Interferometric Phase Error Research Articles

Image-plane self-calibration in interferometry.

We develop a process of image-plane self-calibration for interferometric imaging data. The process is based on shape-orientation-size (SOS) conservation for the principal triangle in an image generated from the three fringes made from a triad of receiving elements, in situations where interferometric phase errors can be factorized into element-based terms. The basis of the SOS conservation principle is that, for a three-element array, the only possible image corruption due to an element-based phase screen is a tilt of the aperture plane, leading to a shift in the image plane. Thus, an image made from any three-element interferometer represents a true image of the source brightness, modulo an unknown translation. Image-plane self-calibration entails deriving the unknown translations for each triad image via cross-correlation of the observed triad image with a model image of the source brightness. After correcting for these independent shifts, and summing the aligned triad images, a good image of the source brightness is generated from the full array, recovering source structure at diffraction-limited resolution. The process is iterative, using improved source models based on previous iterations. We demonstrate the technique in a high signal-to-noise context, and include a configuration based on radio astronomical facilities, and simple models of double sources. We show that the process converges for the simple models considered, although convergence is slower than for aperture-plane self-calibration for large-N arrays. As currently implemented, the process is most relevant for arrays with a small number of elements. More generally, the technique provides geometric insight into closure phase and the self-calibration process. The technique is generalizable to non-astronomical interferometric imaging applications across the electromagnetic spectrum.

An Improved Independent Parameter Decomposition Method for Gaofen-3 Surveying and Mapping Calibration

The Gaofen-3 (GF-3) satellite can provide digital elevation model (DEM) data from its interferogram outputs. However, the accuracy of these data cannot be ensured without applying a surveying and mapping (SAM) calibration process, thus necessitating geometric and interferometric calibration technologies. In this paper, we propose an independent parameter decomposition (IPD) method to conduct SAM calibration on GF-3 data and generate high-accuracy DEMs. We resolved the geometric parameters to improve the location accuracy and resolved the interferometric parameters to improve the height accuracy. First, we established a geometric calibration model, analyzed the Range–Doppler (RD) model and resolved the initial imaging time error as well as the initial slant range error. Then, we established a three-dimensional reconstruction (TDR) model to analyze the height error sources. Finally, the interferometric phase error and baseline vector error were precisely estimated to ensure the vertical accuracy of the interferometric results by establishing the interferometric calibration model. We then used the GF-3 interferometric data derived on the same orbit in a north–south distribution to conduct the calibration experiment. The results show that the plane positioning accuracy was 5.09 m following geometric calibration, that the vertical accuracy of the interferometric results was 4.18 m following interferometric calibration and that the average absolute elevation accuracy of the derived DEM product was better than 3.09 m when using the GF-3 SAR data, thus confirming the correctness and effectiveness of the proposed GF-3 IPD calibration method. These results provide a technical basis for SAM calibration using GF-3 interferograms at the 1:50,000 scale in China.

A New Baseline Measurement Method for Multinode and Multibaseline Interferometric SAR Systems Using Fiber Bragg Gratings

The multinode multibaseline interferometric synthetic aperture radar measurement system is the future development trend in the field of aviation remote sensing. The deformation error between the nodes directly affects the position and orientation error compensation of the load at the node, and the baseline length error directly affects the interferometric phase error compensation. Aiming at the particularity of the wing structure, a structural deformation measurement and baseline measurement method based on the strain mode is proposed. The fiber Bragg grating sensor is used to acquire the strain of each measuring point on the wing in real time, and the deformation of the wing is accurately measured by the modal superposition method, thereby realizing the high-precision measurement of the baseline between the nodes. The measurement result of the dual total station is the benchmark, and the validation of the method was carried out on the existing test system in the laboratory. Under static conditions, the experimental test results show that the wing deformation measurement accuracy is better than 1 mm, and the baseline measurement accuracy is better than 0.5 mm.

