Phase Gradient Autofocus Research Articles

Error analysis and correction of atmospheric disturbance for interferometric imaging radar altimeter

The interferometric imaging radar altimeter (InIRA) is a newly developed microwave remote sensing system in recent years. It is of great significance to analyze the main sources of its height measurement error through simulation, and to develop the corresponding image phase error correction methods. This can provide basis and reference for the subsequent correction of the real images phase error. In this study, according to the interaction principle between atmospheric interference and InIRA radar electromagnetic waves, the influence of background ionosphere and background troposphere on height measurement error is analyzed by introducing ionosphere and troposphere delays into echo signals respectively. The impact of ionospheric scintillation and atmospheric turbulence on the height measurement error is analyzed by building multi-layer phase screen models. Then according to the analysis results, a phase error correction method for InIRA images combined by the improved fruit fly optimization algorithm (IFOA) and the joint minimum entropy criterion (JMEC) is proposed. The image is divided into several sub-images with negligible spatial variation of phase error according to the principle of first range and then azimuth. IFOA is used to search the optimal phase compensation values iteratively to compensate the phase of all sub-images. When the joint entropy of the sub-images reaches the minimum value, the phase error correction of the whole InIRA image is completed. Experimental results show that the proposed method can correct the phase of InIRA images with inconspicuous features and polluted by weak ionospheric scintillation and atmospheric turbulence relatively quickly. After correction, the height measurement error can be reduced from decimeter level to centimeter level. The correction accuracy and efficiency of the proposed method are superior to those of the method combined by particle swarm optimization algorithm and joint minimum entropy criterion (PSO-JMEC), the method combined by genetic algorithm and joint minimum entropy criterion (GA-JMEC), the method combined by phase gradient autofocus and Map Drift (PGA-MD), and improved PGA-MD algorithm.

Phase error compensation for Synthetic Aperture Radar (SAR) images by on non-iteration Phase Gradient Autofocus (PGA) algorithms

Phase error compensation for Synthetic Aperture Radar (SAR) images by on non-iteration Phase Gradient Autofocus (PGA) algorithms

An improved phase gradient autofocus algorithm for ISAR phase autofocus problem

An improved phase gradient autofocus algorithm for ISAR phase autofocus problem

Deep learning-based motion compensation for automotive SAR imaging

In this paper, we propose an unsupervised image-to-image translation (UNIT) network as a deep learning-based motion compensation method to compensate for phase errors that may occur when acquiring data from a synthetic aperture radar (SAR) system. In general, in the SAR system measurement process, a problem arises in obtaining data containing phase errors due to the platform’s non-ideal path or unstable pose. Therefore, we propose a deep learning-based motion compensation method and verify the performance of the proposed method through an experiment using an automotive radar. As a result of comparing the performance with existing motion compensation methods based on actual measurement data, the proposed UNIT network showed 8.68% higher peak signal-to-noise ratio (PSNR) and 11.66% higher structural similarity index measure (SSIM) performance than phase gradient autofocus, and 7.98% higher PSNR and 10.82% higher SSIM performance than minimum entropy autofocus.

Spatially Variant Error Elimination for High-Resolution UAV SAR with Extremely Small Incident Angle

Airborne synthetic aperture radar (SAR) is susceptible to atmospheric disturbance and other factors that cause the position offset error of the antenna phase center and motion error. In close-range detection scenarios, the large elevation angle may make it impossible to directly observe areas near the underlying plane, resulting in observation blind spots. In cases where the illumination elevation angle is extremely large, the influence of range variant envelope error and phase modulations becomes more serious, and traditional two-step motion compensation (MOCO) methods may fail to provide accurate imaging. In addition, conventional phase gradient autofocus (PGA) algorithms suffer from reduced performance in scenes with few strong scattering points. To address these practical challenges, we propose an improved phase-weighted estimation PGA algorithm that analyzes the motion error of UAV SAR under a large elevation angle, providing a solution for high-order range variant motion error. Based on this algorithm, we introduce a combined focusing method that applies a threshold value for selection and optimization. Unlike traditional MOCO methods, our proposed method can more accurately compensate for spatially variant motion error in the case of scenes with few strong scattering points, indicating its wider applicability. The effectiveness of our proposed approach is verified by simulation and real data experimental results.

