Residual Range Cell Migration Research Articles

A Modified Range Doppler Algorithm for High-Squint SAR Data Imaging

The high-squint airborne Synthetic Aperture Radar (SAR) has the ability to detect the target area flexibly, and the detection swath is significantly increased compared with the side-looking SAR system. Therefore, it is of great significance to carry out research on high-precision imaging methods for high-squint airborne SAR. However, the high-squint SAR echoes have large Range Cell Migration (RCM), resulting in severe range–azimuth coupling and strong spatial variation. In this paper, a Modified Range Doppler Algorithm (MRDA) is proposed to cope with these effects introduced by the significant RCM in high-squint airborne SAR imaging. The bulk compensation preprocessing is first adopted to remove the considerable RCM and severe cross-coupling in a two-dimensional frequency domain. Then, Non-Linear Chirp Scaling (NLCS) in the range direction is utilized to equalize the range-variant chirp rate caused by the residual RCM and coupling and, therefore, the consistent range phase compensation can be fulfilled in range frequency domain. The modified correlation processing is executed to compensate the residual Doppler phase modulation, the residual RCM and the range-variant cubic phase modulation, which guarantees the characteristics of high efficiency and high precision. The simulations have demonstrated that the MRDA can focus the SAR echoes with large squint angles more effectively than the algorithms based on the Linear Range Walk Correction (LRWC) method.

Processing of Airborne Microwave Photonic SAR Raw Data With Inaccurate RSF

Due to system instability and other reasons, the actual range sampling frequency of the system may deviate from the ideal value for the microwave photonic synthetic aperture radar (SAR). This deviation may lead to severe residual range cell migration (RCM) and even range defocus after imaging, which can seriously affect the image quality. To resolve this problem, this paper proposes an airborne microwave photonic SAR imaging algorithm based on inaccurate system parameter estimation. Firstly, the algorithm estimates and compensates for the range spatial-variant motion error to eliminate the effect of this motion error on the remaining RCM and range defocus. Secondly, based on the minimum entropy criterion of the image, we use the optimization model to estimate the actual range sampling frequency (RSF). Finally, the existing wide-beam autofocus method is used to correct the azimuth spatial-variant motion error. The simulation data and the measured data processing results verify the effectiveness of the proposed method.

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.

An Efficient Approach for Coherent Integration Detection of High-speed Maneuvering Targets with Arbitrary-Order Doppler Frequency Migrations

In radar detection applications, high-speed maneuvering targets (HSMTs) are commonly encountered. Given the range cell migration (RCM) and arbitrary-order Doppler frequency migrations (DFMs) induced by the complex relative motions between the HSMT and radar, they usually present a great challenge for target detections. In addition, the complex Doppler ambiguity will further aggravate the difficulty in focusing of HSMT. To address these issues, an efficient approach for coherent integration detection of HSMTs is proposed. First, inspired by the symmetrical feature of range frequency, a new range frequency reversal transform is introduced to correct complex arbitrary-order DFMs simultaneously. After that, by exploiting the advantage of range-azimuth joint processing, a modified two-dimensional scaled Fourier transform is developed to remove the residual RCM and a well-focused result is thus achieved. Furthermore, a discrimination procedure is proposed to remove the spurious peak for cross terms of targets with the same parameters. The proposed method has an extremely low computational cost and does not need to know the target motion order a priori because the operations of multidimensional search and parameter estimation are avoided. It also handles complex arbitrary-order DFMs, blind speed sidelobe, and complex Doppler center blur and spectrum ambiguity. The experiments using real data also validate the performance of the proposed method.

Coherent integration for maneuvering target detection via fast nonparametric estimation method

Maneuvering target presents a great threat for radar detection applications. The complex unknown motions between radar and maneuvering target seriously affect the performance of target coherent integration. Existing methods utilizing parameter search or estimation are limited by the high computational burden and the propagation errors of different parameter estimations. In this study, a fast nonparametric estimation method is proposed for coherent integration of maneuvering target. Firstly, the second-order Keystone transform is adopted to eliminate the quadratic range cell migration (RCM). Secondly, the modified range frequency reversal process is proposed to simultaneously remove the complex low- and high-order Doppler frequency broadenings (DFBs) by a one-step matrix multiplication operation. Subsequently, the residual RCM is corrected by the proposed improved time-scaled transform without searching for the Doppler ambiguity number, and then a well-focused result can be obtained. The proposed method is simple to implement and computationally efficient given that searching and estimation of parameters are avoided. It also addresses the high-order DFB and blind speed sidelobe. The processing results of simulated and real data are presented to verify the performance of the presented approach.

