Residual Motion Errors Research Articles

Ku-Band SAR-Drone System and Methodology for Repeat-Pass Interferometry

In recent years, drone-based Synthetic Aperture Radar (SAR) systems have emerged as flexible and cost-efficient solutions for detecting changes in the Earth’s surface, retrieving topographic data, or detecting ground displacement processes in localized areas, among other applications. These systems offer a unique combination of short and versatile revisit times and flexible acquisition geometries that are not achievable with space-borne, airborne, or ground-based SAR sensors. However, due to platform limitations and flight stability issues, they also present significant challenges regarding instrument design and data processing, particularly when generating interferometric repeat-pass datasets. This paper demonstrates the feasibility of repeat-pass interferometry using a Ku-band drone-based SAR system. The system integrates a dual-channel Ku-band Frequency Modulated Continuous Wave (FMCW) radar with cross-track single-pass interferometric capabilities, mounted on a drone platform. The proposed repeat-pass interferometric processing chain leverages an accurate Digital Elevation Model (DEM), generated from the single-pass interferograms, to precisely coregister the entire stack of acquisitions, thereby producing repeat-pass interferograms free from residual motion errors. The results underscore the potential of this system and the processing chain proposed for generating multi-temporal repeat-pass stacks suitable for repeat-pass applications.

Precise Motion Compensation of Multi-Rotor UAV-Borne SAR Based on Improved PTA

In recent years, with the miniaturization of high-precision position and orientation systems (POS), precise motion errors during SAR data collection can be calculated based on high-precision POS. However, compensating for these errors remains a significant challenge for multi-rotor UAV-borne SAR systems. Compared with large aircrafts, multi-rotor UAVs are lighter, slower, have more complex flight trajectories, and have larger squint angles, which result in significant differences in motion errors between building targets and ground targets. If the motion compensation is based on ground elevation, the motion error of the ground target will be fully compensated, but the building target will still have a large residual error; as a result, although the ground targets can be well-focused, the building targets may be severely defocused. Therefore, it is necessary to further compensate for the residual motion error of building targets based on the actual elevation on the SAR image. However, uncompensated errors will affect the time–frequency relationship; furthermore, the ω-k algorithm will further change these errors, resulting in errors in SAR images becoming even more complex and difficult to compensate for. To solve this problem, this paper proposes a novel improved precise topography and aperture-dependent (PTA) method that can precisely compensate for motion errors in the UAV-borne SAR system. After motion compensation and imaging processing based on ground elevation, a secondary focus is applied to defocused buildings. The improved PTA fully considers the coupling of the residual error with the time–frequency relationship and ω-k algorithm, and the precise errors in the two-dimensional frequency domain are determined through numerical calculations without any approximations. Simulation and actual data processing verify the effectiveness of the method, and the experimental results show that the proposed method in this paper is better than the traditional method.

Estimation of Residual Motion Errors and Phase Ambiguity for Repeat-Pass In-CSAR Without External DEMs

Estimation of Residual Motion Errors and Phase Ambiguity for Repeat-Pass In-CSAR Without External DEMs

Enhanced compressed sensing autofocus for high-resolution airborne synthetic aperture radar

The limited accuracy of the navigation system leads to deviations between the real and measured trajectories in airborne synthetic aperture radar (SAR) which results in residual motion (phase) errors and seriously degrades the image quality. The residual errors are usually corrected by using autofocus methods. In this paper, we investigate the autofocus for a high-resolution airborne SAR system which employs stepped-frequency chirp (SFC) signal to achieve high range resolution. As a promising waveform to improve radar range resolution, the SFC signal is widely realized in practical systems. We characterize the backscattering from the scene, phase errors, and receiver noise with a linear matrix-based formulation. In addition, we propose a compressed sampling method that is directly applied to the scene and received signal to provide a sparse raw dataset. We describe the autofocus problem as a constrained optimization problem and propose a new compressed sensing (CS)-based autofocus method to solve it. This method iteratively estimates the phase error and reconstructs the high-resolution SAR image. The image reconstruction is based on the proximity algorithm which applies the shrinkage proximal operator to solve the problem in a computationally efficient manner. We validate the effectiveness of the proposed method using both simulated and real SAR images. Based on visual results and a variety of metrics, the proposed method outperforms the classical autofocus approaches. Also, it provides better or comparable results, with much lower computational complexity, in comparison to that of the recent CS-based autofocus methods.

