Polar Format Algorithm Research Articles

Polar Format Algorithm for Circular Synthetic Aperture Radar

该文提出一种新的用于圆迹合成孔径雷达(Circular Synthetic Aperture Radar, CSAR)成像的极坐标格式算法。在CSAR模式下，点目标的波数域3维频谱为3维曲面。根据这一特点，算法采用逐高度平面成像的方法最终获得3维图像，即通过参考函数相乘，将频谱投影到2维平面，既避免了高度向的插值，又保证了算法的精确性。并且该算法通过两步相位补偿操作校正了越距离单元徙动的高次项，扩大了有效成像范围，避免了场景边缘目标的散焦。最后，点目标仿真验证了该算法的有效性。

AN IMPROVED POLAR FORMAT ALGORITHM WITH PERFORMANCE ANALYSIS FOR GEOSYNCHRONOUS CIRCULAR SAR 2D IMAGING

This paper presents an improved polar format algorithm (PFA) for geosynchronous synthetic aperture radar which undergoes a near-circular track (GeoCSAR). GeoCSAR imaging geometry and signal formulation considering orbit perturbations were derived to ensure accurate slant range between antenna and targets. The illuminated area is more than one million square kilometers due to the long slant distance, resulting in large amount of data to be processed and that the scene is a spherical crown rather than a plane. By assuming spherical wavefronts instead of planar wavefronts, improved polar format algorithm (PFA) was proposed to focus GeoCSAR raw data on a spherical reference surface (ground surface), so that the size of focused scene is no longer limited by the range curvature phase error. Thus, this method could deal with large area imaging for GeoCSAR precisely and e-ciently. The implementation procedure, computational complexity, phase error and achievable resolution were presented to show the focusing capabilities of this imaging algorithm. Numerical simulation was further performed to validate the feasibility of this imaging algorithm and the correctness of analysis.

Bistatic Polar Format Algorithm Based on NUFFT Method

Matched filtering of phase history data is the optimum reconstruction algorithm to bistatic synthetic aperture radar (SAR) image formation. However, it comes at great computational expense scaled with complexity O (M 2 N 2), where M N is the number of pixels in the image. Based on the plane wave assumption, bistatic polar format algorithm (PFA) approximates the matched filtering kernel appropriately, so that the computational complexity in image formation is considerably reduced. In this paper, we propose a novel PFA for bistatic SAR processing. This imaging algorithm is to use non-uniform fast Fourier transform (NUFFT) to compute the matched filtering reconstruction image according the plane wave signal model of bistatic SAR, which scales with complexity O (M Nlog2 M N). Numerical simulations are performed to validate the proposed algorithm. The results prove that, compared with the direct computing of matched filtering, the presented algorithm can provide almost identical imaging performance in a relatively very short computation time.

Analysis of wide-angle radar imaging

In wideband radar imaging, it is necessary to increase the target observation angle, that is, the imaging time to obtain high azimuth resolution. For wide-angle targets, however, migration through resolution cell will occur and the Doppler information of the scatterers will be time varying, which can lead to image defocusing in both the range and azimuth domain if the range–Doppler (RD) method is applied. Aimed at this problem, this study builds up the imaging model for steadily moving targets with a constant rotation axis. Then it compares the RD algorithm, the Keystone algorithm and the polar format algorithm with theoretical analysis and deduces the maximum observation angles that fit for these methods, respectively. Additionally, this study proposes a new algorithm for imaging of targets with large observation angles based on the complex inverse Radon transform. Instead of applying the Taylor's series approximation, this method strictly follows the signal model for scatterers with a wide observation angle and utilises curvilinear integral with phase information for image formation. Therefore it is valid in wide-angle scenarios. Finally, imaging results for both the simulated and measured data are given to analyse the performance of the available algorithms and to prove the validity of the proposed algorithm.

Far-Field Limit of PFA for SAR Moving Target Imaging

A new formulation of the polar format algorithm (PFA) for spotlight synthetic aperture radar (SAR) imaging is presented, which is useful when investigating its response to the moving target. Our work starts with examining the commonly adopted implementation of the PFA, i.e., the separable 1-D range and azimuth resampling procedures for their roles in range cell migration (RCM) correction, respectively. It is shown that the former performs RCM predeformation, while the latter is, substantially, the combination of RCM linearization and the keystone transform (KT), i.e., a well-known technique for SAR imaging of moving targets. The new formulation approach is applied to analyze the moving target. The far-field limit of the PFA for moving target focusing is derived, which can be used to predict the target's impulse response (IPR) function. The work presented might be helpful when considering a SAR system with the capability of ground moving target indication and imaging (GMTI&Im).

Wavefront curvature correction in one stationary bistatic SAR image focused via PFA

The wavefront curvature error in one stationary bistatic synthetic aperture radar (SAR) image focused via the polar format algorithm (PFA) is analysed and a space-variant filtering method for wavefront curvature correction is proposed. The correction method presented, extends the focused scene size when using the bistatic PFA effectively. Point target simulation validates the filtering method.

