SAR Techniques Research Articles

An integrated geophysical approach for urban underground characterization: the Avigliano town (southern Italy) case study

A geophysical approach, based on the integration of satellite differential interferometric SAR technique and in situ geoelectrical and seismic methods, was applied with the aim to characterize a portion of urban area of Avigliano (PZ) town in Basilicata Region (southern Italy) affected by ground instability phenomena. Satellite analysis helped to discriminate areas of the town affected by superficial deformations and to monitor the dynamic behaviour of the structures located in these areas. Results from geoelectrical and seismic (active and passive) methods were compared with direct data (stratigraphic) and were interpreted with the aim to reconstruct the geometry of the subsoil. The joint application of both in situ techniques allowed the overcoming of the specific limits of each method and to improve the poor quality of the data due to the noise conditions typical of measurements carried out in urban areas. A preliminary geophysical model of the subsoil was obtained. The geophysical contrasts highlighted the presence of lithological discontinuities due to the superficial deformation processes that are affecting the portion of the investigated urban area. All the information has been transferred to the public administration technicians involved in the mitigation of hydrogeological risk in Basilicata Region.

PSINSAR COHERENCE BASED DISPLACEMENT ANALYSIS OF KRISHNA DELTA USING SENTINEL-1 INTERFEROMETRIC WIDE SWATH DATA

Abstract. The problem of decorrelation leading to loss of coherence has been a major source of concern to identify the various problems of erosion and deposition in delta. In this study, Permanent Scatter Interferometric SAR (PsInSAR) technique was used to identify the Permanent Scatter Candidates (PSCs) to explore its potential in identifying displacement based on coherence of various features in delta during the dry and wet periods. PSCs are coherent over interferograms acquired during different time periods. The study was conducted using Sentinel-1 C-band Interferometric Wide (IW) swath datasets acquired from 25th October 2016 to 10th June 2017 over Krishna Delta. The datasets were deramped and stitched prior to co-registering the master and slave images. Interferograms were generated, phase unwrapped and filtered after which the PSCs were identified based on Amplitude Stability index. The problem of tropospheric phase delay causing decorrelation was removed based on the difference in the phase residual of the connected PSCs. Ps coherence map was generated showing coherence as low as 0.28 to 0.38 in mangroves due to volume decorrelation and 0.5 to 0.85 in village areas. A prominent feature, vernal pool exhibited high variation in coherence (0.28 to 0.45) depending on monsoon or summer season. An integrated cumulative displacement map was generated indicating the areas where erosion and deposition has taken place and these depositional values of certain deltaic features were in conjunction with coherence.

Long-Term Peatland Condition Assessment via Surface Motion Monitoring Using the ISBAS DInSAR Technique over the Flow Country, Scotland

Satellite Earth Observation (EO) is often used as a cost-effective method to report on the condition of remote and inaccessible peatland areas. Current EO techniques are primarily limited to reporting on the vegetation classes and properties of the immediate peat surface using optical data, which can be used to infer peatland condition. Another useful indicator of peatland condition is that of surface motion, which has the potential to report on mass accumulation and loss of peat. Interferometic SAR (InSAR) techniques can provide this using data from space. However, the most common InSAR techniques for information extraction, such as Persistent Scatterers’ Interferometry (PSI), have seen limited application over peat as they are primarily tuned to work in areas of high coherence (i.e., on hard, non-vegetated surfaces only). A new InSAR technique, called the Intermittent Small BAseline Subset (ISBAS) method, has been recently developed to provide measurements over vegetated areas from SAR data acquired by satellite sensors. This paper examines the feasibility of the ISBAS technique for monitoring long-term surface motion over peatland areas of the Flow Country, in the northeast of Scotland. In particular, the surface motions estimated are compared with ground data over a small forested area (namely the Bad a Cheo forest Reserve). Two sets of satellite SAR data are used: ERS C-band images, covering the period 1992–2000, and Sentinel-1 C-band images, covering the period 2015–2016. We show that the ISBAS measurements are able to identify surface motion over peatland areas, where subsidence is a consequence of known land cover/land use. In particular, the ISBAS products agree with the trend of surface motion, but there are uncertainties with their magnitude and direction (vertical). It is concluded that there is a potential for the ISBAS method to be able to report on trends in subsidence and uplift over peatland areas, and this paper suggests avenues for further investigation, but this requires a well-resourced validation campaign.

