Phase Gradient Autofocus Algorithm Research Articles

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.

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.

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

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.

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.

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.

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.

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.

Wavenumber-Domain Autofocusing for Highly Squinted UAV SAR Imagery

Being capable of enhancing the flexibility and observing ability of synthetic aperture radar (SAR), squint mode is one of the most essential operating modes in SAR applications. However, processing of highly squinted SAR data is usually a challenging task attributed to the spatial-variant range cell migration over a long aperture. The Omega-k algorithm is generally accepted as an ideal solution to this problem. In this paper, we focus on using the wavenumber-domain approach for highly squinted unmanned aerial vehicle (UAV) SAR imagery. A squinted phase gradient autofocus (SPGA) algorithm is proposed to overcome the severe motion errors, including phase and nonsystematic errors. Herein, the inconsistence of phase error and range error in the squinted wavenumber-domain imaging is first presented, which reveals that even the motion error introduces very small phase error, it causes considerable range error due to the Stolt mapping. Based on this, two schemes of SPGA-based motion compensation are developed according to the severity of motion error. By adapting the advantages of weighted phase gradient autofocus and quality phase gradient autofocus, the robustness of SPGA is ensured. Real measured data sets are used to validate the proposed approach for highly squinted UAV-SAR imagery.

Autofocus of synthetic aperture sonar data using the phase adjustment by contrast enhancement algorithm

Imagery from synthetic aperture systems often suffers from imperfect image formation due uncertainties in the collection geometry or environmental parameters. Autofocus techniques aim to estimate and subsequently eliminate the effect of these uncertainties‐‐‐automatically adjusting focus parameters to obtain a “better” image. Typically, autofocus algorithms will optimise for reduced Doppler phase gradients or improved image contrast. The phase adjustment by contrast enhancement (PACE) algorithm belongs to the second class and was first proposed for use in synthetic aperture radar (SAR) autofocus. The algorithm is somewhat unusual for a contrast optimisation in that it avoids lengthy computation through directly solving the equations for optimum contrast. This advance allows for rapid autofocus without the need for complicated iterative optimisers. We compare results from using the PACE algorithm on local region of strip‐map synthetic aperture sonar (SAS) data collected with the HUGIN AUV and compare against a benchmark phase gradient autofocus (PGA) algorithm. We also demonstrate the effect of using the algorithm in circular SAS imagery, something not currently possible with standard PGA‐based autofocus.

Extended PGA for range migration algorithms

The phase gradient autofocus (PGA) algorithm is extended to work for synthetic aperture radar (SAR) spotlight images processed with range migration (w-k) algorithms. Several pre-processing steps are proposed for aligning the range-compressed phase-history data needed for successful autofocusing of the data. The proposed algorithm gave good results for both data with large point targets and data without point targets.

Experimental validation of autofocus algorithms for high-resolution imaging of the seabed using synthetic aperture sonar

The paper outlines the strengths and limitations of the phase gradient autofocus (PGA) algorithm and the displaced phase centre antenna (DPCA) algorithm when applied to synthetic aperture sonar imaging. The PGA algorithm was originally developed for radar, and care is required when implementing it for sonar. Due to the typically high fractional bandwidth of sonar chirp signals compared with radar, the problems of range migration are much more severe. This leads in some cases to a distribution of blur information over many range lines. Both algorithms are demonstrated in their application to seabed data collected at Brest Harbour, France, using a rail-based sonar system with a 15 m track. It is seen that PGA handles successfully an applied sinusoidal range error of 10 mm p-p amplitude (one carrier wavelength) repeating at intervals of 1 m.

Noniterative quality phase-gradient autofocus (QPGA) algorithm for spotlight SAR imagery

The phase-gradient autofocus (PGA) technique is robust over a wide range of imagery and phase error functions, but the convergence usually requires four-six iterations. It is necessarily iterative in an attempt to converge on a dominant target against clutter interference, while sufficiently capturing the blur function. The authors propose to speed the estimation convergence by selectively increasing the pool of quality synchronization sources and not be limited by the range pixels of the SAR map. This is highly probable since each range bin contains more than one prominent scatterer across the integration aperture. It is also highly probable that the least-brightest selected scatterer in a range gate may turn out to be of higher energy as compared to the maximum brightest scatterer of another gate. With appropriate target filtering to final select the quality scatterers out of the large pool and with higher order phase error measurement tool, the new algorithm achieves near-convergence focusing quality without iteration. The authors named this solution the quality PGA (QPGA) algorithm.

Phase gradient autofocus-a robust tool for high resolution SAR phase correction

The phase gradient autofocus (PGA) technique for phase error correction of spotlight mode synthetic aperture radar (SAR) imagery is examined carefully in the context of four fundamental signal processing steps that constitute the algorithm. We demonstrate that excellent results over a wide variety of scene content, and phase error function structure are obtained if and only if all of these steps are included in the processing. Finally, we show that the computational demands of the fun PGA algorithm do not represent a large fraction of the total image formation problem, when mid to large size images are involved. >

Eigenvector method for maximum-likelihood estimation of phase errors in synthetic-aperture-radar imagery

We develop a maximum-likelihood (ML) algorithm for estimation and correction (autofocus) of phase errors induced in synthetic-aperture-radar (SAR) imagery. Here, M pulse vectors in the range-compressed domain are used as input for simultaneously estimating M − 1 phase values across the aperture. The solution involves an eigenvector of the sample covariance matrix of the range-compressed data. The estimator is then used within the basic structure of the phase gradient autofocus (PGA) algorithm, replacing the original phase-estimation kernel. We show that, in practice, the new algorithm provides excellent restorations to defocused SAR imagery, typically in only one or two iterations. The performance of the new phase estimator is demonstrated essentially to achieve the Cramer–Rao lower bound on estimation-error variance for all but small values of target-toclutter ratio. We also show that for the case in which M is equal to 2, the ML estimator is similar to that of the original PGA method but achieves better results in practice, owing to a bias inherent in the original PGA phase estimation kernel. Finally, we discuss the relationship of these algorithms to the shear-averaging and spatial correlation methods, two other phase-correction techniques that utilize the same phase-estimation kernel but that produce substantially poorer performance because they do not employ several fundamental signal-processing steps that are critical to the algorithms of the PGA class.

Application of the phase gradient autofocus algorithm to time delay estimation in linear arrays.

For the purpose of localizing a distant noisy target, estimating the time delay of a wave front as it traverses across the sensors in a SONAR array is of considerable interest. This paper studies the application of the phase gradient autofocus (PGA) algorithm originally developed for extracting degrading phase errors in synthetic aperture radar (SAR) images to the time delay estimation problem in large linear arrays. It is well known that an efficient time delay estimation procedure consists of multiple cross correlations (one for each sensor pair) followed by a linear minimum-variance estimator. Monte Carlo simulation examples are presented that indicate the performance of the PGA method approaches the performance of the multiple correlator method at signal-to-noise ratios (SNRs) exceeding 0 dB with a substantial reduction in computational cost. Furthermore, PGA can easily take advantage of apriori knowledge regarding source bearings or array shape (if not perfectly linear) in order to improve the time delay estimates.