Azimuth Phase Error Research Articles

Analysis and Compensation for Systematical Errors in Airborne Microwave Photonic SAR Imaging by 2-D Autofocus

In the area of synthetic aperture radar (SAR), the ultra-high resolution is always a continuous pursuit for researchers. To realize ultra-high resolution, microwave photonics (MWP) technology is an excellent solution since it has advantages of low transmission loss, ultra-wide bandwidth (UWB), etc. However, with the improvement of resolution, new problems arise as the impact of more systematical errors becomes non-negligible. For example, the synchronization error between the transmit channel and the mixing channel, unknown system delay during signal reception, and fluctuation of frequency for UWB signals. These factors will bring degradation of the focusing quality of SAR images together with the motion errors and the trajectory measurement errors, not only cause residual range cell migration (RCM) and azimuth phase error (APE), but also higher-order phase error along the range frequency dimension. In this paper, we discuss the adverse influence of the above factors and give a detailed analysis of the 2-D phase error of the coarse focused image processed by range migration algorithm (RMA). Then, to compensate for the above unknown systematical errors, a 2-D autofocus method is proposed and the effectiveness is validated by experiments on both simulated and real data.

Image Defocus in an Airborne UWB VHR Microwave Photonic SAR: Analysis and Compensation

With the exploration of synthetic aperture radar (SAR), the requirements for its functionality, precision, and response time are inevitably increasing, in which the technical core is the generation, reception, and processing of wideband signals with low time cost. Owing to the excellent performance of modern photonics, such as the ultra-wide bandwidth (UWB), flat response, low transmission loss, fast analog signal processing, and microwave photonics (MWP) promises to be an appropriate solution to improve the capability of SAR in resolution, coverage, and efficiency. However, on the one hand, due to the high sensitivity of optical fiber, moisture, temperature, or physical vibration can produce an unknown extra propagation delay. On the other hand, the wavelength shift effect should be taken into consideration for the UWB system. Thereby, under very high resolution (VHR) circumstance, two-dimensional (2-D) defocus including migration through resolution cells (MTRC) and azimuth phase error (APE) becomes a challenge for MWP SAR imaging. Unfortunately, existing 2-D autofocus approaches concerning motion errors inherently fail for the commonly underlying assumption that the prominent nonsystematic residual range cell migration (RCM) is global in the azimuth time domain. In this article, we analyze the effects of the above-mentioned negative factors in the image processing of range migration algorithm (RMA) and reveal the structural characteristics of the 2-D phase errors. A novel two-step postprocessing compensation strategy is developed, and experiments on real data acquired by an airborne MWP SAR system demonstrate its effectiveness.

An Autofocus Scheme of Bistatic SAR Considering Cross-Cell Residual Range Migration

Benefiting from the capability of forward-looking imaging, ability of receiver radio silence and resistance of jamming, bistatic SAR has extensive potential applications. However, due to its independent dual platform movement, motion error of bistatic SAR is usually more complicated than monostatic SAR and could easily exceed range resolution cell, which will result in both azimuth and range defocusing if not properly compensated. In this paper, an autofocus scheme for bistatic SAR considering cross-cell residual range migration is proposed. In this scheme, cross-cell residual range migration is firstly compensated by estimating bistatic range error through time-frequency analysis. Meanwhile, azimuth phase error is coarsely compensated by using bistatic range error estimation result. Secondly, maximum image sharpness autofocus method is cascaded to further compensate for azimuth residual phase error and enhance the quality of bistatic SAR image. The effectiveness of proposed scheme is verified by simulation and experiment results.

A Novel Motion Compensation Scheme for Airborne Very High Resolution SAR

Due to the atmospheric turbulence, the motion trajectory of airborne very high resolution (VHR) synthetic aperture radars (SARs) is inevitably affected, which introduces range-variant range cell migration (RCM) and aperture-dependent azimuth phase error (APE). Both types of errors consequently result in defocused images, as residual range- and aperture-dependent motion errors are significant in VHR-SAR images. Nevertheless, little work has been devoted to the range-variant RCM auto-correction and aperture-dependent APE auto-correction. In this paper, a precise motion compensation (MoCo) scheme for airborne VHR-SAR is studied. In the proposed scheme, the motion error is obtained from inertial measurement unit and SAR data, and compensated for with respect to both range and aperture. The proposed MoCo scheme compensates for the motion error without space-invariant approximation. Simulations and experimental data from an airborne 3.6 GHz bandwidth SAR are employed to demonstrate the validity and effectiveness of the proposed MoCo scheme.