COMPARATIVE STUDY OF RMA AND PFA ON THEIR RESPONSES TO MOVING TARGET

The synthetic aperture radar (SAR) signatures of moving target are the basis of ground moving target indication and imaging (GMTI&Im) in the framework of SAR systems. However, previous studies are mainly based on the 2-D separable SAR processing, and little work has been done to investigate the signatures of moving target after the application of a particular flne resolution SAR image formation algorithm. In this paper, we derive the image spectrum of moving target after two representative flne resolution SAR image formation algorithms, i.e., the range migration algorithm (RMA) and polar format algorithm (PFA), respectively. Based on the spectrum derived, detailed analysis on the SAR signatures of moving target, including the geometric displacement, residual range migration, and defocusing efiect in both the range and azimuth dimensions are performed. The presented work might be helpful when considering a SAR system with the capability of ground moving target indication and imaging (GMTI&Im).

Rotational motion estimation for ISAR via triangle pose difference on two range-Doppler images

Rotational motion estimation is essential for inverse synthetic aperture radar (ISAR) imaging and understanding. For an object rotating with a constant acceleration, a closed-form solution is proposed to jointly estimate the initial rotating velocity (IRV) and the rotating acceleration (RA) by exploiting the pose difference of a triangle on two range-Doppler (RD) images. Then, the RA can be compensated with interpolation processing and an equivalent uniformly rotating object may be obtained. After that, the estimated IRV can be used to re-scale the RD image into the homogeneous range-cross range domain, or to provide more satisfactory imaging result via elaborated algorithms such as polar format algorithm or convolution back-projection algorithm. Finally, experimental results with both simulated and real airplane data are provided to demonstrate the effectiveness of the proposed method.

Efficient Wavenumber Domain Focusing for Ground-Based SAR

We present an efficient focusing algorithm for synthetic aperture radar (SAR) data acquired in short bursts by a geometry with a large range spread, i.e., the case of ground-based (GB) SAR. The usual approach for focusing GB SAR data is the polar formatting algorithm, whose computational complexity, however, is quite relevant due to the nonseparability of the kernel. In this letter, we introduce a different format for the focused data, namely, the range-angular domain. Such format keeps the benefit of the polar format that samples data close to the resolution, but allows for the design of a separable kernel in the wavenumber domain. The proposed kernel exploits a modified Stolt interpolation and an efficient space-varying resampling. Results of processing on both simulated and real data are presented.

POLAR FORMAT ALGORITHM FOR SPOTLIGHT BISTATIC SAR WITH ARBITRARY GEOMETRY CONFIGURATION

This paper presents an efiective Polar Format Algorithm (PFA) for spotlight bistatic synthetic aperture radar (SAR) with arbitrary geometry conflguration. Nonuniform interpolation and resampling are adopted when converting raw data from polar coordinates to Cartesian coordinates according to the characteristics of raw data samples in spatial frequency space. Thus, the proposed algorithm avoids both rotation transformation and the calculation of azimuth compensation factor and thereby avoids the corresponding approximate error appeared in the conventional PFA. Meanwhile, the proposed algorithm inherits the character of decomposing 2- D interpolation to two 1-D interpolations from conventional PFA algorithm applied in monostatic SAR imaging. Therefore, the processing ∞ow, computation e-ciency and performance of the proposed algorithm are the same as those of conventional PFA for monostatic spotlight SAR. Point target simulations are provided to validate the proposed algorithm.

An Implementation of Bistatic PFA using Chirp Scaling

This paper discusses an implementation of bistatic polar format algorithm (PFA) using chirp scaling (CS). The new algorithm applies CS in the range direction to realize the range resampling, which involves only complex multiplications and FFTs. The dechirped and the chirped signals are treated separately. The new approach obtains comparable results compared with the original algorithm, however improves the efficiency significantly. Point target simulation validates the new algorithm.

The Application of the Principle of Chirp Scaling in Processing Stepped Chirps in Spotlight SAR

A new approach to process stepped chirps in spotlight synthetic aperture radar is presented in this letter, which is based on exploiting the principle of chirp scaling (PCS). In particular, PCS is integrated into the polar format algorithm (PFA), obtaining a more efficient solution compared with the existing polar interpolation technique. The main contribution of this letter is the implementation of azimuth scaling, in which the bandwidth synthesis is embedded. The algorithm is developed dedicatedly for dealing with stepped chirps. The signal processing flow is investigated in detail, in which no interpolations but only fast Fourier transform and complex multiplications are involved. Point-target simulation has validated the new approach and indicated that it is more efficient than the classic interpolation-based one. The achieved computational gain measured in execution time is around 25%-30%.

SIGNATURES OF MOVING TARGET IN POLAR FORMAT SPOTLIGHT SAR IMAGE

The synthetic aperture radar (SAR) signatures of moving target are the basis of ground moving target detection and imaging (GMTI&Im). However, previous studies are mainly based on the 2-D separable SAR processing, and little work has been done to investigate the signatures of moving target after the application of a particular fine resolution SAR image formation algorithm. In this paper, the spectrum of moving target after polar format algorithm (PFA) processing is derived. Based on this spectrum, detailed analysis on the SAR signatures of moving target, including the geometric displacement, residual range migration, and the defocusing effect in both range and azimuth dimensions are performed. Simulation results validate the theoretical analysis.