An Efficient Full-Aperture Approach for Airborne Spotlight SAR Data Processing Based on Time-Domain Dealiasing

The two-step approach (TSA) is an efficient full-aperture method to solve the Doppler spectrum aliasing when processing data acquired by a synthetic aperture radar (SAR) system operating in beam steering mode. This simple approach solves the spectral aliasing by implementing an azimuth convolution between the raw data and a chirp signal, thus avoiding complex subaperture division and recombination of subaperture approaches. However, as aliasing reoccurs in the slow time-domain after the convolution, the estimation and compensation for residual motion error by autofocus cannot be performed immediately, which is crucial for airborne and high-resolution spaceborne SAR processing. The extended TSA solves this problem by implementing full-aperture azimuth scaling, but it is inefficient when the scaling factor deviates from unity severely, which is common in the data acquisition geometry of an airborne SAR. Aiming at addressing the existing shortcomings, this article combines the TSA with autofocus by the time-domain dealiasing and provides an efficient full-aperture processing framework of airborne spotlight SAR data. Simulated and experimental airborne spotlight SAR data with the transmission signal bandwidth of 1.2 GHz and a coherent integration angle of 15<inline-formula><tex-math notation="LaTeX">$^\circ$</tex-math></inline-formula> are processed by the proposed algorithm and the clarity of the processed results shows its effectiveness.

Geolocation Error Transfer Model and Trajectory Calibration Method for Airborne SAR Considering Motion Compensation Residual Error

Airborne Synthetic Aperture Radar (SAR) location error is affected by the position/speed measurement error of the aircraft, system time error, etc., and also related to the residual error of motion compensation. However, the existing airborne SAR location model rarely considers the effect of residual motion error. Considering that motion and trajectory measurement errors are common in practice, this paper derives a location error transfer model of an airborne SAR image based on the motion compensation and frequency-domain imaging algorithms. The proposed model clarifies the influence of trajectory measurement error on location deviation when residual motion error exists and provides a method of error calibration measurement. The simulation experiments validate the correctness of the proposed location error transfer model. The present method obtains a more accurate error calibration measurement result than the location error model that does not consider the residual motion error, proving the superiority of the proposed model.

Correction of Time-Varying Baseline Errors Based on Multibaseline Airborne Interferometric Data Without High-Precision DEMs

The time-varying baseline error (TVBE) caused by the residual motion errors is one of the most significant error sources in the airborne interferometric synthetic aperture radar (InSAR). Although global digital elevation model (DEM) products can be used to extract the TVBE for areas without high-precision DEMs, they cause remarkable height differences (HDs) relative to the actual InSAR-measured topography. In addition, due to the low flight height of airborne SAR platforms, the range-dependent phases resulted from the HDs have significant impacts on the TVBE estimation. Through the mutual restraint of multibaseline observations, this research establishes a multibaseline parameterized model jointly considering HDs and TVBEs in each range direction for the absolute phase calibration. A weighted truncated singular value decomposition (TSVD) algorithm is used to solve the ill-posed problem in joint parameter estimation. Note that, to improve the TVBE extraction, a two-step strategy is adopted. In step one, TVBEs and HDs are preliminarily estimated by the multibaseline parameterized model. After that, bare areas with flat topography, where the truths of HDs can be assumed to be 0, are selected to correct the bias of the estimated HDs. If the flat and bare areas are absent, global ecosystem dynamics investigation (GEDI) or Ice, Cloud, and land Elevation Satellite (ICESAT) points can be used instead. In step two, the multibaseline parameterized model is updated by the calibrated DEM and then used to reestimate the TVBEs. The proposed method was validated by using a simulated data set and two real data sets (i.e., the P- and L-band data sets acquired by the airborne E-SAR system during the BioSAR2008 campaign). The results show that, with respect to the reference values, the root-mean-square error (RMSE) of the calibrated DEMs is 0.48 m for the simulated data set, 2.6 m for the P-band data set, and 3.6 m for the L-band data set, suggesting that the high-precision DEMs are well reconstructed and the TVBE-induced phases can be precisely extracted. After correcting the TVBE-induced phases, the accuracy of the DEMs generated by every linked phase (LP) is improved by at least 38.2% for P-band and by at least 51.0% for L-band. To assess the effectiveness and practicability of the proposed model, we further investigated the influence of the limited multibaseline number, and the baseline combination, and the precision of external DEMs on the TVBE correction. In conclusion, without high-precision DEMs, the multibaseline parameterized method can work well in accurately extracting the TVBE, even for the limited airborne InSAR data set.