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.

Two-Dimensional Autofocus Technique Based on Spatial Frequency Domain Fragmentation.

Existing two-dimensional (2-D) autofocus algorithms, exploiting the known structure of 2-D phase error, lack the error estimation accuracy in the case of a low signal-tonoise ratio (SNR) due to the non-exhaustive use of the echo signal. In this paper, we propose a novel 2-D autofocus algorithm, thoroughly utilizing all the available data and therefore achieving superior estimation performance. Via analytical study, we show that the partial derivative of the 2-D error with respect to the azimuth frequency is approximable as a function of single argument, after appropriate change of variable. The established property enables a scheme for the azimuth phase error (APE) measurement, where the polar formatted data are fragmented along the range frequency and then aligned along the azimuth frequency, in order to equalize phase gradients in different fragments. On the one hand, such a scheme avoids the necessity to divide the full-aperture signal into subapertures, while on the other hand, it involves the whole signal support. Improved accuracy of the resulting estimate is achieved through the joint inter-fragment estimation of the APE gradient. The proposed algorithm, based on the mentioned scheme, was validated via computer simulations. The conducted experiments confirmed its preference against the existing techniques. The preference is particularly distinct for low SNR imagery.

Improved entropy‐based autofocus correction for synthetic aperture radar

Autofocus is an essential step in order to obtain the well-focused synthetic aperture radar image. Compared to the non-parametric autofocus, the parametric way is not subjected to the prominent targets so much. Entropy is widely used in parametric autofocus. It is sensitive to the clutter and not a convex function either. In this article, the authors present a new modified entropy to improve the robust of the parametric autofocus by reducing the number of the local optimal solutions remarkably. During the searching process, the residual azimuth phase error (RAPE) is decomposed as the summation of the polynomials. Of course, the used first derivative of the new entropy with respect to the model coefficients is given in detail. Moreover, for applying azimuth subaperture strategy, the authors remove the linear difference of adjacent RAPE via estimating the Doppler centroid, which is more effective than the map-drift method. Finally, real data experiment validates the authors’ approach.

Fast Compressive Sensing-Based SAR Imaging Integrated With Motion Compensation

Recently, compressive sensing (CS) has been applied in synthetic aperture radar (SAR) imaging, which is increasingly in the focus of study and shows great potential. In CS-based SAR imaging, motion errors of the moving platform introduce inaccuracies in the observation model, which cause various degradations in the final images. To accomplish accurate motion compensation during CS-based SAR imaging, we propose a fast CS-based SAR imaging integrated with motion compensation method. First, CS-based imaging based on the utilization of inverse observation deduced from the inversion of conventional imaging procedures is applied, which is much more computational efficient than the exact observation model. Then, an improved inverse observation model integrated with motion compensation is derived. In the improved model, spatially variant azimuth phase errors are taken into consideration. Joint SAR imaging and motion compensation are formulated as a sparse recovery problem and solved in an iterative way, wherein each iteration both image formation and motion compensation are carried out. The processing of SAR data shows that the proposed method can obtain better focused images compared with the existing SAR imaging and motion compensation methods.

Nonsystematic Range Cell Migration Analysis and Autofocus Correction for Bistatic Forward-looking SAR

In general, autofocus methods integrated with frequency-domain imaging algorithms are instrumental to obtain a well-focused bistatic forward-looking synthetic aperture radar (BFSAR) image in the presence of motion errors. Nevertheless, before applying autofocus methods to correct the azimuth phase errors, range cell migration (RCM) should be eliminated by the RCM correction (RCMC) procedure in frequency-domain imaging algorithms. With motion errors being taken into account, there always exists some residual nonsystematic RCM (NsRCM), which refers to the residual migration components after the RCMC procedure. For the conventional side-looking SAR, NsRCM is caused by motion errors. On the other hand, NsRCM of BFSAR is originated from motion errors before RCMC and the NsRCM amplified by the RCMC procedure. In this paper, we analyze the different types of NsRCM in BFSAR imaging and their relationship. Based on the analyses, we propose an autofocus NsRCM correction scheme for BFSAR imagery using frequency-domain imaging algorithms that can eliminate the range-dependent NsRCM. The proposed scheme consists of three steps. First, for the BFSAR data after range compression and RCMC, a division procedure is carried out in the azimuth direction. The subblocks with the highest signal-to-clutter ratio along the range direction are selected after the azimuth segmentation procedure. Second, for the selected subblocks, the total NsRCM is estimated based on the minimum-entropy criterion. Based on the estimation results, different parts of the NsRCM are obtained by solving an ordinary differential equation. Third, a two-step compensation of the NsRCM is executed to reach the spatially variant correction. Simulations and experimental results are provided to demonstrate that our proposed scheme is effective for BFSAR imaging.