Modified Auto-Focusing Algorithm for High Squint Diving SAR Imaging Based on the Back-Projection Algorithm with Spectrum Alignment and Truncation

The study focuses on addressing the image defocusing issue caused by motion errors in highly squinted Synthetic Aperture Radar (SAR). The traditional auto-focusing algorithm, Phase Gradient Autofocus (PGA), is not effective in this mode due to difficulties in estimating the phase gradient accurately from strong point targets. Two main reasons contribute to this problem. Firstly, the direction of the energy-distributed lines in the Point Spread Function (PSF) does not align with the image’s azimuth direction in highly squinted mode. Secondly, the wavenumber spectrum of high squint SAR images obtained using the Back-Projection Algorithm (BPA) varies spatially, causing aliasing in the azimuth spectrum of all targets. In this paper, a new auto-focusing method is proposed for highly squinted SAR imaging. The modifications to the BP imaging grids have been implemented to address the first problem, while a novel wavenumber spectrum shifting and truncation method is proposed to accurately extract the phase gradient and tackle the spatial variation issue. The feasibility of the proposed algorithm is verified through simulations with point targets and processing of real data. The evaluation of the image shows an average improvement of four times in PSLR (Peak-Sidelobe-to-Noise Ratio).

Joint correction method for ionospheric phase pollution of high‐frequency sky‐surface wave radar based on adaptive optimal path

AbstractThe high‐frequency (HF) hybrid sky‐surface wave system is a new early warning radar. However, due to the influence of bistatic angle and ionospheric phase path disturbance, the echo spectrum will be widened, which seriously affects the ability of detecting slow targets of ships. In view of the overlapping of positive and negative Bragg broadening peaks caused by the large amplitude ionospheric phase path disturbance in the echo spectrum of HF sky‐surface wave radar, a joint correction method of ionospheric phase pollution based on adaptive optimal path is proposed in this paper. Firstly, the time‐frequency spectrum polluted by ionospheric phase is obtained by high resolution time‐frequency MUSIC transform, then the ionospheric phase disturbance curve in the time spectrum of polluted echo is extracted by the proposed adaptive optimal path method, and then the polluted echo is initially compensated to obtain the sharpened ocean echo spectrum. Finally, the residual phase of pollution curve is estimated by the Phase Gradient Autofocus method, and then the pollution echo is accurately corrected. The results of theoretical and measured data show that this method is effective in correcting the overlapping of positive and negative Bragg broadening peaks caused by serious ionospheric phase pollution.

A High-Resolution Airborne SAR Autofocusing Approach Based on SR-PGA and Subimage Resampling With Precise Hyperbolic Model

High-resolution airborne synthetic aperture radar (SAR) imaging requires long synthetic aperture time (LSAT). However, the LSAT invalidates the Fresnel approximation in the traditional autofocusing method, leaving a residual signal phase in the motion error. To solve the problem, a signal-reconstruction-based phase gradient autofocus (SR-PGA) and a sub-image resampling (SIR) methods are proposed. They are developed on the hyperbolic model. First, a sub-aperture division strategy divides the full-aperture high-order error into multiple low-order sub-aperture errors. Then, the SR-PGA is developed to estimate the sub-aperture error (SPE), in which the precise deramping is reconstructed to eliminate the residual signal phase in the SPE. Third, the SIR is proposed to eliminate residual Doppler-variant shift of the adjacent sub-images, improving the accuracy of the SPE combination. Finally, simulation and actual data processing verify the effectiveness and validity of the algorithm.