A Novel Motion Compensation Scheme for 2-D Multichannel SAR Systems With Quaternion Posture Calculation

The displaced phase center antennas in azimuth and digital beamforming (DBF) in elevation are two state-of-the-art techniques for achieving high-resolution wide swath (HRWS) imaging in the multichannel synthetic aperture radar (SAR) systems. However, due to the atmospheric turbulence, airborne HRWS-SARs inevitably suffer trajectory disturbances, which will consequently defocus the SAR image. Although various motion compensation (MoCo) methods have been proposed, they are mostly designed for the traditional single-channel SAR and, therefore, ignore the channel-dependent posture error. The posture motion error will introduce residual motion and time-variant channel errors, which not only defocuses the image but also causes azimuth ambiguity and degrades the SNR improvement of the final images of the azimuth multichannel and DBF-SAR, respectively. To solve these problems, a novel MoCo scheme for 2-D multichannel SAR systems is proposed. The posture error is described and calculated in matrix form through the use of quaternions. Then, the posture error is transformed into the translational motion error for each receiving channel and is subsequently compensated precisely. To address the residual aperture-variant motion error, a modified aperture-dependent MoCo is integrated into the proposed scheme. Simulations and airborne experiments, including processing the data of a C-band SAR system with four azimuth channels and an X-band DBF-SAR system with 16 elevation channels, have been implemented to validate the effectiveness of the proposed MoCo scheme.

An Extended Two Step Approach to High-Resolution Airborne and Spaceborne SAR Full-Aperture Processing

The processing of synthetic aperture radar (SAR) echoes collected during radar antenna beam steering, such as in the staring spotlight, sliding spotlight, and TOPS operating modes, requires additional efforts due to the limited pulse repetition frequency (PRF). Subaperture processing is mostly used in these cases, but the complexity arising from subaperture dividing and recombination is preferably avoided. The two-step approach (TSA) is an elegant solution to full-aperture processing. Nevertheless, for high-resolution airborne and spaceborne SAR processing, the TSA is still faced with a number of difficulties, which does not occur, however, in subaperture processing. For instance, the high range bandwidth induces Doppler spectrum aliasing during the spectral analysis (SPECAN) stage of the original TSA. Moreover, the Doppler spectrum obtained in TSA, when inverse Fourier transformed back to the slow time domain, might also suffer from aliasing, which precludes the estimation and correction of the unknown residual motion error or tropospheric disturbance. In this article, we extend the TSA to address these problems and present a full-aperture processing framework to precisely focus the high-resolution airborne and spaceborne SAR data. Simulation of X-band spaceborne SAR echoes with transmission signal bandwidth of 3.6 GHz and coherent integration angle of 12.5° has validated the extended TSA (ETSA). Meanwhile, experimental X-band airborne SAR data with the same range and azimuth resolution are also processed using the ETSA, where the conventional autofocusing techniques have been smoothly incorporated.