Knowledge-Aided 2-D Autofocus for Spotlight SAR Range Migration Algorithm Imagery

With continuous improvement of the synthetic aperture radar (SAR) resolution, the 2-D defocus effect in SAR image resulting from uncompensated motion error has made autofocus become a new challenging problem. Conventional 2-D autofocus approaches assume that the 2-D phase error is absolutely unknown and estimate them directly. Due to high dimensionality of the unknown parameters, these approaches often suffer from high computational burden and low estimate accuracy. In this paper, we analyze the effect of range migration algorithm (RMA) processing on the 2-D echo phase, and reveal the analytical structure of the residual 2-D phase error in RMA imagery. Then, by exploiting the derived prior knowledge on the phase error structure, an accurate and efficient 2-D autofocus approach is proposed. In the new method, only 1-D error, e.g., azimuth phase error, or residual range cell migration, is required to be estimated directly, while the 2-D phase error is computed directly from the estimated 1-D error by exploiting the analytical structure of the 2-D phase error. The experimental results clearly demonstrate the effectiveness and robustness of the proposed method.

스포트라이트 모드 SAR 영상 형성에서의 수정된 가중치 최소 자승기법에 의한 자동 초점 알고리즘

In the existence of motion, azimuth phase error due to accuracy limitation of GPS/IMU and system delay is unavoidable and it is essential to apply autofocus to estimate and compensate the azimuth phase error. In this paper, autofocus algorithm using MWLS(Modified WLS) is proposed. It shows the robust performance compared with original WLS using new target selection/sorting metric and iterative azimuth phase estimation technique. SAR raw data obtained in a captive flight test is used to validate the performance of the proposed algorithm.

Autofocus correction of residual low-order and high-frequency phase error in synthetic aperture radar

Due to the presence of atmospheric turbulence, motion error (ME) arises and causes residual azimuth phase error (APE) during synthetic aperture radar (SAR) data acquisition. APE can degrade SAR images, especially for light-weight SAR. Moreover, different kinds of APE have different impacts on the image, which makes it hard to compensate for. A parametric autofocus based on a cost metric consisting of the modified entropy and the residual entropy (MERE) is developed to compensate the APE. This approach using the optimization transfer method aims to minimize the MERE. The polynomial decomposition is applied to fit the low-order APE while inverse discrete cosine transform model is adopted for the high-frequency case. Additionally, we also design a modified adaptive-order search strategy, and it helps to remarkably reduce the computational load while maintaining accuracy. In the case of correcting high-frequency APE, the MERE metric could effectively avoid the over-fitted problem that arises in entropy-based autofocus. The real airborne SAR data experiments and comparisons demonstrate the validity and effectiveness of the proposed autofocus.

A residual range cell migration correction algorithm for bistatic forward-looking SAR

For bistatic forward-looking synthetic aperture radar (BFSAR), images are often blurred by uncompensated radar motion errors. To get refocused images, autofocus is a useful postprocessing technique. However, a severe drawback of the autofocus algorithms is that they are only capable of removing one-dimensional azimuth phase errors. In BFSAR, motion errors and approximations of imaging algorithms introduce residual range cell migration (RCM) on BFSAR data as well. When residual RCM is within a range resolution cell, it can be neglected. However, the residual migration, which exceeds a range cell, is increasingly encountered as resolution becomes finer and finer. A novel residual RCM correction method is proposed in this paper. By fitting the low-frequency phase difference of adjacent azimuth cells, residual RCM of each azimuth cell can be corrected precisely and effectively. Simulations and real data experiments are carried out to validate the effectiveness of the proposed method.