Practical Multichannel SAR Imaging in the Maritime Environment

The U.S. Naval Research Laboratory (NRL) recently developed an X-band airborne multichannel synthetic aperture radar (MSAR) test bed system that consists of 32 along-track phase centers. This system was deployed in September 2014 and again in October 2015 to perform extensive and systematic data collections on a variety of land and maritime scenes under different environmental conditions. This paper presents a detailed experimental analysis of imaging in the maritime domain using data captured by the NRL MSAR system. After presenting some of the important details of our NRL MSAR system, we demonstrate velocity-based imaging of a variety of moving backscatter sources including ships and shoaling ocean waves. Our analysis is based on the velocity SAR (VSAR) technique, which was originally conceived by Friedlander and Porat. Practical application of this algorithm in the maritime domain requires a number of pre- and postprocessing stages, which are described here in detail. Our results are then benchmarked against the traditional along-track interferometry, where it is demonstrated that VSAR processing is better able to correctly compensate motion-induced distortion.

Performance Evaluation of TanDEM-X Quad-Polarization Products in Bistatic Mode

In the TanDEM-X mission, quad-polarization data (HH, HV, VH, and VV-polarization channels) can be acquired at an experimental basis by acquiring images in the dual-receive antenna (DRA) mode. This mode was activated during the so-called TanDEM-X science phase, from October 2014 up to January 2016, serving the science community with a unique dataset for the demonstration of new SAR techniques and applications. Quad-polarization data has been firstly acquired in pursuit monostatic mode and, secondly, in bistatic configuration as well. TanDEM-X is the first spaceborne mission which allows for the acquisition of quad-polarization data in bistatic formation, with across-track baselines varying up to 4 km at the Equator. The current work completes the one presented in [1] , where TanDEM-X quadpolarization data, acquired in pursuit monostatic mode only, was analyzed and recommendations were drawn, in order to optimize the acquisition parameters, aiming at improving the final data quality. Such recommendations were then taken into account for the acquisition of quad-polarization data in bistatic configuration, starting from April 2015, and the obtained results are presented in this paper. Investigations have been performed, aiming at monitoring the effective improvement in data quality. For example, we investigated the impact of different system parameters, such as noise equivalent sigma zero (NESZ) or processing bandwidth on the SAR performance, together with their influence on the interferometric SAR (InSAR) performance, assessed in terms of interferometric coherence and relative height error. Finally, we introduce and discuss an experimental acquisition mode, which allows to synthesize a quad-polarization product by combining two simultaneous dual-polarization acquisitions.

Glacial and tidal strain of landfast sea ice in Terra Nova Bay, East Antarctica, observed by interferometric SAR techniques

The dynamics of landfast sea ice, also called fast ice for short, has a large influence on the variability of polynyas and marine ecosystems, and the logistics for research stations near the Antarctic coast. Therefore, it is important to accurately measure the strain of fast ice and its seasonal variations, and to identify the cause of stresses on the ice. In this paper, we separate the strains from glacial stress and tidal stress of fast ice near the Campbell Glacier Tongue (CGT) in Terra Nova Bay, East Antarctica. This was done using observations from a series of one-day tandem COSMO-SkyMed Interferometric Synthetic Aperture Radar (InSAR) images obtained from December 2010 to January 2012. Firstly, we discriminated fast ice from pack ice and open water by analyzing the interferometric coherence values. We then identified the characteristics of the strains by investigating the equi-displacement lines of fringes in weekly InSAR and double-differential InSAR (DDInSAR) images. The weekly InSAR images predominantly showed glacial shear strain of the fast ice with fringes parallel to the sides of the CGT. This was due to the cumulative flow of the CGT for a week, while oscillating tidal signals were relatively small. The DDInSAR images, which cancelled glacial strain rates in two one-day InSAR images, showed a deformation of the fast ice by tidal sea surface tilt, with the fringes parallel to the coastline. Based on the unique characteristics of these strains, we separated them from the one-day InSAR images by decomposing the fringe patterns into glacial and tidal strain. Glacial shear strain rates of fast ice attached to the east of the CGT decreased from May to August owing to ice thickening and then stabilized until December. Those to the west of the CGT increased from May to July. This was possibly due to bottom melting of the ice by the increased ocean circulation during the expansion period of the nearby polynya. The glacial strain then decreased until December because of reduced polynya activity. The fast ice near the Jang Bogo Station (JBS) only showed tidal strain as it was isolated from the CGT by cracks and leads. Tidal strain rates of the fast ice were strongly correlated with the magnitude of tidal variations in all these regions, which represents shows that the tidal strain represents tidal sea surface tilt. The tidal response of fast ice to the west of the CGT and near the JBS was stronger than that to the east of the CGT, probably owing to thinner ice thickness there.

