Phase Gradient Autofocus Research Articles

An Improved Phase Gradient Autofocus Algorithm Used in Real-time Processing

An Improved Phase Gradient Autofocus Algorithm Used in Real-time Processing

A Synthetic Bandwidth Method for High-Resolution SAR Based on PGA in the Range Dimension.

The synthetic bandwidth technique is an effective method to achieve ultra-high range resolution in an SAR system. There are mainly two challenges in its implementation. The first one is the estimation and compensation of system errors, such as the timing deviation and the amplitude-phase error. Due to precision limitation of the radar instrument, construction of the sub-band signals becomes much more complicated with these errors. The second challenge lies in the combination method, that is how to fit the sub-band signals together into a much wider bandwidth. In this paper, a novel synthetic bandwidth approach is presented. It considers two main errors of the multi-sub-band SAR system and compensates them by a two-order PGA (phase gradient auto-focus)-based method, named TRPGA. Furthermore, an improved cut-paste method is proposed to combine the signals in the frequency domain. It exploits the redundancy of errors and requires only a limited amount of data in the azimuth direction for error estimation. Moreover, the up-sampling operation can be avoided in the combination process. Imaging results based on both simulated and real data are presented to validate the proposed approach.

Performance Analysis of Phase Gradient Autofocus for Compensating Ionospheric Phase Scintillation in BIOMASS P-Band SAR Data

The P-band synthetic aperture radar of the European Space Agency BIOMASS mission will be affected by ionospheric phase scintillation at high latitudes, which introduces a random high-order azimuth phase error. The dependence of the performance of the phase gradient autofocus (PGA) algorithm for scintillation compensation on the strength of ionospheric turbulence and the signal-to-clutter ratio (SCR) is analyzed. In order to keep resolution degradation below 2%, the SCR must exceed 16 and 20 dB for turbulence strengths $C_kL=10^{33}$ and $10^{34}$ , respectively. For large values of $C_kL$ , phase scintillation adds significantly to post-PGA degradation in the integrated and peak sidelobe ratios. Simulations based on scenes derived from PALSAR data demonstrate the effectiveness of PGA.

Highly efficient synthetic aperture radar processing system for airborne sensors using CPU+GPU architecture

Wuhan University, State Key Laboratory of Information Engineering in Surveying,Mapping and Remote Sensing, Wuhan 430079, ChinaAbstract. A comprehensive and effective parallel airborne synthetic aperture radar (SAR)processing system using the architecture of central processing units (CPU) and graphicalprocessing units (GPU) is proposed first in this paper. By using the techniques of ComputeUnified Device Architecture, the SAR processing system is much more efficient and robust,thereby enabling it to work with high efficiency. This paper focuses on the optimizations ofmotioncompensation,subaperturechirpscalingalgorithm,phasegradientautofocus(PGA),andevenvisualizationwithOpenSourceComputerVision Library.Apart from this,itisalsothe firsttime the PGA has been run on the architecture of CPU and GPU. Experimental results show aspeedup of ∼37 times compared with a nonoptimized CPU-based approach.

Extension and Evaluation of PGA in ScanSAR Mode using Full-Aperture Approach

In order to enable a testbed for spaceborne scanning synthetic aperture radar (ScanSAR) mode, in this letter, a ScanSAR autofocusing approach for airborne platforms has been developed. Autofocusing algorithms, such as the phase gradient autofocus (PGA) algorithm, prove to be a useful postprocessing technique to get refocused synthetic aperture radar images. However, conventional stripmap PGA does not work in ScanSAR mode when the full-aperture approach is used, due to the periodic data gaps in each subswath. To solve this problem, we extend the stripmap PGA to ScanSAR with some modifications, mainly in the subaperture segmentation and phase error estimation steps. The performance of extended stripmap PGA is evaluated by an airborne ScanSAR data set containing different types of terrain, with a high spatial resolution up to 3.5 m in azimuth.

Improved phase gradient autofocus algorithm based on segments of variable lengths and minimum‐entropy phase correction

Unmanned aerial vehicle (UAV) synthetic aperture radar (SAR) is an essential tool for modern remote sensing applications. Owing to its size and weight constraints, UAV is very sensitive to atmospheric turbulence that causes serious trajectory deviations. In this study, an improved phase gradient autofocus (PGA) motion compensation approach is proposed for UAV-SAR imagery. The approach is implemented in two steps. The first step determines the length of each segment depending on number of good quality scatterers and motion errors obtained from navigation data. In the second step, a novel minimum-entropy phase correction based on the discrete cosine transform (DCT) coefficients is proposed. In this approach, transform phase error estimated by PGA to DCT-coefficients that represent the phase error in the frequency or time-frequency domain. The entropy of a focused image is utilised as the optimisation function of the DCT-coefficients to improve the final image quality. Finally, real-data experiments show that the proposed approach is appropriate for highly precise imaging of UAV-SAR equipped with only low-accuracy inertial navigation systems.