Radar Interferometric Phase Errors Induced by Faraday Rotation

Ionospheric Faraday rotation distorts satellite radar observations of the Earth’s surface. While its impact on radiometric observables is well understood, the errors in repeat-pass interferometric synthetic aperture radar (InSAR) observations and hence in deformation analysis are largely unknown. Because Faraday rotation cannot rigorously be compensated for in nonquad-pol systems, it is imperative to determine the magnitude and nature of the deformation errors. Focusing on distributed targets at L-band, we assess the errors for a range of land covers using airborne observations with simulated Faraday rotation. We find that the deformation error may reach 2 mm in the copol channels over a solar cycle. It can exceed 5 mm for intense solar maxima. The cross-pol channel is more susceptible to severe errors. We identify the leakage of polarimetric phase contributions into the interferometric phase as a dominant error source. The polarimetric scattering characteristics induce a systematic dependence of the Faraday-induced deformation errors on land cover and topography. Also, their temporal characteristics, with pronounced seasonal and quasi-decadal variability, predispose these systematic errors to be misinterpreted as deformation. While the relatively small magnitude of 1–2 mm is of limited concern in many applications, the persistence on semiannual to multiannual time scales compels attention when long-term deformation is to be estimated with millimetric accuracy. Phase errors induced by uncompensated Faraday rotation constitute a nonnegligible source of bias in interferometric deformation measurements.

Assessing the Impact of Positioning Errors in Car-Borne Repeat-Pass SAR Interferometry With a Controlled Rail-Based Experiment

Agile synthetic aperture radar (SAR) platforms such as car-borne and UAV-borne SAR systems require combined inertial navigation systems (INS) and global navigation satellite systems (GNSS) to measure the radar sensor trajectories used for focusing and interferometric processing. Measurement inaccuracies from INS/GNSS systems lead to residual phase errors in the SAR products whose minimisation is crucial to derive accurate topographic and deformation information. In this work, we analyse the impact of residual positioning errors on car-borne repeat-pass SAR interferometry at L-band for different INS/GNSS measurement configurations and for the typical car-borne acquisition geometry. The positioning errors are evaluated both during single SAR acquisitions with long integration times and between different acquisitions as a function of the distance of the radar platform from the GNSS reference stations. We show the reduction of interferometric phase errors achievable by additionally using a GNSS receiver mounted in the vicinity of the SAR platform as compared to remote reference stations of the national network of permanent GNSS receivers. Test results obtained in a controlled setup with a rail-based SAR system equipped with a navigation-grade INS/GNSS system show maximum repeat-pass trajectory errors on the order of 1–2 cm using a local GNSS reference station and up to 10–15 cm using the remote reference stations, leading to azimuth and range phase trends in the interferometric products.

Influence analysis of time synchronization error on altimetry accuracy of multibaseline SARs

To verify the necessity of the time synchronization mechanism in a multibaseline synthetic aperture radar (SAR) system and to acquire the allowable magnitude of the residual time synchronization error after compensation, the influence of the time synchronization error on the altimetry accuracy of multibaseline SAR is studied. Based on a time synchronization error model, the influence of the time synchronization error on the interferometric phase and the influence of the interferometric phase error on the altimetry accuracy of the multibaseline SAR are analyzed, and accordingly, an error transfer model from the time synchronization error to the altimetry accuracy of the multibaseline SAR is established. According to the established error transfer model, the necessity of the time synchronization mechanism in the multibaseline SAR system is verified, and a formula of the allowable magnitude of the residual time synchronization error is derived. The formulas of the single-baseline SAR and the multibaseline SAR to evaluate the altimetry accuracy are compared, and the condition that the altimetry accuracy of the multibaseline SAR is higher than that of the single-baseline SAR is clarified. The accuracy of the derived formula is verified by the performed simulation.

A Flexible Baseline Measuring System Based on Optics for Airborne DPOS.

Three-dimensional imaging for multi-node interferometric synthetic aperture radar (InSAR) or multi-task imaging sensors has become the prevailing trend in the field of aerial remote sensing, which requires multi-node motion information to carry out the motion compensation. A distributed position and orientation system (DPOS) can provide multi-node motion information for InSAR by transfer alignment technology. However, due to wing deformation, the relative spatial relationship between the nodes will change, which will lead to lower accuracy of the transfer alignment. As a result, the flexible baseline between the nodes affects the interferometric phase error compensation and further deteriorates the imaging quality. This paper proposes a flexible baseline measuring system based on optics, which achieves non-connect measurement and overcomes the problem that it is difficult to build an accurate wing deformation model. An accuracy test was conducted in the laboratory, and results showed that the measurement accuracy of the baseline under static and dynamic conditions was less than 0.3 mm and 0.67 mm, respectively.

