatable assumption of spatial ergodicity, using the clutter of the surrounding as representative of the clutter at the point target. Here, we estimate the SCR of a corner reflector using a time series of SAR measurements, i.e., assuming temporal ergodicity. This assumption is often more realistic, particularly in a complex environment, in the presence of other point scatterers, and for small-sized reflectors. Empirical results on a corner reflector network, using Sentinel-1 SAR measurements, show that the temporal method yields a less biased and more precise estimate of the average SCR. A second experiment shows that the InSAR phase variance as well as positioning precision, predicted using SCR estimated by the temporal estimation method, is closer to the truth.

Several researchers have shown that the Capon algorithm can be applied to reprocess SAR images, resulting in super-resolution reconstructed scenes with lower sidelobe levels. Thus by employing the Capon-based reprocessed images in Persistent Scatterer Interferometry (PSI), the persistent scatterer (PS) density can be increased. In this letter, we exploit the Capon-based PS densification method for Sentinel-1 (S-1)Terrain Observation by Progressive Scans(TOPS) data. We propose a revised robust approach of the Capon algorithm, which applies the automatic diagonal loading (DL) method when the condition number of the covariance matrix is big enough. The proposed approach is robust and can avoid spurious persistent scatterer candidate (PSC) points introduced by DL approaches. We also consider and analyze the spectral property caused by the scanning mode of TOPS in the reprocessing. We applied the revised-robust-Capon-based reprocessing algorithm to a stack of real-life S-1 data and selected PSCs from them. The final result shows that the number of PSs increases by approximately 30% with respect to the original stack.

Phase unwrapping, also known as ambiguity resolution, is an underdetermined problem in which assumptions must be made to obtain a result in SAR interferometry (InSAR) time series analysis. This problem is particularly acute for distributed scatterer InSAR, in which noise levels can be so large that they are comparable in magnitude to the signal of investigation. In addition, deformation rates can be highly nonlinear and orders of magnitude larger than neighboring point scatterers, which may be part of a more stable object. The combination of these factors has often proven too challenging for the conventional InSAR processing methods to successfully monitor these regions. We present a methodology which allows for additional environmental information to be integrated into the phase unwrapping procedure, thereby alleviating the problems described above. We show how problematic epochs that cause errors in the temporal phase unwrapping process can be anticipated by the machine learning algorithms which can create categorical predictions about the relative ambiguity level based on the readily available meteorological data. These predictions significantly assist in the interpretation of large changes in the wrapped interferometric phase and enable the monitoring of environments not previously possible using standard minimum gradient phase unwrapping techniques.

Synthetic aperture radar (SAR) missions with short repeat times enable opportunities for near real-time deformation monitoring. Traditional multitemporal interferometric SAR (MT-InSAR) is able to monitor long-term and periodic deformation with high precision by time-series analysis. However, as time series lengthen, it is time-consuming to update the current results by reprocessing the whole dataset. Additionally, the number of coherent scatterers varies over time due to disappearing and emerging scatterers due to inevitable changes in surface scattering, and potential deformation anomalies require changes in the prevailing deformation model. Here, we propose a novel method to analyze InSAR time series recursively and detect both significant changes in scattering as well as deformation anomalies based on the new acquisitions. Sequential change detection is developed to identify temporary coherent scatterers (TCSs) using amplitude time series. Based on the predicted phase residuals, scatterers with abnormal deformation displacements are identified by a generalized ratio test, while the parameters of stable scatterers are updated using Kalman filtering. The quality of the anomaly detection is assessed based on the detectability power and the minimum detectable deformation. This facilitates (near) real-time data processing and decreases the false alarm likelihood. Experimental results show that the technique can be used for the real-time evaluation of deformation risks.

Numerical weather prediction (NWP) models are used to predict the weather based on current observations in combination with physical and mathematical models. Yet, they are limited by the spatial density and the accuracy of the available observations. Satellite radar interferometry (InSAR) is known to be extremely sensitive to the 3D atmospheric refractivity distribution, and has a high spatial resolution, providing information that can be used for assimilation in NWP models. However, due to the inherent superposition of two or more atmospheric states, only biased and temporally differenced signals can be retrieved, that can also be contaminated by deformation signals and decorrelation. Here we present a method to estimate single-epoch absolute atmospheric delays by combining InSAR time series with prior NWP model prediction time series, using a constrained least-squares estimation. We show that this leads to a solution that reliably extracts the single-epoch relative delays from InSAR data and uses prior NWP model data to find the absolute reference for these delays, while mitigating long-term deformation and decorrelation signal. This approach leads to repetitive delay updates with a spatial resolution of 500 m, that can be directly assimilated into numerical weather models.