PGA(Phase Gradient Autofocus)기반 ISAR영상 자동초점기법 성능개선

PGA(phase gradient autofocus) has been widely used to remove motion induced phase errors in the ISAR(inverse synthetic aperture radar) imaging. The critical process for the processing time and image quality is windowing stage in PGA. In this paper, the new method to determine window size based on polynomial least square approximation is proposed. Moreover, dominant range bins are selected for efficient phase error estimation, which improve image quality and speed up convergence. The simulation results show that the proposed algorithm provides high quality ISAR images while computational efficiency of inherent PGA is retained.

Focusing the acoustic signal of a maneuvering rotorcraft

An algorithm was developed and tested to blindly focus the acoustic spectra of a rotorcraft that was blurred by time-varying Doppler shifts and other effects such atmospheric distortion. First, the fundamental frequency generated by the main rotor blades of a rotorcraft was tracked using a fix-lag smoother. Then, the frequency estimates were used to resample the data in time using interpolation. Next, the motion compensated data were further focused using a technique based upon the phase gradient autofocus algorithm. The performance of the focusing algorithm was evaluated by analyzing the increase in the amplitude of the harmonics. For most of the data, the algorithm focused the harmonics between approximately 10–90 Hz to within 1–2 dB of an estimated upper bound obtained from conservation of energy and estimates of the Doppler shift. In addition, the algorithm was able to separate two closely spaced frequencies in the spectra of the rotorcraft. The algorithm developed can be used to preprocess data for classification, nulling, and tracking algorithms.

Synthetic aperture ladar imaging demonstrations and information at very low return levels.

We present synthetic aperture ladar (SAL) imaging demonstrations where the return-signal level from the target is near the single-photon level per resolved pixel. Scenes consisting of both specular-point targets and diffuse-reflection, fully speckled targets are studied. Artificial retro-reflector-based phase references and/or phase-gradient-autofocus (PGA) algorithms were utilized for compensation of phase errors during the aperture motion. It was found that SAL images could reliably be formed with both methods even when the final max pixel intensity was at the few photon level, which means the SNR before azimuth compression is below unity. Mutual information-based comparison of SAL images show that average mutual information is reduced when the PGA is utilized for image-based phase compensation. The photon information efficiency of SAL and coherent imaging is discussed.

Motion compensation using substrip PGA

MOtion COmpensation (MOCO) is an essential step in high resolution airborne Synthetic Aperture Radar (SAR) imaging. Generally, a reference altitude level is assumed and external Digital Elevation Model (DEM) is required for the scene topography heavily varied. To overcome the shortcoming, we propose a MOCO method based on Phase Gradient Autofocus (PGA) which can obtain well focused images without DEM. In the implementation, we first compensate the normal range-invariant term. Then the data are divided into strips in range-compressed domain and PGA is applied to each substrip to extract the phase errors. Finally, the phase error surface is obtained using interpolation and then compensated. Real airborne SAR data of a UAV-SAR system experiments and comparisons demonstrate the validity and effectiveness of the proposed algorithm. The results show that our algorithm is effective.

Blind focusing algorithm applied to the acoustic signal of a maneuvering rotorcraft

An algorithm was developed and tested to blindly focus the acoustic spectra of a rotorcraft that was blurred by time-varying Doppler shifts and other effects such atmospheric distortion. First, the fundamental frequency generated by the main rotor blades of a rotorcraft was tracked using a fixed-lag smoother. Then, the frequency estimates were used to resample the data using interpolation. Next, the motion-compensated data were further focused using a technique based upon the phase gradient autofocus (PGA) algorithm. The performance of the algorithm was evaluated by analyzing the increase in the amplitude of the harmonics due to focusing the data. For most of the data, the algorithm focused the harmonics between approximately 10-90 Hz to within 1-2 dB of an estimated upper bound (UB) obtained from conservation of energy and estimates of the Doppler shift. In addition, the algorithm was able to separate two closely spaced frequencies in the spectra of the rotorcraft. The algorithm developed can be used to preprocess data for classification, nulling, and tracking algorithms.

A Modified Phase Gradient Autofocus (PGA) Algorithm for Airborne/Stationary Bistatic SAR Imaging

A Modified Phase Gradient Autofocus (PGA) Algorithm for Airborne/Stationary Bistatic SAR Imaging

An Azimuth-Dependent Phase Gradient Autofocus (APGA) Algorithm for Airborne/Stationary BiSAR Imagery

In airborne/stationary bistatic-synthetic-aperture-radar imaging, translational invariance was no longer valid. After range cell migration correction, the range-compressed signal under the same range gate exhibited azimuth-dependent FM rates that made the motion-induced phase error difficult to separate from the echoes. To solve this problem, an azimuth-dependent phase gradient autofocus (PGA) algorithm was proposed. Different from the conventional PGA, the residual quadratic phase arising from the azimuth-dependent FM rates was additionally estimated and compensated. As the influence of the azimuth-dependent FM rates was greatly reduced, a phase gradient estimator was subsequently applied for accurate phase error retrieval. Acquired raw data were analyzed to verify the proposed algorithm.