Segmental Aperture Imaging Algorithm for Multirotor UAV-Borne MiniSAR

This article takes on the challenges of synthetic aperture radar (SAR) imaging for miniaturized SAR (MiniSAR) onboard a multirotor unmanned aerial vehicle (UAV). Several unique challenges are systematically analyzed, and a corresponding analytical phase error model is established, which accurately models the effects of both translational and rotational motions of UAVs. A segmental aperture imaging (SAI) algorithm, an autofocus algorithm based on strong scatterers, is proposed. It simply divides the platform trajectory into uneven segments, which are first independently focused with motion compensation and then stitched together to form a complete SAR image. Both the theoretical derivation of the signal model and the implementation of the imaging algorithm are presented. A simulation analysis with actual UAV trajectory and attitude data is conducted, which demonstrates the efficacy and performance of the proposed imaging algorithm. It shows that the ideal focusing effect can be achieved as evaluated by various metrics, and the proposed algorithm has superior performance compared to the subaperture phase gradient autofocus (PGA) and minimum entropy autofocus (MEA) methods. Finally, the multirotor-borne MiniSAR system FUSAR-Ku is used for experiments to verify the proposed algorithm. Experimental results show that the proposed algorithm can achieve the theoretical decimeter-resolution imaging performance as measured by various metrics.

Maintenance method of signal coherence in lidar and experimental validation.

According to the self-heterodyne signal obtained by lidar under different fiber delay times, the model of the local oscillator signal was established, and the maintenance method of signal coherence in lidar based on the digital delay was improved by using multiple sinusoidal frequency modulation components. An imaging detection experiment was carried out at a distance of 5.4 km. The coherence of the lidar signal was maintained by combining the transmitting reference channel correction method and the local oscillator reference channel compensation method, accompanied by the use of a phase spectrum to analyze the improvement effect. The processing results of the echo signal showed that the method could remove the high-order phase errors that cannot be compensated by the phase gradient autofocus algorithm and improve the signal coherence, which could be used for the detection and imaging of long-range targets.

A Novel Phase Compensation Method for Urban 3D Reconstruction Using SAR Tomography

Synthetic aperture radar (SAR) tomography (TomoSAR) has been widely used in the three-dimensional (3D) reconstruction of urban areas using the multi-baseline (MB) SAR data. For urban scenarios, the MB SAR data are often acquired by repeat-pass using the spaceborne SAR system. Such a data stack generally has long time baselines, which result in different atmospheric disturbances of the data acquired by different tracks. These factors can lead to the presence of phase errors (PEs). PEs are multiplicative noise for observation data, which can cause diffusion and defocus in TomoSAR imaging and seriously affect the extraction of target 3D information. In this paper, we combine the methods of the block-building network (BBN) and phase gradient autofocus (PGA) to propose a novel phase compensation method called BBN-PGA. The BBN-PGA method can effectively and efficiently compensate for PEs of the MB SAR data over a wide area and improve the accuracy of 3D reconstruction of urban areas. The applicability of this proposed BBN-PGA method is proved by using simulated data and the spaceborne MB SAR data acquired by the TerraSAR-X satellite over an area in Barcelona, Spain.

Inverse synthetic aperture lidar imaging and compensation in slant atmospheric turbulence with phase gradient algorithm compensation

To systematically study the influence of slant atmospheric turbulence on the inverse synthetic aperture lidar (ISAL) imaging, the atmospheric random phase screen with the modified von Kármán spectrum was numerically simulated via the fast Fourier transform spectral inversion method. Intensity phase distribution and brightness images of the Gaussian beam slant transmission were simulated under different turbulence intensities. Using the Kirchhoff approximation and convolution back-projection algorithm, ISAL images of rough surface (rough square and rough circular plates), rough graphics and rough body with different roughnesses under various turbulence intensities were obtained. The analyses showed that these ISAL images of rough targets can be resolved under weak turbulence but not under moderately strong turbulence. Aiming at the reduction of the resolution of the rough target ISAL images caused by atmospheric turbulence, the phase gradient autofocus (PGA) algorithm was used to improve image focusing and distinguish the shapes of rough targets.

An Improved Spatially Variant MOCO Approach Based on an MDA for High-Resolution UAV SAR Imaging with Large Measurement Errors

For unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) imaging, motion errors cannot be obtained accurately when high precision motion sensors are not equipped on the platform. This means that traditional data-based motion compensation (MOCO) cannot be directly implemented due to large measurement errors. In addition, classic autofocusing techniques, such as phase gradient autofocus (PGA) or map-drift algorithm (MDA), do not perform well with spatially variant errors, greatly affecting the imaging qualities, especially for high-resolution and large-swath cases. In this study, an improved spatially variant MOCO approach based on an MDA is developed to effectively eliminate the spatially variant errors. Based on the coarse and precise MDA chirp rate error estimation, motion errors are optimally acquired by the random sample consensus (RANSAC) iteration. Two-dimensional (2D) mapping is used to decouple the spatially variant residual errors into two linear independent dimensions so that the chirp-z transform (CZT) can be performed for echo data correction. Unlike traditional approaches, the spatially variant components can be compensated without any measured motion information, which indicates that the proposed approach can be applied to the common UAV SAR system with significant measurement errors. Simulations and real data experiments were used to evaluate the performance of the proposed method. The simulation results show that the proposed algorithm is able to effectively minimize spatially variant errors and generate much better imaging results.

An Autofocus Approach With Applications to Ionospheric Scintillation Compensation for Spaceborne SAR Images

Spaceborne synthetic aperture radar (SAR) systems, operating at L-band or lower, are very susceptible to ionospheric scintillation. The scintillation phase error (SPE) can bring about serious azimuth decorrelation and resolution loss. Compared with the motion phase error, the SPE takes on a much stronger spatial-variation both in along-track and across-track orientations, and its anisotropic feature makes the compensation more intractable. In this article, the phase gradient autofocus (PGA) is used for the first time to compensate the spatial-varying and anisotropic SPE for spaceborne SAR images. It begins with achieving a reliable SPE estimate by applying PGA to a strong scatterer. According to the preknowledge of the phase screen altitude and the anisotropic elongation heading, the emphasis is then on estimating the SPEs for other pixels from the well-estimated SPE, based on the mutual correlation and overlapping of SPEs. The pixel-by-pixel strategy is adopted for the final compensation. The proposed methodology is very appropriate for SAR images with few corner reflectors, which is validated on a simulated L-band stripmap data and a PALSAR-2 spotlight real data. It shows more powerful utility than the classical PGA. The performance analysis is implemented with regard to two necessary factors, which further confirms the effectiveness of the proposed methodology.

GEO SAR Imaging of Maneuvering Ships Based on Time–frequency Features Extraction

Geosynchronous synthetic aperture radar (GEO SAR) system has the ability of observing targets for several hours in a large field of view. Complex and irregular rotating motion of the ship on sea in long aperture time makes it difficult to focus. To accomplish the imaging of maneuvering ships, a novel imaging algorithm is proposed in this article. A spatial filter constructed by convolutional neural network (CNN) is utilized to extract the time–frequency features. Combined with local generalized Radon–Fourier transform (GRFT) and phase gradient autofocus (PGA), the extraction accuracy further increases. Validation results based on simulation experiment, airborne experiment, and wave pool experiment show that the proposed algorithm achieves good imaging performance.

A Modified PGA for Spaceborne SAR Scintillation Compensation Based on the Weighted Maximum Likelihood Estimator and Data Division

The P-band spaceborne synthetic aperture radar (SAR) is significantly affected by ionospheric scintillation. Although the traditional phase gradient autofocus (PGA) can estimate and compensate the scintillation phase of the single polarization SAR data, the quality of the refocused image will degrade at the scene edge. In this paper, a modified PGA based on the weighted maximum likelihood (WML) estimator and data division is proposed for full-scene image refocusing. First, a data division strategy for scintillation corrupted image is introduced, which is based on the prior scintillation information including its power spectral density (PSD) and autocorrelation function (ACF). Then, some pre-processing steps including data selection, circular shifting and windowing are performed for suppressing the noise and clutter. Finally, the scintillation phase is estimated by the WML estimator with fewer iterations, and after the scintillation phase of all data blocks are obtained, the distorted full-scene image is refocused. Using the generated wide-band ionospheric scintillation model (WBMOD) phase screen, numerical simulations based on point targets and scenes derived from real spaceborne SAR data are carried out. The evaluation results about resolution, peak side-lobe ratio (PSLR), integral side-lobe ratio (ISLR), correlation coefficient and image entropy demonstrate the effectiveness of the proposed algorithm.