Interferometric Phase Error Analysis and Compensation in GNSS-InSAR: A Case Study of Structural Monitoring

Global navigation satellite system (GNSS)-based synthetic aperture radar interferometry (InSAR) employs GNSS satellites as transmitters of opportunity and a fixed receiver with two channels, i.e., direct wave and echo, on the ground. The repeat-pass concept is adopted in GNSS-based InSAR to retrieve the deformation of the target area, and it has inherited advantages from the GNSS system, such as a short repeat-pass period and multi-angle retrieval. However, several interferometric phase errors, such as inter-channel and atmospheric errors, are introduced into GNSS-based InSAR, which seriously decreases the accuracy of the retrieved deformation. In this paper, a deformation retrieval algorithm is presented to assess the compensation of the interferometric phase errors in GNSS-based InSAR. Firstly, the topological phase error was eliminated based on accurate digital elevation model (DEM) information from a light detection and ranging (lidar) system. Secondly, the inter-channel phase error was compensated, using direct wave in the echo channel, i.e., a back lobe signal. Finally, by modeling the atmospheric phase, the residual atmospheric phase error was compensated for. This is the first realization of the deformation detection of urban scenes using a GNSS-based system, and the results suggest the effectiveness of the phase error compensation algorithm.

Accuracy analysis of multi‐base InSAR altimeter in ocean surface relative elevation measurement

A new sea-level elevation measurement system was introduced, which uses a distributed multi-base forward-scattering mechanism. After introducing the working principle of the system, this study analyses the main influencing factors of relative elevation measurement in detail. It is proved through quantitative expression that the interferometric phase error is the main error source affecting relative elevation measurement. In order to evaluate the system capability and prove that the multi-base InSAR (MbInSAR) can meet the application requirements of gravity field inversion through relative ocean surface elevation measurement, three aspects of decorrelation, geometric decorrelation, volumetric decorrelation, and SNR decorrelation, are analysed as the interferometric phase error sources.

Modeling and Robust Estimation for the Residual Motion Error in Airborne SAR Interferometry

Due to the limited accuracy of the current navigation systems, uncompensated motion errors during airborne synthetic aperture radar (SAR) preprocessing, i.e., the residual motion error (RME), cause undesirable phase errors in the final interferogram. Especially in airborne repeat-pass interferometric SAR (InSAR), the removal of RME is critical for topographic mapping. In this letter, based on the geometry of a single-baseline interferogram, a model is first developed for describing the relationship between the time-varying baseline parameters and the interferometric phase errors. A robust estimation is then employed to estimate the RME-induced phase errors. The performance of the proposed method was validated by the use of P- and L-band single-baseline interferograms acquired by the airborne E-SAR system. The results showed that the phase artifacts in the initial differential interferograms can be greatly mitigated. In addition, the corrected interferograms acquired in the P- and L-bands were used to estimate the digital elevation model (DEM). After correction, the root-mean-square errors (RMSEs) of the two DEMs with respect to the light detection and ranging (LiDAR) DEM were 2.6 and 4.6 m, respectively, which are improvements of 48.0% and 63.8%. Furthermore, even in the case of low coherence, the proposed method can still work well.

Synthetic Aperture Radar Interferometry Based on Vortex Electromagnetic Waves

The vortex electromagnetic (EM) wave carrying orbital angular momentum (OAM) offers a new degree of freedom for synthetic aperture radar (SAR) imaging. Because vortex EM waves have helical wavefronts, the vortex EM wave-based SAR echo contains the three-dimensional (3D) information of the target. In this paper, an OAM-based synthetic aperture radar interferometry (InSAR) technique is proposed to obtain 3D target information accurately without the existence of baseline. First, a vortex EM waves' SAR imaging model is established, and an improved range-Doppler algorithm is proposed correspondingly. Subsequently, the scheme of the OAM-based InSAR without the physical baseline is proposed. Compared with the conventional InSAR, the OAM-based InSAR can avoid the baseline decorrelation and reduce the requirement of the platform. Besides, the processing procedure of the OAM-based InSAR is simplified, which avoids the image registration and the interferogram flattening. The simulation results demonstrate the effectiveness of the proposed technique. Besides, the height estimation accuracy of the OAM-based InSAR was analyzed, in terms of interferometric phase error and OAM mode error. The height estimation accuracy can be improved by increasing the OAM mode difference appropriately. The OAM, which is completely independent of time, frequency, and polarization, offers a new scheme for the InSAR.