Design and virtual screening of novel fluoroquinolone analogs as effective mutant DNA GyrA inhibitors against urinary tract infection-causing fluoroquinolone resistant Escherichia coli.

Fluoroquinolones (FQs) belong to the class of quinolone drugs that are used to treat Urinary tract infections (UTIs) through inhibition of E. coli DNA gyrase. Resistance to FQs poses a serious problem in the treatment against resistant strains of E. coli which are associated with Ser83 to Leu and Asp87 to Asn mutations at the quinolone resistance determining region (QRDR) of the GyrA subunit of DNA gyrase. Mutant DNA GyrA (mtDNA GyrA) is deemed to be a significant target for the development of novel FQ drugs. Due to resistance to FQ drugs, discovery or development of novel FQs is crucial to inhibit the mtDNA GyrA. Hence, the present study attempts to design and develop novel FQs that are efficient against resistant E. coli strains. A three-dimensional structure of the mtDNA GyrA protein was developed by homology modeling, following which 204 novel FQ analogs were designed using target based SAR. The designed ligands were then screened using molecular docking studies, through which the pattern of interaction between the ligands and the target protein was studied. As expected, the results of the docking study revealed that the molecules FQ-147, FQ-151 and FQ-37 formed hydrogen bonding and Van der Waals interactions with Leu83 and Asn87 (mutated residues), respectively. Further, the wild-type (WT), mtDNA GyrA and docking complex were studied by molecular dynamics (MD) simulations. Subsequently, all the screened compounds were subjected to a structure and ligand based pharmacophore study followed by ADMET and toxicity (TOPKAT) prediction. Finally, eighteen hit FQ analogs which showed good results for the following properties, viz., best binding score, estimated activity (MIC value) and calculated drug-like properties, and least toxicity, were shortlisted and identified as potential leads to treat UTI caused by FQ resistant E. coli. Apart from development of novel drug candidates for inhibition of mtDNA GyrA, the present study also contributes towards a superior comprehension of the interaction pattern of ligands in the target protein. To a more extensive degree, the present work will be useful for the rational design of novel and potent drugs for UTIs.

RESEARCH ON INVERSION MODELS FOR FOREST HEIGHT ESTIMATION USING POLARIMETRIC SAR INTERFEROMETRY

Abstract. The forest height is an important forest resource information parameter and usually used in biomass estimation. Forest height extraction with PolInSAR is a hot research field of imaging SAR remote sensing. SAR interferometry is a well-established SAR technique to estimate the vertical location of the effective scattering center in each resolution cell through the phase difference in images acquired from spatially separated antennas. The manipulation of PolInSAR has applications ranging from climate monitoring to disaster detection especially when used in forest area, is of particular interest because it is quite sensitive to the location and vertical distribution of vegetation structure components. However, some of the existing methods can’t estimate forest height accurately. Here we introduce several available inversion models and compare the precision of some classical inversion approaches using simulated data. By comparing the advantages and disadvantages of these inversion methods, researchers can find better solutions conveniently based on these inversion methods.

Construction of high-resolution digital elevation model using SAR technique for terrain referred navigation

Construction of high-resolution digital elevation model using SAR technique for terrain referred navigation

Geometric features of LOS data derived by SAR PSI technologies and the three-dimensional data fusion