A Dual-Band Difference Ionosphere Compensation Algorithm for Mars Orbiter Subsurface Investigation Radar

When detecting the underground structure of Mars using an orbital subsurface investigation radar, it is essential to compensate for the ionosphere distortion of the received echo. The existing algorithms, such as the contrast method (CM) and the phase-gradient-autofocus (PGA) algorithm, can mainly compensate for the defocus of the echo, but it is difficult to compensate for the group delay at the same time, resulting in the deviation between the echo position and the terrain profile. This article analyzes the interference of Martian ionosphere to the echo of subsurface investigation radar and proposes a dual-band difference (DBD) ionosphere compensation algorithm. First, the group delay model of radar echo under ionospheric interference is established. Then, the equivalent plasma frequency of the ionosphere is calculated according to the group delay difference of echoes in two bands, and the Taylor coefficients of the phase error are calculated. Finally, the echoes are accurately compensated with the Taylor series model of phase shift. This algorithm can correct the defocus and sidelobe interference and simultaneously compensate for the group delay, which is greatly significant to accurately locate the subsurface structure of Mars. The experiments on the simulation data and the echo of the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) show the feasibility of this method. Compared with the traditional way, this algorithm is suitable for both high- and low-frequency situations, and the high computational efficiency without iteration makes on-orbit real-time ionosphere compensation possible. Moreover, with the effective correction of topographic offset, the total electron content (TEC) can also be accurately retrieved.

An Autofocus Approach for UAV-Based Ultrawideband Ultrawidebeam SAR Data With Frequency-Dependent and 2-D Space-Variant Motion Errors

Unmanned-aerial-vehicle-based (UAV-based) ultrawideband and ultrawidebeam (UWB) synthetic aperture radar (SAR) is very sensitive to atmospheric turbulence and suffers from serious 2-D space-variant motion errors (SVMEs) caused by the ultrawide beam and frequency-dependent phase errors caused by the ultrawideband. This article proposes an autofocus approach for UAV-based UWB SAR data based on the quasi-polar grid fast factorized backprojection (FFBP) imaging framework, multiple subband local autofocus (MSBLA), and trajectory deviation estimation. First, based on an improved weighted phase gradient autofocus (WPGA) method for subband-division local images, MSBLA is introduced to solve the local motion error estimation problem with frequency-dependent phase errors. Then, trajectory deviation estimation based on the weighted least square (WLS) method is performed to solve the 2-D SVME problem. Finally, the subaperture trajectory deviations are fused into a full-aperture trajectory deviation by an improved fusion strategy based on piecewise weighting. This approach is applied to real data from a new UAV-based UWB SAR. The results of both simulation and real data experiments are presented and verify the effectiveness of the proposed approach.

SAR Imaging of Swing Ships Based on Two-Dimensional Spatial Variance Correction

The ship on the sea has the phenomenon of swing under the combined action of sea waves, wind and its stability system in the case of synthetic aperture radar (SAR) imaging, which makes it difficult to focus. In order to correct the two-dimensional (2-D) spatial variance and accomplish the imaging of swing ship, this paper proposes a new imaging algorithm based on spatial variant phase gradient autofocus (SV-PGA). Firstly, the entropy difference is used to determine the specific position of the ship. Then the ship image is extracted and segmented by a variable-size segmentation strategy. PGA is used to focus each sub image, and a well-focused ship image is obtained. The results of simulation experiments and real data show that the algorithm has good focusing performance.

An Ionospheric Phase Screen Projection Method of Phase Gradient Autofocus in Spaceborne SAR

The phase scintillation induced by ionospheric irregularities can reduce azimuth decorrelation and cause defocusing in the low-frequency spaceborne synthetic aperture radar (SAR) imaging. Thus, it demands for an autofocus approach to correct the scintillation phase error (SPE) and to refocus the deteriorated SAR image. However, the azimuth variation of the SPE has been rarely considered and poorly tackled in previous research studies. In this letter, an ionospheric phase screen (PS) projection method of phase gradient autofocus (PSP-PGA) is proposed to deal with this issue and compensate the azimuth-varying SPE in SAR images. The PSP is used to project the SAR image onto the PS, by using the part decompression and spectral analysis, so as to realize the decoupling of the SAR data with SPE. Then, the projected image can be directly applied to the PGA to accurately estimate the SPE. The proposed PSP-PGA is validated by using several simulation processing experiments and its performance is finally evaluated with respect to the parameter of the PS height.