A Minimum-Entropy Based Residual Range Cell Migration Correction for Bistatic Forward-Looking SAR

For bistatic forward-looking synthetic aperture radar (BFSAR), motion errors induce two adverse effects on the echo, namely, azimuth phase error and residual range cell migration (RCM). Under the presumption that residual RCM is within a range resolution cell, residual RCM can be neglected, and azimuth phase error can be compensated utilizing autofocus methods. However, in the case that residual RCM exceeds the range resolution, two-dimensional defocus would emerge in the final image. Generally speaking, residual RCM is relatively small and can be neglected in monostatic SAR, while the unique characteristics of BFSAR makes the residual RCM exceeding range resolution cell inevitable. Furthermore, the excessive residual migration is increasingly encountered as resolutions become finer. To cope with such a problem, minimum-entropy based residual RCM correction method is developed in this paper. The proposed method eliminates the necessity of the parametric model when estimating the residual RCM. Moreover, it meets the practical needs of BFSAR owing to no requirement of exhaustive computation. Simulations validate the effectiveness of the proposed method.

Two-dimensional Autofocus for Spotlight SAR Polar Format Imagery

Conventional two-dimensional (2-D) autofocus algorithms blindly estimate the phase error in the sense that they do not exploit any a priori information on the structure of the 2-D phase error. As such, they often suffer from low computational efficiency and lack of data redundancy to accurately estimate the 2-D phase error. In this paper, a knowledge-aided (KA) 2-D autofocus algorithm which is based on exploiting a priori knowledge about the 2-D phase error structure, is presented. First, as a prerequisite of the proposed KA method, the analytical structure of residual 2-D phase error in SAR imagery is investigated in the polar format algorithm (PFA) framework. Then, by incorporating this a priori information, a novel 2-D autofocus approach is proposed. The new method only requires an estimate of azimuth phase error and/or residual range cell migration, while the 2-D phase error can then be computed directly from the estimated azimuth phase error or residual range cell migration. This 2-D autofocus method can also be applied to refocus moving targets in PFA imagery. Experimental results clearly demonstrate the effectiveness and robustness of the proposed method.

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.

Compensation for the NsRCM and Phase Error After Polar Format Resampling for Airborne Spotlight SAR Raw Data of High Resolution

When the range migration caused by motion error exceeds the range cell resolution, the performance of a conventional phase autofocus approach degrades. In this paper, a new adaptive motion compensation (MoCo) algorithm with the removal of the migration that is nonsystematic has been developed for airborne spotlight synthetic aperture radar (SAR) imagery with high resolution. In the algorithm, the relationship between nonsystematic range cell migration (NsRCM) and phase error was first explicitly revealed after the polar format algorithm resampling. The NsRCM could be readily calculated by coarse but reliable phase error estimation. Subsequently, the NsRCM and the bulk of the azimuth phase error were corrected. After the removal of the NsRCM, degradation of the conventional phase autofocus resulting from sidelobe increase as well as mainlobe broadening was avoided. Finally, a fine MoCo procedure was performed to remove the residual azimuth phase error satisfactorily. Through the analysis of the airborne spotlight SAR raw data with high-resolution and wide-swath illumination, a well-focused imagery was obtained. Quantitative assessment of the image quality was satisfactory. The MoCo algorithm was validated.

Autofocus Correction of APE and Residual RCM in Spotlight SAR Polar Format Imagery

Synthetic aperture radar (SAR) images are often blurred by phase perturbations induced by uncompensated sensor motion and /or unknown propagation effects caused by turbulent media. To get refocused images, autofocus proves to be useful post-processing technique applied to estimate and compensate the unknown phase errors. However, a severe drawback of the conventional autofocus algorithms is that they are only capable of removing one-dimensional azimuth phase errors (APE). As the resolution becomes finer, residual range cell migration (RCM), which makes the defocus inherently two-dimensional, becomes a new challenge. In this paper, correction of APE and residual RCM are presented in the framework of polar format algorithm (PFA). First, an insight into the underlying mathematical mechanism of polar reformatting is presented. Then based on this new formulation, the effect of polar reformatting on the uncompensated APE and residual RCM is investigated in detail. By using the derived analytical relationship between APE and residual RCM, an efficient two-dimensional (2-D) autofocus method is proposed. Experimental results indicate the effectiveness of the proposed method.