Phase Gradient Autofocus Research Articles

A Robust Motion Compensation Approach for UAV SAR Imagery

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 paper, a novel databased motion compensation (MOCO) approach is proposed for the UAV SAR imagery. The approach is implemented by a three-step process: 1) The range-invariant motion error is estimated by the weighted phase gradient autofocus (WPGA), and the nonsystematic range cell migration function is calculated from the estimate for each subaperture SAR data; 2) the retrieval of the range-dependent phase error is executed by a local maximum-likelihood WPGA algorithm; and 3) the subaperture phase errors are coherently combined to perform the MOCO for the full-aperture data. Both simulated and real-data experiments show that the proposed approach is appropriate for highly precise imaging for UAV SAR equipped with only low-accuracy inertial navigation system.

Synthetic aperture radar autofocus based on projection approximation subspace tracking

An eigenvector method for maximum-likelihood estimation (MLE) of phase error has better algorithmic performance than phase gradient autofocus (PGA), which is implemented by the simultaneous processing of multiple-pulse vectors of the range-compressed data. However, this method requires eigendecomposition of the sample covariance matrix, which is a computationally expensive task and also limits the real-time application. In order to overcome such difficulty, this study proposes a novel autofocus algorithm using the projection approximation subspace tracking (PAST) approach. With this methodology, the computational cost can be reduced effectively to the level of PGA via avoiding the procedures of covariance matrix estimation and eigendecomposition. Monte Carlo tests and real synthetic aperture radar (SAR) data validate that although undergoing performance loss compare with the original multiple-pulse MLE algorithm, the new approach outperforms the mostly used PGA.

A Robust Motion Error Estimation Method Based on Raw Data

High-resolution airborne synthetic aperture radar (SAR) systems are very sensible to deviations of the aircraft from the reference track. In high-resolution imagery, the improvement of range resolution increases the difficulty of implementing range cell migration correction (RCMC), while a wider synthetic aperture increases the cumulative time of motion errors which will affect the image quality. To enable accurate motion compensation in image processing, a high-precision navigation system is needed. However, in many cases, due to the limit of accuracy of such systems, motion errors are hard to be compensated correctly, causing mainly the resolution decrease in final image. Moreover, in large swath mode, the range-dependent phase errors are difficult to be compensated by using the conventional autofocus algorithm only. In this paper, we propose a robust motion error estimation method based on raw SAR data. To apply this estimation method, we first estimate the double phase gradients in subaperture. Second, a filtering method based on curve fitting was proposed to reduce the phase estimation errors caused by low signal-to-clutter ratio (SCR). Finally, we propose a weighted total least square method to calculate the motion errors using the filtered phase gradients. Because the proposed algorithm is nonparametric, it can estimate high-order motion errors. This is very important for the airborne SAR, particularly the light aircraft SAR platform, due to their more complicated movement in air turbulence. The versatility that the proposed method can be used in any imaging algorithms is another advantage. The processing of large number of raw SAR data shows that the algorithm is as robust and practical as phase gradient autofocus and can generate better focused images.

A range-dependent autofocus algorithm based on the Tikhonov regularization method

Phase Gradient Autofocus (PGA) is an algorithm developed to estimate phase errors in synthetic aperture radar (SAR) images. It is widely used in SAR image processing and has been shown to be very robust on a variety of imagery and phase error functions. Original PGA makes a narrow beam assumption, which is valid for most SAR systems. But it is known that the narrow beam assumption is not valid for large swath or low-altitude mode SAR, where range-dependent phase errors need to be compensated. Some PGA-based range-dependent autofocus algorithms were proposed to deal with this problem, but during raw data processing, we found that there are ill-posed problems in the linear motion error estimation model that will affect the accuracy of the estimation. In this article, combining the Tikhonov regularization (TR) method with phase gradient estimation, a novel autofocus algorithm is proposed to deal with the ill-posed problem in estimation. Real data processing demonstrates that the new method avoids the effect of parameter errors, estimates the range-dependent phase errors more precisely and finally leads to better focusing quality.

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.