In radar interferometry, the method of storage for coherent scatterers and their attributes directly influences the ability for interpretation. Especially with the complexity and ambiguity of InSAR observations, the need for a consistent and queryable spatial data-platform becomes relevant. Our proposed method uses the concept of a spacetime matrix to store the coherent scatterers, implemented by means of a spatial database. The stored InSAR data are partitioned in modules of the displacement time series, inherent scatterer and processing-related attributes, and their corresponding contextual attributes. Data and context-driven queries are facilitated by the use of spatial indices. The method is illustrated by a case study for building stability in the northwestern part of Rotterdam, the Netherlands. The contextual attributes used characterize building foundations in part of the city.

InSAR and GNSS not only provide an additional source of ground motion measurements with respect to the conventional techniques, with different characteristics, also the data volumes increased significantly. This poses challenges on the integration of the various data sets available. The Integrated Geodetic Processing (IGP) software provides a systematic framework for the integration of geodetic data, including testing and quality assessment. The concept of the software is described, as well as an illustrative example of the output.

The main objective of this paper is to develop and evaluate a pragmatic approach to obtain an InSAR stochastic model for reduced InSAR datasets. This goal is achieved by calculation of the stochastic parameters per InSAR stack, propagating the noise structure to reduced datasets. The propagation of full covariance matrices when using a reduced dataset in space and time is avoided, using the derived analytical functions. This way, a computationally efficient approximation of the exact covariance matrix is obtained for reduced datasets.

Well-identifiable reference benchmarks are important in SAR interferometry to enable linking between different measurement techniques, or to enable datum connection between the local InSAR datum and Terrestrial Reference Systems. As corner reflectors for C-band are rather large, weather sensitive, and difficult to maintain over time frames of several years, active electronic transponders are an alternative. However, low cost transponders have not been on the market until recently. Here we report results from field tests of a new type of transponder. We show that the phase precision is in the order of an equivalent displacement of 0.5 mm, and that the RCS of the transponder is equivalent to a trihedral corner reflector with a leg length of 1.03 m.

This contribution proposes a new approach for the analysis and preparation of geodetic data for the use in geophysical modeling. The approach resolves the problem of non-uniformity in the datasets obtained by different measurement techniques. The approach is based on two main steps: uniformization of the data using a standardized data format, and the application of the CUPiDO conversion tool to construct double-difference observations. Both steps are described in detail. By using double-difference observations, the effect of different reference points and geodetic datums is eliminated, thereby making the outcomes of the CUPiDO tool well suited for an integrated inversion to estimate a model. The CUPiDO tool will be made publicly available.

Multi-temporal and multi-sensor solutions are essential to increase timeliness and reliability of land monitoring systems. This paper advocates the exploitation of the temporal contextual information provided by temporally dense SAR and optical data series series through the use of a Hidden Markov model (HMM)-based approach. An efficient strategy to incorporate the C-Band SAR data into the HMM framework, relying so far on Landsat, will be debated and assessed over a dynamic agricultural scenario, i.e. characterized by high temporal and spatial diversity in cropping practices. The site is located in the state of São Paulo (Brazil), where recent ground surveying activities has been conducted.

InSAR deformation estimates form a `free network' referred to an arbitrary datum, e.g. by assuming a reference point in the image to be stable. Consequently, the estimates of any measurement point in the image are dependent of these postulations on reference point stability, and the estimates cannot be compared with datasets of other types of measurement (e.g. historical levelling data or sea-level changes). Yet, some applications require `absolute' InSAR estimates, i.e. expressed in a well-defined terrestrial reference frame (TRF). We achieve this using collocated InSAR and GNSS measurements, achieved by rigidly attaching phase-stable millimetre-precision compact active transponders to permanent GNSS antennas. The InSAR deformation estimates at these transponders are then estimated in a TRF using the GNSS measurements. Consequently, deformation estimates at all other scatterers are now also defined in the same TRF.