Ionospheric Scintillation Impacts on L-band Geosynchronous D-InSAR System: Models and Analysis

The upcoming L -band geosynchronous differential interferometric synthetic aperture radar (GEO D-InSAR) system has the capability to monitor rapid deformations due to its excellent revisit capability. However, because of its low working frequency, the random ionospheric scintillation signal will degrade the deformation retrieval accuracy by giving rise to extra interferometric phase errors and obvious decorrelations in GEO D-InSAR interferograms. In this paper, aiming at impacts of ionospheric scintillations on GEO D-InSAR system, we theoretically establish its interferometric phase error and decorrelation models by using the scintillation statistical parameters directly. Simulations based on the scintillation sampling model, the Cornell university scintillation model, the phase screen mode, and the ionospheric scintillation signal acquired by the ground-based global positioning system receiver are carried out to verify the proposed model. Moreover, quantitative analyses of the ionospheric scintillation interferometric phase error and decorrelation impacts under different scintillation cases are obtained. The results verify that the proposed models and the analyses are effective. Meanwhile, they also suggest that the generated defocusing decorrelation dominates the ionospheric scintillation impacts on GEO D-InSAR, which can induce a coherence loss of more than 0.1 in the interferogram when only one image of the interferometric pair suffers the weak ionospheric scintillation.

Investigations on the Coregistration of Sentinel-1 TOPS with the Conventional Cross-Correlation Technique

In Sentinel-1 TOPS mode, the antenna sweeps in the azimuth direction for the purpose of illuminating the targets with the entire azimuth antenna pattern (AAP). This azimuth sweeping introduces an extra high-frequency Doppler term into the impulse response function (IRF), which poses a more strict coregistration accuracy for the interferometric purpose. A 1/1000 pixel coregistration accuracy is required for the interferometric phase error to be negligible, and the enhanced spectral diversity (ESD) method is applied for achieving such accuracy. However, since ESD derives miscoregistration from cross-interferometric phase, and phase is always wrapped to [ − π , π ) , an initial coregistration method with enough accuracy is required to resolve the phase ambiguity in ESD. The mainstream for initial coregistration that meets this requirement is the geometrical approach, which accuracy mainly depends on the accuracy of orbits. In this article, the authors propose to investigate the feasibility of using the conventional coregistration approach, namely the cross-correlation-and-rigid-transformation, as the initial coregistration method. The aim is to quantify the coregistration accuracy for cross-correlation-and-rigid-transformation using the Cramér-Rao lower bound (CRLB) and determine whether this method could eventually help to resolve the phase ambiguities of ESD. In addition, we studied the feasibility and robustness of the cross-correlation plus ESD under different conditions. For validation, we checked whether the cross-correlation plus ESD approach could reach the same coregistration accuracy as geometrical plus ESD approach. In general, for large areas with enough coherence and little topography variance, the cross-correlation method could be used as an alternative to the geometrical approach. The interferogram from the two different approaches (with ESD applied afterward) shows a negligible difference under such circumstances.

Design Principles and Considerations for Spaceborne ATI SAR-Based Observations of Ocean Surface Velocity Vectors

This paper presents a methodology to design a spaceborne dual-beam along-track synthetic aperture radar interferometer to retrieve ocean surface velocity vectors. All related aspects and necessary tradeoffs are identified and discussed or reviewed, respectively. This includes a review of the measurement principle and the relation between baseline and sensitivity, the relation between wind and radar backscatter, a discussion of the observation geometry, including the antenna concept, polarization diversity, and all main error contributions. The design methodology consists of a sensitivity-based derivation of explicit instrument requirements from scientific requirements. In turn, this derivation is based on a statistical model for the interferometric phase error. This allows a quantitative, well-grounded instrument design offering an additional degree of freedom to the approach, which we call “noise-equivalent-sigma-zero requirement space.” Crucial tradeoffs for the system design, such as the resolution, the number of independent looks, the minimum wind speed, and the coherence and ambiguities, are pointed out and discussed. Finally, this paper concludes with a single platform system concept operating in Ku-band, which provides the measurement quality needed to achieve a surface velocity estimation accuracy of 5 cm/s, 200-km swath coverage, for 4 $\times$ 4 km2 L2-product resolution and winds starting at 3 m/s.