At present, the satellite SAR persistent scatterer interferometry can already estimate surface changes with a near to 1 mm theoretical precision limit. However, the ascending and descending acquisitions of available SAR services cannot provide three-dimensional changes routinely, though the slow deformation processes are basically three-dimensional (3D). In this paper the geometric features of ascending and descending SAR data and possible fusion with geodetic data are summarised. All the geometric equations are introduced, which are necessary to derive the two characteristic changes in the observation plain defined by ascending and descending unit vectors pointing to SAR satellite positions. The unambiguously derivable characteristic changes can be transformed into vertical and east changes, but they may be biased by possible north displacement. The geometric features of symmetric and asymmetric acquisitions are also investigated. Monte-Carlo simulation is used to investigate the precision of two estimated components. It is experienced that the precisions are not sensitive to one degree standard deviations of positional angles. The Gauss–Markov model of least square adjustment method is used to derive only the statistical properties of reasonable data fusion which can contribute to the 3D applications. Although complementary satellites, which are already proposed in the literature, could provide precise autonomous solutions, in the practise GNSS and levelling data can be used for direct data fusion. Whereas, even errorless levelled high changes cannot contribute to the proper estimation of northern components, GNSS derived changes are the best candidates, which can be interpolated or measured directly. Moreover, these two techniques can properly compensate the weaknesses of each other. The interferometric SAR techniques are not sensitive enough to the north changes, but can contribute to the precision of height estimation, which are the weakest components of the GNSS technique. This statement is valid if the standard deviations of combined data are comparable. For test computations the geometric parameters of available Sentinel-1A images are used, which cover the area of the Szechenyi Istvan Geophysical Observatory, where experimental integrated geodetic benchmark is located combining ascending and descending backscatterers with the possibility of the GNSS, gravimetric and traditional geodetic measurements, as well.

Potential of SAR intensity tracking technique to estimate displacement rate in a landslide-prone area in Haridwar region, India

Landslides constitute one of the major natural hazards that could cause significant loss of life and various human settlements. Mansa Devi hill near Haridwar city has encountered with such potential hazard for several years due to the instability of the slopes. Therefore, preparedness both on regional and site-specific basis at spatial level in the form of surface movements is extremely important to diminish the damage of human life and settlements. Though the surface movement measurement through field-based technique is always very accurate, this technique is time-consuming and unfeasible over a widely affected region. Therefore, areal and satellite remote sensing is gaining importance in landslide investigation due to its wide coverage. In recent years, synthetic aperture radar has already proven its potential for mapping ground deformation due to earthquake, landslide, volcano, etc. Therefore, in this study, an attempt has been made to identify the potential landslide-affected region in Mansa Devi area using one multi-temporal SAR technique and intensity tracking technique. Intensity tracking technique has identified significant mass movement in the landslide-affected region where the other conventional multi-temporal technique, SBAS, fails. An error analysis has been carried out in order to demonstrate the applicability of intensity tracking technique. This study demonstrated that intensity tracking can be considered as an alternative to conventional interferometry for the estimation of land surface displacement when latter is limited by loss of coherence due to rapid and incoherent surface movement and/or large acquisition time intervals between the two SAR images.

Detecting, mapping and monitoring of land subsidence in Jharia Coalfield, Jharkhand, India by spaceborne differential interferometric SAR, GPS and precision levelling techniques

The study aims at detection, mapping and monitoring of land subsidence in Jharia Coalfield, Jharkhand, India by spaceborne DInSAR, GPS and precision levelling techniques. Using multi-frequency C- and L-band DInSAR, both slowly and rapidly subsiding areas were identified and DInSAR-based subsidence maps were prepared. C-band DInSAR was found useful for detection of slowly subsiding areas whereas L-band DInSAR for rapidly subsiding and/or adverse land cover areas. Due to dynamic nature of mining and adverse land cover, temporal decorrelation poses a serious problem particularly in C-band DInSAR. Specially designed InSAR coherence guided adaptive filtering was found useful to highlight the deformation fringes. Collateral GPS and levelling observations were conducted in three test sites to validate DInSAR measurements and to determine the net displacement vectors. We observed an appreciable horizontal displacement component of land subsidence in all the test sites. For comparison of results, we calculated InSAR coherence weighted LOS displacement rates from the unwrapped differential interferograms of smaller spatial subsets and LOS projected ground-based displacement rates in three test sites. We found good agreement between DInSAR and ground-based measurements except for C-band observation in Dobari test site primarily due to large difference in observation periods and temporally inconsistent land subsidence. Collateral spaceborne and ground-based observations were also found useful for characterization of subsidence phenomena to determine net displacement vector and horizontal displacement component. In coal mining areas with spatially scattered and temporally irregular land subsidence phenomena, the adopted methodology can be used successfully for detection, mapping and monitoring of the subsiding areas vulnerable to future collapse. This will facilitate efficient planning and designing of surface infrastructures and other developmental structures in the mining areas and mitigation management of subsidence induced hazards.