Two-stage autofocus algorithm with filled function for synthetic aperture radar

Entropy-based parametric autofocus is commonly applied to correct the residual azimuth phase error (APE) that arises from the residual motion errors (RME) in synthetic aperture radar. However, the image’s entropy trends to a convex function only when a great number of range bins are selected according to the law of large numbers, which means that the average residual APE is finally obtained via this method for the space-variant characteristics of RME. A two-stage parametric autofocus algorithm is carried out to derive the exact residual APE with several range bins selected for iteration. To this end, a new objective function in the first stage is designed to reduce the number of local solutions and protect targets from energy leaking. In the second stage, the filled function is imported to jump out of the current solution to a more optimal one until no other optimal solution exists. In the final part, both simulated and real data experiments validate the performance of the proposed method.

Synthetic aperture ladar motion compensation method based on symmetrical triangular linear frequency modulation continuous wave

Synthetic Aperture Ladar (SAL) has the ability to achieve fast high-resolution imaging due to the characteristics of ultra-high resolution and ultra-short synthetic aperture time. However, because synthetic aperture ladar operates in the near-infrared band and the operating wavelength is extremely short, small variations in flightpath can produce artifacts in the phase history that corrupt SAL image generation. This work proposes a motion compensation method based on symmetrical triangular linear frequency modulation continuous wave (T-FMCW) combining with Phase Gradient Autofocus (PGA). Firstly, the ambiguity function of T-FMCW is deduced and its characteristics are analyzed. Then the principle of velocity measurement and Cramer–Rao lower bound of speed estimation error based on this waveform are given. T-FMCW is used to estimate the radial velocity error of the platform in SAL system, and then the radial motion error is estimated by integration along azimuth to realize coarsely focused SAL image. For the coarsely focused SAL image, the residual motion error is extracted to improve the image quality by using PGA. The effectiveness and accuracy of the method is verified by simulation experiments.

A Novel Motion Compensation Approach Based on Symmetric Triangle Wave Interferometry for UAV SAR Imagery

The combination of synthetic aperture radar (SAR) with unmanned aerial vehicles (UAVs) is attractive for acquiring high-resolution images without the restrictions of time and weather. However, because UAVs are lightweight and small in size, the UAV SAR system is very sensitive to turbulence, resulting in serious trajectory deviations and remaining residual motion errors (RMEs), such as residual range cell migration (RCM) and aperture phase errors (APEs). In this paper, a novel motion compensation (MoCo) strategy is developed based on the symmetric triangle linear frequency modulated continuous wave (STLFMCW) signal. The STLFMCW signal model is first presented, which reveals the relevance between the positive-negative frequency modulations and motion errors. The residual RCMs and relative phase errors are estimated directly through the phase differential interferometry of up-ramp and down-ramp chirp signals, instead of the traditional approach of relying on the range-shift gradient of adjacent range profiles. The proposed approach is independent of conventional prominent point processing (PPP) and calculates the range deviation to avoid the accumulation of errors, thereby achieving high precision and efficiency. Experiments based on simulated and measured data sets validate the proposed approach.

Synthetic Aperture Sonar Track Registration With Motion Compensation for Coherent Change Detection