GEOMETRIC ACCURACY ANALYSIS OF WORLDDEM IN RELATION TO AW3D30, SRTM AND ASTER GDEM2

Abstract. In a project area close to Istanbul the quality of WorldDEM, AW3D30, SRTM DSM and ASTER GDEM2 have been analyzed in relation to a reference aerial LiDAR DEM and to each other. The random and the systematic height errors have been separated. The absolute offset for all height models in X, Y and Z is within the expectation. The shifts have been respected in advance for a satisfying estimation of the random error component. All height models are influenced by some tilts, different in size. In addition systematic deformations can be seen not influencing the standard deviation too much. The delivery of WorldDEM includes information about the height error map which is based on the interferometric phase errors, and the number and location of coverage’s from different orbits. A dependency of the height accuracy from the height error map information and the number of coverage’s can be seen, but it is smaller as expected. WorldDEM is more accurate as the other investigated height models and with 10 m point spacing it includes more morphologic details, visible at contour lines. The morphologic details are close to the details based on the LiDAR digital surface model (DSM). As usual a dependency of the accuracy from the terrain slope can be seen. In forest areas the canopy definition of InSAR X- and C-band height models as well as for the height models based on optical satellite images is not the same as the height definition by LiDAR. In addition the interferometric phase uncertainty over forest areas is larger. Both effects lead to lower height accuracy in forest areas, also visible in the height error map.

Performance Analysis of TanDEM-X Quad-Polarization Products in Pursuit Monostatic Mode

Since 2010, the two twin synthetic aperture radar (SAR) satellites TerraSAR-X and TanDEM-X have been acquiring high-resolution images to generate a global Earth's digital elevation model (DEM). Both satellites have been flying in a controlled close orbit formation, acquiring data in the nominal bistatic stripmap single-polarization mode. Once the acquisition of the dataset for the generation of the DEM has been completed, the flexibility offered by both SAR instruments in terms of interferometric, imaging, and polarization modes has been further exploited to demonstrate the different capabilities of the TanDEM-X experimental modes. By activating the dual-receive antenna mode, full polarimetric data can be acquired. For the first time, it has been possible to systematically command quad-polarization acquisitions in a dedicated TanDEM-X mission science phase, started in October 2014. In this paper, we present a first performance analysis and quality assessment of such quad-polarization products. The SAR image resolution and the noise equivalent sigma zero have been evaluated to show the quality of the focused SAR products. The influence of different instrument parameters on the SAR and interferometric performance, such as chirp bandwidth, pulse repetition frequency, or block adaptive quantization, has been investigated as well. For the evaluation of the interferometric performance, key parameters such as coherence and interferometric phase error have been analyzed. In this paper, the obtained results are presented and recommendations are given for the optimization in the commanding of TanDEM-X quad-polarization acquisitions.

Bandwidth Considerations for Interferometric Applications Based on TanDEM-X

For present and next-generation spaceborne synthetic aperture radar (SAR) missions the use of always larger bandwidths, higher pulse repetition frequencies (PRFs), and multiple acquisition channels is being required. Among the numerous parameters characterizing a SAR system, the specific range and azimuth bandwidth, selected for the SAR image formation, are of primary importance, since they directly affect the quality, the resolution, and the accuracy of the derived products. The purpose of this paper is to investigate their influence with particular focus on interferometric SAR (InSAR) applications. Exploiting the well-known relationships available from SAR theory, the impact of the range and the azimuth bandwidths on the coherence and on the interferometric phase errors is evaluated by means of simulations based on typical TanDEM-X acquisition scenarios. Some examples from real TanDEM-X data are provided as well. The results discussed in this paper can be used as recommendation for those who want to apply for a TanDEM-X science acquisitions proposal, exploiting the high commanding flexibility of the TanDEM-X system, and represent a valuable input for all users dealing with interferometric SAR data and for the design of future InSAR systems in general.