Correction of Range-Variant Motion Error and Residual RCM in Sparse Regularization SAR Imaging.

Lq (0 < q ≤ 1) regularization has been confirmed effective when applied to sparse SAR imaging. However, the inaccuracies caused by motion errors in the observation model will lead to various degradations and defocus in the reconstructed image. For high-resolution and light-small SAR systems, the range-variant motion errors will decrease the accuracy of range cell migration correction (RCMC), and residual range cell migration (RCM) will exceed multiple range resolution cells and degrade the image quality substantially. Aiming at this problem, in this paper, a novel azimuth-range decoupled sparse SAR imaging method with coarse-to-fine range-variant motion errors and residual RCM correction method is proposed. First, a one-step motion compensation (MOCO) operator is proposed using the inertial navigation systems (INS)/global positioning systems (GPS) information, which can significantly reduce the residual RCM and improve the reconstruction accuracy. Second, a fine high-order phase-error correction method is performed to correct the range and cross-range-varying phase errors using a joint imaging and phase-error estimation scheme, which will further improve the image focusing quality. Experimental results indicate the effectiveness of the proposed method.

An Efficient Multichannel SAR Channel Phase Error Calibration Method Based on Fine-Focused HRWS SAR Image Entropy

Azimuth multichannel synthetic aperture radar (SAR) is a useful approach to solving minimum antenna area constraint and realizing high resolution and wide swath (HRWS) imaging by multichannel signal reconstruction. However, channel phase error will significantly degrade the reconstruction performance and leads to azimuth ghost. This article presents an efficient minimum entropy channel error estimation method based on fine-focused SAR image. The multichannel SAR images are obtained by using Range-Doppler imaging algorithm applied for preprocessed data of each channel. Then, the reconstruction and the residual range cell migration and residual second range compression compensation are performed to achieve multichannel fine-focused SAR images. After overlapping these multichannel fine-focused SAR images and iteratively calibrating the channel phase error, fine-focused HRWS SAR image can be achieved. Therefore, the SAR image used in the channel error estimation process can directly obtain the fine focused HRWS SAR image after minimum entropy iteration without additional imaging operations. Compared with the minimum entropy method by using the coarse-focused SAR image based on azimuth deramp, redundant reconstruction, and imaging operations are avoided. Thus, error estimation and imaging processing procedures are optimized. Processing efficiency improvement are analyzed, and simulation and acquired data processing verify the effectiveness of the proposed method.

Focusing High Maneuvering Bistatic Forward-Looking SAR With Stationary Transmitter Using Extended Keystone Transform and Modified Frequency Nonlinear Chirp Scaling

This article presents an imaging solution for high maneuvering bistatic forward-looking SAR with stationary transmitter (STHM-BFSAR). In STHM-BFSAR configuration that the transmitter is mounted on a stationary platform in side-looking mode while the receiver does high-speed maneuvering in forward-looking mode, high speed and acceleration induced by high dynamic characteristics of receiver in both along-track and height direction cause larger range cell migration (RCM) and more severe 2-D spatial variation of Doppler characteristics, which makes it more difficult to obtain well-focused bistatic SAR image. Furthermore, different from the general airborne bistatic SAR, STHM-BFSAR has a larger azimuth cubic phase term that exceeds <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pi /4$</tex-math></inline-formula> rad, which seriously affects the image quality. To deal with these problems, an imaging algorithm based on extended keystone transform (EKT) and modified frequency nonlinear chirp scaling (FNCS) is proposed in this article. EKT can correct spatial variant range curvature and bulk linear RCM, and the residual RCM is smaller than traditional keystone transform. The proposed modified FNCS is used to equalize the azimuth-range-dependent Doppler parameters in the frequency domain, which produces lower side-lobes and higher accuracy by compensating for the second-order spatial variation of the azimuth cubic coefficients. The final simulation results in this article verify the effectiveness of the proposed algorithm.

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.