The capability to detect changes in an underwater scene has many applications, including environmental monitoring, surveillance of strategic maritime waterways, and naval mine countermeasures. This paper examines the automated detection of changes in repeat-pass synthetic aperture sonar (SAS) imagery by exploiting the loss of phase coherence caused by differences in the scene. A renavigation method based on track registration is developed for performing the coregistration of images. The method first determines the corrections to be applied to the repeat-pass navigation data by optimizing a linear track model using the estimated across-track pixel displacements. A second optimization is then performed using the along-track pixel displacements to determine a velocity correction for each ping location of the repeat-pass image to compensate for residual motion errors. The corrected navigation solution is then used to rebeamform the repeat-pass image onto the same focal points as the reference image. The method is demonstrated on a pair of repeat-pass SAS images acquired using the AquaPix INSAS2 sonar, where it is shown that it is not necessary to have access to raw element data to coregister images accurately enough for coherent change detection requirements. This technique is then applied to the second data set obtained using the HISAS 1030 sonar for the purpose of comparing both coherent and noncoherent (amplitude-only) approaches to change detection in scenes with low and high clutters. False alarms caused by the acoustic shadows of objects in high-clutter areas are mitigated using the single-pass interferometric coherence as a reference mask. The results show the successful use of the repeat-pass coherence to detect changes between SAS images with temporal baselines of several days on scenes consisting of mud, gravel, and sand, and demonstrate that a coherent approach is capable of detecting large-scale differences (caused by the introduction or removal of targets) as well as subtle scene changes that are not detectable using noncoherent methods.

Residual Motion Error Correction with Backprojection Multisquint Algorithm for Airborne Synthetic Aperture Radar Interferometry.

For airborne interferometric synthetic aperture radar (InSAR) data processing, it is essential to achieve precise motion compensation to obtain high-quality digital elevation models (DEMs). In this paper, a novel InSAR motion compensation method is developed, which combines the backprojection (BP) focusing and the multisquint (MSQ) technique. The algorithm is two-fold. For SAR image focusing, BP algorithm is applied to fully use the navigation information. Additionally, an explicit mathematical expression of residual motion error (RME) in the BP image is derived, which paves a way to integrating the MSQ algorithm in the azimuth spatial wavenumber domain for a refined RME correction. It is revealed that the proposed backprojection multisquint (BP-MSQ) algorithm exploits the motion error correction advantages of BP and MSQ simultaneously, which leads to significant improvements of InSAR image quality. Simulation and real data experiments are employed to illustrate the effectiveness of the proposed algorithm.

Range- and Aperture-Dependent Motion Compensation Based on Precise Frequency Division and Chirp Scaling for Synthetic Aperture Radar

The complicated vibrations of the radar sensor, referred to as motion error, generally produce extra range cell migration (RCM) along the range direction as well as spectral replicas along the azimuth direction, which severely impairs the quality of a focused synthetic aperture radar (SAR) image. This paper concerns the compensation of motion error that is deemed to be range- and aperture-dependent. To this end, two pairs of relations, such as shift range and angle frequency, are analyzed. Based on the derived relations, we propose a chirp scaling-based range envelope correction to cope with the range-dependent position shifts (i.e., RCM) and a precise frequency division approach to account for the residual aperture-dependent motion error. The proposed algorithm can compensate bulk and complicated motion error completely before RCM correction and ensure the focusing quality of an SAR image without autofocus. Both simulated and real data experiments validate the effectiveness of the proposed algorithm.

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.

Integrating Motion Compensation With Polar Format Interpolation for Enhanced Highly Squinted Airborne SAR Imagery

Spatial-variant motion compensation (MOCO) is critical for high resolution and highly squinted airborne synthetic aperture radar (SAR) imaging. Conventional imaging strategies generally perform systematic imaging algorithm and motion compensation algorithm in a separate way, the residual azimuth-variant motion error usually causes defocusing in the image. It is difficult for existing post-filtering strategies to realize high precision and high efficiency imaging simultaneously. To solve this problem, a novel parametric polar format algorithm (PPFA) is proposed in this paper. The polar format interpolation kernel is redefined and improved by inducing motion error parameter, so the proposed algorithm can realize fast imaging and precise spatial-variant motion compensation at the same time. The proposed algorithm has advantage of high processing efficiency as polar format algorithm (PFA) and effectively improves the focusing precision. Extensive comparisons with conventional algorithms illustrate the superiority of the proposed algorithm in both precision and efficiency.