A novel SAR interferometry processing method in high resolution spotlight SAR

Synthetic Aperture Radar Interferometry (InSAR) can produce accurate Digital Elevation Model (DEM), and a novel spotlight SAR can get higher azimuth resolution than conventional strip-map SAR. Hence, the combination of InSAR and spotlight SAR techniques implies the potential to obtain higher resolution DEMs which will show more tiny terrain variations. However, in spotlight InSAR processing, additional azimuth interferometric fringes and misregistration decorrelation will be induced by conventional co-registration methods which ignore azimuth varied Doppler centroids in interpolations. Meanwhile, because interferometric fringes in regions with high resolution terrain variations can easily be damaged by random phase noise, there will generate more unreliable unwrapped phase areas with conventional phase unwrapping methods. To eliminate residual azimuth fringes, misregistration decorrelation and unreliable unwrapped phase areas, this paper firstly proposes a novel spotlight SAR interferometry processing method based on co-registration related to two-dimensional Doppler centroid estimation and joint phase unwrapping, and it is validated by using TerraSAR-X spotlight data. The final generated 4 m × 4 m grid space DEM not only preserves high resolution, but also has low root mean square error and absolute mean error which are less than 3 m with respect to the Google earth DEM.

Multi-dimensional SAR tomography for monitoring the deformation of newly built concrete buildings

Deformation often occurs in buildings at early ages, and the constant inspection of deformation is of significant importance to discover possible cracking and avoid wall failure. This paper exploits the multi-dimensional SAR tomography technique to monitor the deformation performances of two newly built buildings (B1 and B2) with a special focus on the effects of concrete creep and shrinkage. To separate the nonlinear thermal expansion from total deformations, the extended 4-D SAR technique is exploited. The thermal map estimated from 44 TerraSAR-X images demonstrates that the derived thermal amplitude is highly related to the building height due to the upward accumulative effect of thermal expansion. The linear deformation velocity map reveals that B1 is subject to settlement during the construction period, in addition, the creep and shrinkage of B1 lead to wall shortening that is a height-dependent movement in the downward direction, and the asymmetrical creep of B2 triggers wall deflection that is a height-dependent movement in the deflection direction. It is also validated that the extended 4-D SAR can rectify the bias of estimated wall shortening and wall deflection by 4-D SAR.

Space-surface bistatic synthetic aperture radar with navigation satellite transmissions: a review

This paper reviews the theory and practice of Space-Surface Bistatic Synthetic Aperture Radar (SS-BSAR) using navigation satellites as transmitters. In recent years, this innovative technology has reached a maturity stage which allows it to be considered for a wide range of applications. The paper covers the fundamental aspects of this technology as a radar system, such as the resolution, power budget and Point Spread Function (PSF) analysis, as well as its signal processing aspects and the state of the art in terms of advanced SAR techniques that it enables. Finally, the theoretical aspects of the paper may be directly transferred to the more generic SS-BSAR concept.

Modified omega-k algorithm for high-speed platform highly-squint staggered SAR based on azimuth non-uniform interpolation.

In this work, the staggered SAR technique is employed for high-speed platform highly-squint SAR by varying the pulse repetition interval (PRI) as a linear function of range-walk. To focus the staggered SAR data more efficiently, a low-complexity modified Omega-k algorithm is proposed based on a novel method for optimal azimuth non-uniform interpolation, avoiding zero padding in range direction for recovering range cell migration (RCM) and saving in both data storage and computational load. An approximate model on continuous PRI variation with respect to sliding receive-window is employed in the proposed algorithm, leaving a residual phase error only due to the effect of a time-varying Doppler phase caused by staggered SAR. Then, azimuth non-uniform interpolation (ANI) at baseband is carried out to compensate the azimuth non-uniform sampling (ANS) effect resulting from continuous PRI variation, which is further followed by the modified Omega-k algorithm. The proposed algorithm has a significantly lower computational complexity, but with an equally effective imaging performance, as shown in our simulation results.

Simulation of Bi-static Radar System Based on Reflected GPS L5 Signals

Reflected GPS signals can have novel application for remote-sensing as they can provide valuable information about the reflecting surface. This paper focuses on the image formation of stationary targets using GPS L5 reflected signals which are processed based on SAR signal processing techniques. At first the power budget analysis for both reflected GPS L1 and L5 signal is carried out for different target to receiver ranges and results are discussed. The complete imaging scenario has been simulated and images using both reflected GPS L1 and L5 signals are presented. Simulations are carried out for different observation time periods and SNR(signal to noise ratio) is calculated for both L1 and L5 frequency signals and results are compared. The results conclude that the SNR and image resolution for L5 signal is superior as compared to L1 signal. The spatial resolution of image reconstructed for reflected L5 signal based on SAR technique is also improved as compared to GPS L1 signal.