Focusing High-Maneuverability Bistatic Forward-Looking SAR Using Extended Azimuth Nonlinear Chirp Scaling Algorithm

In high-maneuverability bistatic forward-looking synthetic aperture radar (HMBF-SAR) imaging, the acceleration leads to an increased residual range curve and a deepened two-dimensional spatial variance of Doppler parameters, which cannot be processed by the traditional algorithms. To address these problems, this paper establishes a more accurate digital representation for HMBF-SAR model and investigates an extended azimuth nonlinear Chirp Scaling (EANLCS) imaging method. In the flowchart of this paper, we first propose a more precise slant range model with improved expansion coefficients, and defines the range and azimuth direction of HMBF-SAR imaging. Then, a novel fast reference point (i.e., azimuth and range reference point) selection method is proposed to analyze two-dimensional spatial variance of signal characteristics, which is used to construct a high order model of residual range cell migration and Doppler parameters. Based on above analysis, we put forward an advanced imaging algorithm of combining the Second-order keystone and extended azimuth nonlinear chirp scaling (EANLCS) to compensate the increased residual range curve and two-dimensional spatial variance of Doppler parameters. Finally, the effectiveness of the proposed HBMF-SAR method is verified by several numerical simulations and comparative studies based on both the simulated and raw data.

High Speed Maneuvering Platform Squint TOPS SAR Imaging Based on Local Polar Coordinate and Angular Division

This paper proposes an imaging algorithm for synthetic aperture radar (SAR) mounted on a high-speed maneuvering platform with squint terrain observation by progressive scan mode. To overcome the mismatch between range model and the signal after range walk correction, the range history is calculated in local polar format. The Doppler ambiguity is resolved by nonlinear derotation and zero-padding. The recovered signal is divided into several blocks in Doppler according to the angular division. Keystone transform is used to remove the space-variant range cell migration (RCM) components. Thus, the residual RCM terms can be compensated by a unified phase function. Frequency domain perturbation terms are introduced to correct the space-variant Doppler chirp rate term. The focusing parameters are calculated according to the scene center of each angular block and the signal of each block can be processed in parallel. The image of each block is focused in range-Doppler domain. After the geometric correction, the final focused image can be obtained by directly combined the images of all angular blocks. Simulated SAR data has verified the effectiveness of the proposed algorithm.

Focus Improvement of Airborne High-Squint Bistatic SAR Data Using Modified Azimuth NLCS Algorithm Based on Lagrange Inversion Theorem

In this paper, a modified azimuth nonlinear chirp scaling (NLCS) algorithm is derived for high-squint bistatic synthetic aperture radar (BiSAR) imaging to solve its inherent difficult issues, including the large range cell migration (RCM), azimuth-dependent Doppler parameters, and the sensibility of the higher order terms. First, using the Lagrange inversion theorem, an accurate spectrum suitable for processing airborne high-squint BiSAR data is introduced. Different from the spectrum that is based on the method of series reversion (MSR), it is allowed to derive the bistatic stationary phase point while retaining the double square root (DSR) of the slant range history. Based the spectrum, a linear RCM correction is used to remove the most of the linear RCM components and mitigate the range-azimuth coupling, and, then, bulk secondary range compression is implemented to compensate the residual RCM and cross-coupling terms. Following this, a modified azimuth NLCS operation is applied to eliminate the azimuth-dependence of Doppler parameters and equalize the azimuth frequency modulation for azimuth compression. The experimental results, with better focusing performance, prove the high accuracy and effectiveness of the proposed algorithm.

Spatial-Variant SAR Range Cell Migration Correction Using Subaperture Strategy

The coupling between range and azimuth dimensions is the main obstacle for highly squinted synthetic aperture radar (SAR) data focusing. Range walk correction (RWC) processing is effective to remove the linear coupling term, but the residual high order range cell migration (RCM) parts are spatial-variant in both range and azimuth dimensions. In this paper, we propose a precise spatial-variant range cell migration correction (RCMC) method with subaperture processing. The method contains two stages. Firstly, the main component of range-variant RCM is corrected in the coarse RCMC stage. Secondly, data are derived into azimuth subapertures (SAs), an SA-image-domain RCMC is developed by interp correction, where the SA image is obtained using a modified spectrum analysis (SPECAN) algorithm by establishing the relationship between Doppler frequency and residual spatial-variant RCM. In the proposed algorithm, precise compensation of space-variant RCM is implemented by SA processing, which is designed for a better practicality in real-time processing system. Simulated and real measured data experiments are designed to validate the effectiveness of the proposed approach for highly squinted SAR imaging.