In recent years, new algorithms have been proposed to retrieve maximum available information in synthetic aperture radar (SAR) interferometric stacks with focus on distributed scatterers. The key step in these algorithms is to optimally estimate single-master (SM) wrapped phases for each pixel from all possible interferometric combinations, preserving useful information and filtering noise. In this paper, we propose a new method for SM-phase estimation based on the integer least squares principle. We model the SM-phase estimation problem in a linear form by introducing additional integer ambiguities and use a bootstrap estimator for joint estimation of SM-phases and the integer unknowns. In addition, a full error propagation scheme is introduced in order to evaluate the precision of the final SM-phase estimates. The main advantages of the proposed method are the flexibility to be applied on any (connected) subset of interferograms and the quality description via the provision of a full covariance matrix of the estimates. Results from both synthetic experiments and a case study over the Torfajökull volcano in Iceland demonstrate that the proposed method can efficiently filter noise from wrapped multibaseline interferometric stacks, resulting in doubling the number of detected coherent pixels with respect to conventional persistent scatterer interferometry.

SAOCOM is an Argentinian L band system formed by two satellites (SAOCOM-1A and SAOCOM-1B). ESA is investigating the possible applications of a companion satellite (SAOCOM-CS) carrying a passive receiver working in concert with one of the SAOCOM-1 satellites. During the mission there will be cycles with a long along-track bistatic baseline, suitable for deformation monitoring. Together with the combination of ascending and descending orbits, this geometry will produce four measurements from different viewing geometries, enabling us to estimate the 3D motion vector. Here we investigate the sensitivity of such a configuration, and the opportunities for increasing the density of persistent scatterers.

The telecommunications sector has proposed to use the 5.350–5.470 GHz frequency band for ground-based communication services. The Sentinel-1, RadarSAT-2, and future RadarSAT constellation SAR satellites are operating in the same band. Here we assess the impact of these ground-based uncorrelated radio frequency interference (RFI) sources to radar interferometry-based ground motion analysis. Apart from a theoretical assessment, a Persistent Scatterer Interferometry analysis is performed based on a combination of real ENVISAT data and simulated RFI noise at different levels. The analysis shows that the RFI sources significantly reduce the applicability of radar interferometry, with a reduction of detected Persistent Scatterers with more than 50%. If the telecommunication sector would proceed with this plan, operational ground motion services based on Sentinel-1 data would no longer be possible.

The potential of differential SAR interferometry (D-InSAR) techniques for the study of the 3-D deformation phenomena has been extensively demonstrated. In particular, two different performance approaches (one analytical and one numerical solutions) have been implemented and analyzed. The primary objective is to investigate the capabilities of the Sentinel-1 follow-on SAR mission (named here HRWS) and its preferred acquisition modes for this particular application domain, which might help to the mission optimization.

Here we present an efficient algorithm to analyze the deformation behavior of line infrastructure, such as water defense structures and railways, using radar interferometric time series. Due to the limited amount of pixels and the consistent reflection properties, a detailed analysis can be performed. By considering neighboring pixels, the influence of a large part of error sources is reduced. However, the strong correlation between pixels should be considered. The algorithm is applied to dikes in the Netherlands, showing global as well as local deformation effects.

InSAR data acquired from independent overlapping tracks can be exploited for a reliability assessment of the Persistent Scatterer InSAR (PS-InSAR) technique. This is obtained by means of the datum connection of multiple tracks, simultaneously evaluating the misclosures between multi-track PS-InSAR estimates. Due to a different viewing geometry, many of the detected PS will physically not be the same. However, their estimates may still refer to the same deformation signal. The existence of independent observations of the same deformation signal provides a powerful tool to increase the redundancy and evaluate the reliability. The datum connection can be subdivided in two steps. The first step consists of the conversion of PS locations to a common datum. Secondly, the PS-InSAR parameter estimates (velocities, displacements, heights) are connected. In stead of the conventional approach of separately geocoding each track, we propose the use of a common radar datum defined by the acquisition geometry of the 'master track'. Multi-track datum connection has been applied in the Groningen region, the Netherlands, which is affected by subsidence due to gas extraction with displacement rates up to 7 mm/year. The main reservoir is (partly) visible in 6 independent overlapping ERS tracks from 1992 (ascending and descending). Datum connection resulted in a consistent set of PS-InSAR deformation estimates. Additionally, the deformation signal was decomposed in horizontal and vertical movements, utilizing the different viewing geometries of the tracks.

Because the quality assessment of Persistent Scatterers (PS) is dependent on the deformation model chosen, PS may be falsely rejected due to model imperfections. To accept these PS, more advanced deformation models should be used. Two methods applying adaptive deformation models are proposed. The first is based on a sequential scheme of alternative hypothesis testing of extended deformation models within the integer least- squares framework. The second uses a iterative scheme of global deformation modeling based on previous PS results. Application of the techniques to a salt mining area in The Netherlands confirms the increase in the number of detected PS.