Correction to “An Azimuth-Dependent Phase Gradient Autofocus (APGA) Algorithm for Airborne/Stationary BiSAR Imagery” [Nov 13 1290-1294

In the above paper (ibid., vol. 10, no, 6, pp. 1290-1294, Nov. 2013), there is an error in equation (5). The correction is presented here.

SAR Image Autofocus Utilizing Minimum-Entropy Criterion

An autofocus method was presented based on an entropy criterion for synthetic aperture radar imaging. An iterative method, through minimizing the entropy, was derived to obtain the phase error which corrupted the image and increases image entropy. Moreover, dominant scatterers were selected as the input of the phase-error estimation, which was similar to the phase gradient autofocus algorithm. There were not any model assumptions for the phase error in the proposed method. Phase estimation accuracy was also analyzed. Finally, the simulation and experimental results were utilized to validate the feasibility and effectiveness of the proposed method.

Robust Autofocusing Approach for Highly Squinted SAR Imagery Using the Extended Wavenumber Algorithm

For highly squinted synthetic aperture radar (SAR) imaging, the wavenumber domain SAR processing algorithm is commonly accepted as an ideal solution to SAR focusing in the case of an ideal straight sensor trajectory. However, airborne SAR is very sensitive to atmospheric turbulence that causes serious trajectory deviations. In this paper, we propose a robust autofocusing approach for highly squinted airborne SAR imagery using the extended wavenumber algorithm, being capable of estimating the range-dependent phase errors. To apply the proposed autofocusing scheme, a detailed analysis of the motion error model in the conical reference system is presented, where the formulation of range-dependent phase errors for squinted SAR is given. The proposed autofocusing approach is performed by a three-step process: referring to the inevitable residual phase after deramping for highly squinted SAR, a modified squinted phase gradient autofocusing (SPGA) algorithm is put forward to retrieve the range-independent phase errors; based on the established motion error model, the residual range-dependent phase errors are estimated using a local maximum likelihood-weighted SPGA algorithm; and motion compensation is executed by a two-step approach to reach the range-independent and range-dependent corrections, respectively. Experiments based on measured data have shown that the proposed autofocusing approach performs well for highly squinted SAR imaging.

A Novel Autofocus Algorithm Based on DCT Criteria for SAR Images

A novel autofocus algorithm based on Discrete Cosine Transform (DCT) for Synthetic Aperture Radar (SAR) images is presented in this paper. The method, which starts with complex phase-degraded SAR images, with the phase errors model is introduced into the range-compressed phase-history domain, carries out phase errors correction by changing the focus until the intensity weight function of the azimuth profile’s DCT coefficients in the area of high sequences is maximized. Compared with Phase Gradient Autofocus (PGA) algorithm, the proposed method does not need to isolate prominent point target in image domain and is especially suitable for the images without specific characteristic. Due to the fact that there are fast algorithms for DCT, this autofocus algorithm is of less computational complexity and easy to implement. The simulation and the processing results of the measured data show the validity of the proposed method.

Synthetic Aperture Radar Autofocus via Semidefinite Relaxation

The autofocus problem in synthetic aperture radar imaging amounts to estimating unknown phase errors caused by unknown platform or target motion. At the heart of three state-of-the-art autofocus algorithms, namely, phase gradient autofocus, multichannel autofocus (MCA), and Fourier-domain multichannel autofocus (FMCA), is the solution of a constant modulus quadratic program (CMQP). Currently, these algorithms solve a CMQP by using an eigenvalue relaxation approach. We propose an alternative relaxation approach based on semidefinite programming, which has recently attracted considerable attention in other signal processing problems. Experimental results show that our proposed methods provide promising performance improvements for MCA and FMCA through an increase in computational complexity.

Multi-Subaperture PGA for SAR Autofocusing

For spotlight mode synthetic aperture radar (SAR) autofocusing, the traditional full-aperture phase gradient autofocus (PGA) algorithm might suffer from performance degradation in the presence of significant high-order phase error and residual range cell migration (RCM), which tend to occur when the coherent processing interval (CPI) is long. Meanwhile, PGA does not perform satisfactorily when applied directly on the stripmap data. To address these shortcomings, we present a multi-subaperture PGA algorithm, which takes advantage of the map drift (MD) technique. It smoothly incorporates the estimation of residual RCM and combines the subaperture phase error (SPE) estimated by PGA in a very precise manner. The methodology and accuracy of PGA-MD are investigated in detail. Experimental results indicate the effectiveness of PGA-MD in both the spotlight and the stripmap modes.

Synthetic aperture ladar imaging with one-way far-field diffraction

A laboratory SAL setup produced well-focused SAL images using laser illumination with one-way far-field diffraction.Using 1550 nm fiber laser,the SAL can focus images from target distance of about 2.4 m w ith azimuth resolution of about 560 μm and range resolution of about 170 μm.High-resolution SAL images are generated by straightforw ardly follow ing standard SAL image formation theory,w ithout the aid of phase gradient autofocus(PGA) technique.Detailed results show a typical tw o-step SAL focusing process and a high resolution image.