Stripmap SAR 신호처리를 위한 PGA 적용 기법

SAR(Synthetic Aperture Radar) 영상의 화질을 개선하기 위한 autofocus 기법 중에 대표적 인 것이 PGA(Phase Gradient Autofocus) 이다. PGA는 고차항 위상 오차를 추정할 수 있으며 잡음이 많은 환경에 강인성을 가지는 장점이 있지만, spotlight 모드에 최적화 되어있는 기법으로 stripmap 모드에서 사용하기에는 부적합하다는 단점이 있다. 본 논문에서는 PGA를 stripmap 모드에서 적용한 기법을 소개하고, PGA 성능에 많은 영향을 미치는 ROI(Region of Interest) 선정 방식을 제시하였다. 또한 제안된 기법은 먼저 점표적 시뮬레이션을 통해 검증되었고, 최종적으로 이를 실제 비행 시험을 통해 획득한 SAR 원시데이터에 적용하여 SAR 영상 화질을 개선시킨 결과를 보였다. PGA(Phase Gradient Autofocus) is a representative autofocus technique to improve the SAR(Synthetic Aperture Radar) image quality. PGA can estimate high order phase errors and have good robustness in noisy environments. However, PGA is not suitable to apply to the stripmap mode data directly because it is based on the spotlight mode operation. In this paper, the PGA implementation technique for stripmap mode data and the method of ROI(Region of Interest) selection that affects severely on PGA performance have been proposed. The proposed technique was verified by the point target simulation first, and was applied to the real SAR signal data acquired by the flight test. Finally, the significant improvements in focusing quality were shown in the processed SAR images using the proposed method.

Pitch estimation for non-cooperative maritime targets in ISAR scenarios

Maritime targets are usually involved in complex motions that complicate the generation of focused inverse synthetic aperture radar (ISAR) images and their scaling in cross-range. By assuming some hypotheses that translate to some restrictions in the maritime surveillance scenario, a signal model for the phase history is derived. This function is calculated here using phase gradient autofocus and can be related to the pitch motion of the ship, which may consequently be estimated. The amplitude and the period of this pitch estimate allow us to select imaging times at which the ISAR images are descriptive for classification purposes. The cross-range scaling of these images is also achieved. Simulated data are used to validate the technique and to evaluate its performance when deviations from the nominal scenario are present. Results obtained with live data acquired by a high-resolution radar confirm the effectiveness of the approach.

SAR System for UAV Operation with Motion Error Compensation beyond the Resolution Cell.

This paper presents an experimental Synthetic Aperture Radar (SAR) system that is under development in the Universidad Politécnica de Madrid. The system uses Linear Frequency Modulated Continuous Wave (LFM-CW) radar with a two antenna configuration for transmission and reception. The radar operates in the millimeter-wave band with a maximum transmitted bandwidth of 2 GHz. The proposed system is being developed for Unmanned Aerial Vehicle (UAV) operation. Motion errors in UAV operation can be critical. Therefore, this paper proposes a method for focusing SAR images with movement errors larger than the resolution cell. Typically, this problem is solved using two processing steps: first, coarse motion compensation based on the information provided by an Inertial Measuring Unit (IMU); and second, fine motion compensation for the residual errors within the resolution cell based on the received raw data. The proposed technique tries to focus the image without using data of an IMU. The method is based on a combination of the well known Phase Gradient Autofocus (PGA) for SAR imagery and typical algorithms for translational motion compensation on Inverse SAR (ISAR). This paper shows the first real experiments for obtaining high resolution SAR images using a car as a mobile platform for our radar.

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.

Comments on "Non-iterative quality phase-gradient autofocus (QPGA) algorithm for spotlight SAR imagery"

For original paper see ibid., vol.36, no.5, pt.1, p.1531-9 (1998). The quality phase-gradient autofocus (QPGA) technique was proposed to speed up the estimation convergence of phase-gradient autofocus by selectively increasing the pool of quality synchronization sources instead of selecting the "brightest" pixels within the image. It is now found that the QPGA, with its inherent scatter "growing" concept and target-filtering procedure, is also able to focus in environments with stationary and moving targets.

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.