Effects of residual motion compensation errors on the performance of airborne along-track interferometric SAR

Two approximations, center-beam approximation and reference digital elevation model (DEM) approximation, are used in synthetic aperture radar (SAR) motion compensation procedures. They usually introduce residual motion compensation errors for airborne single-antenna SAR imaging and SAR interferometry. In this paper, we investigate the effects of residual uncompensated motion errors, which are caused by the above two approximations, on the performance of airborne along-track interferometric SAR (ATI-SAR). The residual uncompensated errors caused by center-beam approximation in the absence and in the presence of elevation errors are derived, respectively. Airborne simulation parameters are used to verify the correctness of the analysis and to show the impacts of residual uncompensated errors on the interferometric phase errors for ATI-SAR. It is shown that the interferometric phase errors caused by the center-beam approximation with an accurate DEM could be neglected, while the interferometric phase errors caused by the center-beam approximation with an inaccurate DEM cannot be neglected when the elevation errors exceed a threshold. This research provides theoretical bases for the error source analysis and signal processing of airborne ATI-SAR.

High-precision deformation monitoring algorithm for GBSAR system: rail determination phase error compensation

In recent years, the repeat-pass GBSAR (ground based synthetic aperture radar) system has demonstrated its capacity to acquire deformation. Nevertheless, in a variety of applications, it needs to measure the deformation with the precision up to 0.1 mm, which could not be reached by utilizing the traditional PS (permanent scatterer) algorithm in most cases. Generally, one of the main reasons could be summarized into the phase error caused by the rail determination error, because the precision of rail determination might degrade during long working hours. However, the traditional PS algorithm could not compensate for the phase error caused by the rail determination error. In order to solve the problems, we modify the conventional PS algorithm. Firstly, we deduced the transformation relationship between the rail determination error and its corresponding interferometric phase error. Then, the phase errors caused by the atmosphere and the rail determination error were jointly compensated. The experimental data, which were obtained in Fangshan District in Beijing (China), were used to test and verify the performance of the new algorithm. After the comparison between the results processed by the new algorithm and those processed by the traditional algorithm, the proposed method demonstrated its ability to obtain high-precision deformation.

Joint interferometric calibration based on block adjustment for an airborne dual-antenna InSAR system

Mapping large areas using airborne dual-antenna interferometric synthetic aperture radar (InSAR) usually requires processing and mosaicking of different scenes from multiple strips. The overlapping areas of these multiple strips should have consistent elevation values. Due to the unstable attitude of the plane, the interferometric parameters usually vary for each scene during mapping. Therefore, interferometric calibration technology for high-precision height retrieval is required for the correction of the interferometric errors. The traditional interferometric calibration methods for a single scene usually use ground control points (GCPs) to estimate the interferometric parameters – this method cannot guarantee a consistent height in the area of overlap. Besides, GCPs are difficult to deploy over rough terrain, making it impossible to use traditional calibration methods. In this article, a joint interferometric calibration method based on the block adjustment theory used in photogrammetry is proposed for airborne dual-antenna InSAR. This method considers the accurate digital elevation model (DEM) height reconstruction model and can be applied with sparse GCPs. The principle of the proposed method is to make the best use of the GCPs within all the scenes and the tie points (TPs) between the adjacent scenes to establish an error relationship model. First, the weighting values of all GCPs and TPs based on their retrieval elevation error caused by the interferometric phase error and the position distribution difference are introduced in the proposed method. Next, the interferometric parameters are weighted to reduce the condition number of the normal equation. Then, an alternative approximation approach combined with the sparse matrix decomposition technique LDLT is utilized to solve the normal equation, and the corrected interferometric parameters for each scene are obtained. High-precision joint interferometric calibration results for airborne InSAR systems are achieved by the proposed method and validated by experiment. Using the proposed method, the average mean error (AME) and root mean square error (RMSE) are below 0.6037 and 0.9176 m, respectively. Meanwhile, the maximum AME and RMSE of the reconstructed DEM height difference for the validation TPs in the overlapped area of the adjacent scenes are reduced from 1.2909 and 1.7245 m to 0.8864 and 1.2087 m, respectively.