Evaluation of DEM generation based on Interferometric SAR using TanDEM-X data in Tokyo

This study is focused on the evaluation of a Digital Elevation Model (DEM) for Tokyo, Japan from data collected by the recently launched TerraSAR add-on for Digital Elevation Measurements (TanDEM-X), satellite of the German Aerospace Center (DLR). The aim of the TanDEM-X mission is to use Interferometric SAR techniques to generate a consistent high resolution global DEM dataset. In order to generate an accurate global DEM using TanDEM-X data, it is important to evaluate the accuracy at different sites around the world. Here, we report our efforts to generate a high-resolution DEM of the Tokyo metropolitan region using TanDEM-X data. We also compare the TanDEM-X DEM with other existing DEMs for the Tokyo region. Statistical techniques were used to calculate the elevation differences between the TanDEM-X DEM and the reference data. Two high-resolution LiDAR DEMs are used as independent reference data. The vertical accuracy of the TanDEM-X DEM evaluated using the Root Mean Square Error (RMSE) is considerably higher than the existing global digital elevation models. However, the local area DEM generated by Geospatial Information Authority of Japan (GSI DEM) showed the highest accuracy among all non-LiDAR DEM’s. The vertical accuracy in terms of RMSE estimated using the 2m LiDAR as reference is 3.20m for TanDEM-X, 2.44m for the GSI, 7.00m for SRTM DEM and 10.24m for ASTER-GDEM. We also compared the accuracy of TanDEM-X with the other DEMs for different types of land cover classes. The results show that the absolute elevation error of TanDEM-X is higher for urban and vegetated areas, likewise to those observed for other global DEM’s. This is probably because the radar signals used by TanDEM-X tend to measure the first reflective surface that is encountered, which is often the top of the buildings or canopy. Hence, the TanDEM-X based DEM is more akin to a Digital Surface Model (DSM).

SAR interferometry and optical remote sensing for analysis of co-seismic deformation, source characteristics and mass wasting pattern of Lushan (China, April 2013) earthquake

Co-seismic deformation associated with the Lushan (China) earthquake that occurred along the south-western segment of the Longmenshan Fault Zone (LFZ) on the 20th April 2013 has been estimated by differential interferometric SAR (DInSAR) technique using Radarsat-2 data. The Lushan earthquake resulted in the deformation of the Sichuan basin and the Longmenshan ranges in proximity to the LFZ. The line of sight (LOS) displacement values obtained from DInSAR technique mainly range between −4.0cm to +3.0cm. The western Sichuan basin shows oblique westward movement with predominant downward component in areas farther from LFZ and predominant westward component over the downward movement in areas closer to the source fault. Inversion modelling has been used to derive the seismic source characteristics from DInSAR derived deformation values using elastic dislocation source type. The linear inversion model converged at a double-fault source solution consisting of a deeper, steep, NW dipping fault plane-1 of 60km×16km dimension and a shallower, gentle, NW dipping fault plane-2 of 60km×15km dimension, with distributed slip values varying between 0 to 2.26m. These fault planes (fault planes-1 and -2) coincide with the Dachuan-Shuangshi fault and the buried Range Front Fault, respectively. The inversion model gives a moment magnitude of 6.81 and the geodetic moment of 2.07×1019Nm, comparable to those given in literature, derived using teleseismic body wave data. Thus DInSAR technique helped to quantify the co-seismic deformation and to retrieve the source characteristics from the estimated deformation values. The study also evaluated the distribution pattern of earthquake induced landslides (EIL) triggered fresh or re-activated during the Lushan earthquake and found that they show spatial association with the seismic source zone and also with various pre-conditioning factors of slope instability.

Invariant Contrast Parameters of PolInSAR Homogenous RVoG Model

It has been shown that the Cramer-Rao bound (CRB) can be helpful to characterize vegetation and ground height estimations based on the homogenous random volume over ground (RVoG) model and polarimetric interferometric SAR techniques. However, this model is a function of 20 unknown parameters, which makes the performance analysis a tedious task. We show that the group invariance property of the RVoG model can greatly reduce the complexity of the analysis since the CRB of the vegetation and ground heights only depends on four unknown parameters instead of 20. Furthermore, for the considered situations analyzed in this letter, only three of these four parameters have a nonnegligible influence and can be interpreted as contrast parameters.