The Polar Format Imaging Algorithm Based on Double Chirp-Z Transforms

Spotlight mode offers finer azimuth resolution than that achievable in stripmap mode using the same physical antenna. The most popular spotlight synthetic aperture radar (SAR) reconstruction method is the classic polar format algorithm (PFA). However, PFA needs to perform range and azimuth interpolation operations during SAR imaging, which, in turn, affect the imaging precision and the computation efficiency. In this letter, we present a novel polar format algorithm, which may avoid interpolation operations by double chirp-Z transform. In this letter, we also analyze the nondefocus and the nondistortion constraints and discuss the along-track acceleration constraint for the PFA as well.

Polar format agorithm using chirp scaling for spotlight SAR image formation

A novel implementation of the polar format algorithm (PFA) using the principle of chirp scaling (PCS) for spotlight synthetic aperture radar (SAR) image formation is addressed. A PFA completely free of interpolation has been achieved in moderate squinted imaging geometry. The presented approach consists of the range and azimuth scaling of the polar samples, in which only fast Fourier transforms (FFTs) and complex vector multiplications are involved. Following different processing chains, the dechirped and the chirped SAR signals are treated separately in this paper. Relative to the classic polyphase filter that uses the long sinc kernel, the new solution is able to attain a comparable result, but is much quicker by exploiting inherent properties of the linear frequency modulated (LFM) signal. Point target simulation has validated the presented methodology.

A Two Dimensional Overlapped Subaperture Polar Format Algorithm Based on Stepped-chirp Signal.

In this work, a 2-D subaperture polar format algorithm (PFA) based on stepped-chirp signal is proposed. Instead of traditional pulse synthesis preprocessing, the presented method integrates the pulse synthesis process into the range subaperture processing. Meanwhile, due to the multi-resolution property of subaperture processing, this algorithm is able to compensate the space-variant phase error caused by the radar motion during the period of a pulse cluster. Point target simulation has validated the presented algorithm.

APPLICATION OF SYNTHETIC BANDWIDTH APPROACH IN SAR POLAR FORMAT ALGORITHM USING THE DERAMP TECHNIQUE

The problem of wide bandwidth management in ultra-high resolution SAR systems can be solved by adopting stepped chirps and applying synthetic bandwidth approach. However, high resolution SAR image formation is a non-separable 2-D impulse compression processing, so the synthetic bandwidth procedure should be modified correspondingly with the image formation algorithm adopted. This paper demonstrates the application of synthetic bandwidth approach in SAR Polar Format Algorithm (PFA) using the deramp technique. The problem of motion compensation between the sub-pulses within a burst is discussed, and the signalprocessing flows are investigated in detail. The presented approach is validated by point target simulation.

Range Resampling in the Polar Format Algorithm for Spotlight SAR Image Formation Using the Chirp $z$-Transform

Besides an inverse two-dimensional (2-D) Fourier transform, the polar format algorithm (PFA) for the spotlight synthetic aperture radar (SAR) image formation can be normally divided into two cascaded processing stages, which are called the range and azimuth resampling, respectively. This paper focuses on a new implementation of the first stage, i.e., the range resampling, using the chirp z-transform (CZT). The presented algorithm requires no interpolation. It works for the SAR system directly digitizing the echo signal, as well as that employing the dechirp-on-receive approach. The parameters of the CZT, including the frequency spacing and the start frequency, are derived to accommodate the PFA in both cases. Related filtering and compensation procedures are developed for the chirp z-transformed range signal with and without dechirp, respectively, in order to achieve a signal format entirely suitable for the azimuth resampling. Furthermore, incorporating the new algorithm with the existing CZT-based azimuth resampling and focusing algorithm, we can achieve a PFA totally free of interpolation. The presented approach has been validated by point target simulation, and the test is carried out with a very critical relative bandwidth of 30%

Taylor expansion of the differential range for monostatic SAR

The polar format algorithm (PFA) for spotlight synthetic aperture radar (SAR) is based on a linear approximation for the differential range to a scatterer. We derive a second-order Taylor series approximation of the differential range. We provide a simple and concise derivation of both the far-field linear approximation of the differential range, which forms the basis of the PFA, and the corresponding approximation limits based on the second-order terms of the approximation.

Polar format algorithm for bistatic SAR

Matched filtering (MF) of phase history data is a mathematically ideal but computationally expensive approach to bistatic synthetic aperture radar (SAR) image formation. Fast backprojection algorithms (BPAs) for image formation have recently been shown to give improved O(N/sup 2/ log/sub 2/N) performance. An O(N/sup 2/ log/sub 2/N) bistatic polar format algorithm (PFA) based on a bistatic far-field assumption is derived. This algorithm is a generalization of the popular PFA for monostatic SAR image formation and is highly amenable to implementation with existing monostatic image formation processors. Limits on the size of an imaged scene, analogous to those in monostatic systems, are derived for the bistatic PFA.