SAR amplitude calibration is performed prior to the selection of potential Persistent Scatterers (PS) to avoid amplitude variations due to sensor characteristics and viewing geometry. As only the interferometric phases of a small percentage of the radar pixels in an image is used in the PS-InSAR analysis, it is investigated if this time and storage space consuming step can be omitted. We present an integrated method which does not perform amplitude calibration explicitly, but integrates it into the PS point selection procedure for validation purposes by evaluating the hypothesis that a point would have been selected if all images were calibrated beforehand. Its performance assessment is based on coherent phase behavior of the selected potential PS and indicates that empirical calibration validation is an alternative for calibrating full images based on physical sensor parameters.

PS-InSAR has proven to be an accurate and ef- ficient technique for the joint estimation of topographic and displacement signal from stacked interferometric combinations. In this contribution a new method for PS-Insert processing is introduced, which enables the recursive estimation of parameters of interest. The method is based on the ILSQ PS-InSAR concept and makes use of the estimation vector and corresponding variance-covariance matrix of the initial estimation epoch. The presented methodology systematically adds a new acquisition (or set of acquisitions) to the existing stack, updates the solution of the previous run, and analyzes whether the behaviour of the (pre-) selected points fits the expected one. This contribution focuses on a mathematical framework, rather then on specific applicational problems. Nevertheless, the performed numerical analysis on simulated data sets is analyzed and discussed, which shows that the preset aims of the recursive PS-InSAR estimation technique is achieved. I. INTRODUCTION Time series InSAR analysis using persistent scatterer (PS) techniques aims at the joint estimation of topographic and displacement signal from a number of interferometric com- binations, (1), (2). Since the estimates of both parameters are correlated and error signal due to, e.g., atmospheric signal can significantly affect the adjustment, an accurate estimation depends on the availability of a large data stack, i.e., more than 20-30 images. A smaller number of images usually results in problems like detecting the potential PS, reducing the atmospheric signal, separating topography and displacement, and phase ambiguity estimation. An additional problem for all current multi-image pro- cessing concepts is that the parameter estimation is usually performed in batches, i.e., by using all available acquisitions at once. Hence, in order to incorporate a newly available acquisition into the processing chain, and consequently update the estimates, the whole processing (at least the PS part) has to be performed again. Such an approach consequently leads to an increase of processing time, limits the application to the areas where only a sufficient number of images is available, and reduces the potential application of the method to a semi- real-time deformation monitoring. The two main processing concepts of PS-InSAR are the concept of the ambiguity function, (1), and Integer Least Squares (ILSQ) method, (2). The main drawback of the first one is that the propagation concept of observations to the unknown parameters is suboptimal. Moreover, the method strongly depends on the discretization of the solution space and it treats unknown ambiguities as deterministic parameters instead of stochastic ones. The ILSQ approach is based on the principles of Best Linear Unbiased Estimation (BLUE) - it is based on the minimization of the mean squared error and it is formulated as a constrained minimization problem on the integer nature of the unknowns, (6). By means of the ILSQ method, the quality description of estimated parameters is the one of the end products of the analysis, which can conse- quently be used to determine the significance and reliability of the estimated parameters. The ILSQ PS-InSAR processing framework sets the basis for a recursive data processing strategy, where new acquisi- tions can be easily added to an existing data stack, significantly reducing the computational requirements. This implies that the presented methodology systematically adds a new acquisition to the existing stack, updates the solution of the previous run, and analyzes whether the behaviour of the (pre-)selected points fits to the expected behaviour of parameters of interest. If not, an alternative hypothesis is tested against the prior solution, leading to the rejection of the point, adaptation of the model, or manual intervention. For the conditions on the practical application of recursive PS-InSAR processing, it can be referred to the block-diagonal structure of the variance-covariance matrix of the introduced recursive model (the estimates from the initialization run and phase observations of the additional acquisition are assumed to be uncorrelated). Secondly, the atmospheric and non-modelled displacement contributions to the interferometric phase have to be modelled and incorporated into the variance matrix by means of covariance functions, (4), (5) - in the presented study the covariance functions are not further elaborated on. Moreover, in numerical experiments, phase contributions are isolated by low-pass filtering in the spatial domain and high- pass filtering in the temporal domain. Furtheron, in order to correctly perform the initialization run (candidate selection and unwrapping), a sufficient number of images (15-20) is needed. In the following sections the concept of the recursive PS- InSAR is presented. Examples on simulated data are used