A Motion Compensation Strategy for Airborne Repeat-Pass SAR Data

Generating accurate repeat-pass interferometric airborne synthetic aperture radar (SAR) products demands the precise compensation of the 3-D motion of the aircraft. This requires to estimate and correct small residual motion errors (RMEs) within the accuracy limits of the sensor navigation subsystem, e.g., using residual motion compensation (MoCo) algorithms. Because of their data-driven nature, the performance of these algorithms severely degrades for heavily decorrelated interferograms. This letter proposes a generic RME estimation and compensation strategy optimally estimating RME in a stack of SAR acquisitions, where some interferometric pairs are strongly affected by decorrelation. The algorithm works even if the whole scene decorrelates, as long as the coherence magnitude is reasonably high over short temporal and spatial baselines. The approach entails correcting the navigation data of each slave image of a one-to-many interferometric network with a cumulative correction. The summation is over the results of a precursory application of a general data-driven residual MoCo algorithm (e.g., multisquint) to interferometric pairs for which the impact of interferometric decorrelation is marginal (i.e., small temporal and/or spatial baselines). Compared to other RME correction strategies, the main appeal of the proposed approach lies in the simplicity of its implementation. The overall methodology is tested on a zero-baseline time series acquired at L-band by the German Aerospace Center’s airborne system F-SAR.

Estimation of Residual Motion Errors in Airborne SAR Interferometry Based on Time-Domain Backprojection and Multisquint Techniques

For airborne repeat-pass synthetic aperture radar interferometry (InSAR), precise trajectory information is needed to compensate for deviations of the platform movement from a linear track. Using the trajectory information, motion compensation (MoCo) can be implemented within SAR data focusing. Due to the inaccuracy of current navigation systems, residual motion errors (RMEs) exist between the real and measured trajectory, causing phase undulations in the final interferograms. Up to now, MoCo and RME estimation have usually been combined in airborne InSAR to estimate ground deformation. Conventional MoCo methods generally involve azimuthal and range resampling and phase correction. Then frequency-domain focusing techniques can be used to generate the SAR images. After focusing SAR images with MoCo, both multisquint and autofocus approaches can be used to estimate RME. In addition to the MoCo-based frequency-domain focusing, the time-domain backprojection (BP) technique can also focus the SAR data obtained from highly nonlinear platform trajectories. In this paper, we present, for the first time, the combination of BP and multisquint techniques for RME estimation. A detailed derivation of the implementation of the multisquint approach using the BP-focusing images is presented. Repeat-pass data from the SlimSAR system over Slumgullion landslide are used to demonstrate the feasibility of RME estimation for both stationary and nonstationary scenes. We conclude that the proposed method can effectively remove the RME.

A Wavelet Decomposition and Polynomial Fitting-Based Method for the Estimation of Time-Varying Residual Motion Error in Airborne Interferometric SAR

Compensating the residual motion error (RME) is very important in airborne interferometric synthetic aperture radar (InSAR). In this paper, the wavelet decomposition and polynomial fitting-based (WDPF) method is proposed for detecting and correcting the RME. Wavelet decomposition with root-mean-square error (RMSE) change ratio-based decomposition scale identification is used to detect the RME from the differential interferogram. Polynomial fitting in combination with robust estimation-based least squares is used to absorb the incidence-angle-dependent and topography-dependent components of the RME. A simulated experiment was conducted to test the proposed WDPF method. High-precision RME (with an RMSE of 0.0375 rad) was obtained, which can meet the requirements of InSAR. Real-data L- and P-band InSAR experiments were also performed to test the WDPF method. The results confirmed that the WDPF method can effectively correct the RME for the interferogram. The RMSE of the estimated digital elevation model (DEM) was reduced from 8.03 to 3.46 m and 8.18 to 3.10 m for the L- and P-band interferograms, respectively. Finally, the effects of the external DEM error and polarization on the RME calibration were investigated. The results indicated that the global InSAR DEM products can fulfill the requirement of differential interferogram generation for the WDPF method, and the multipolarization interferograms can help to reduce the effect of the topographic error phase on RME estimation.