Focusing Nonparallel-Track Bistatic SAR Data Using Modified Frequency Extended Nonlinear Chirp Scaling

Unsynchronization of the separate transmit–receive beams makes it a challenging task to obtain high-quality images for nonparallel-track bistatic synthetic aperture radar (NP-BiSAR). To accommodate this issue, we propose an imaging configuration where the receiver’s beam follows the transmitter’s one actively by adjusting the squint angle of receiver. And a frequency extended nonlinear chirp scaling (FENLCS) algorithm is modified to cope with new effects introduced by the innovative configuration, which is based on an improved quadratic ellipse model. Based on the new model, some innovative improvements on image formation are made, including a residual azimuth-dependent high-order range cell migration correction (ADH-RCMC) and a rederived FENLCS that takes highly varying Doppler centroid into consideration, which contribute to better imaging quality. Simulation results validate the effectiveness of the proposed configuration and algorithm.

Migration Correction Algorithm for Coherent Integration of Low-Observable Target With Uniform Radial Acceleration

Range and Doppler frequency cell migration induced by the movement of the low-observable target would bring about serious integration loss, which may deteriorate the target detection or imaging performance. Hence, this article proposes a migration correction algorithm based on keystone transform and modified generalized radon Fourier transform (KT-MGRFT). More specifically, KT is first utilized to eliminate the linear range cell migration (RCM) induced by the target unambiguous velocity. Then, MGRFT is presented to estimate the fold factor and acceleration. After that, the residual RCM and Doppler frequency cell migration (DFCM) are compensated by multiplying a reference signal constructed by the estimated fold factor and acceleration. Finally, the coherent integration can be achieved via the inverse Fourier transform (IFT) and the Fourier transform (FT) with respect to range frequency and scaled slow time, respectively. Compared with standard GRFT, the proposed method can remove the searching procedure of unambiguous velocity, and thus, it has lower computational complexity. In addition, through taking the maximum value in searching the range-Doppler frequency domain, the blind speed sidelobe (BSSL) effect is suppressed. Both the numerical simulations and the real experiment with the X-band radar are given to verify the effectiveness of the proposed method.

KT and azimuth sub‐region deramp‐based high‐squint SAR imaging algorithm mounted on manoeuvring platforms

Owing to the existence of high-order motion parameters and vertical velocity, severe range–azimuth coupling and two-dimensional spatial variability of the imaging parameters degrade the image quality of high-squint synthetic aperture radar (SAR) mounted on manoeuvring platforms. To accommodate these issues, a novel sub-aperture SAR imaging algorithm based on keystone transform (KT) and azimuth sub-region deramp is proposed. In the range dimension processing, a correction function is constructed based on the scene centre to realise non-spatial-variant range cell migration (RCM) correction and range–azimuth decoupling, and then the residual spatial-variant RCM is removed by the KT. In the azimuth dimension processing, considering the impact of the range distortion on the azimuth modulated phase, accurate analytical formula of the signal in the azimuth time domain is deduced. On this basis, a fast azimuth compression method based on the azimuth sub-region deramp is proposed, and the theoretical effective imaging area is analysed. The theoretical analysis and the simulations show that the proposed imaging algorithm has high computational efficiency and can effectively expand the imaging area of high-squint SAR mounted on manoeuvring platforms.

A Novel Motion Compensation Approach Based on Symmetric Triangle Wave Interferometry for UAV SAR Imagery

The combination of synthetic aperture radar (SAR) with unmanned aerial vehicles (UAVs) is attractive for acquiring high-resolution images without the restrictions of time and weather. However, because UAVs are lightweight and small in size, the UAV SAR system is very sensitive to turbulence, resulting in serious trajectory deviations and remaining residual motion errors (RMEs), such as residual range cell migration (RCM) and aperture phase errors (APEs). In this paper, a novel motion compensation (MoCo) strategy is developed based on the symmetric triangle linear frequency modulated continuous wave (STLFMCW) signal. The STLFMCW signal model is first presented, which reveals the relevance between the positive-negative frequency modulations and motion errors. The residual RCMs and relative phase errors are estimated directly through the phase differential interferometry of up-ramp and down-ramp chirp signals, instead of the traditional approach of relying on the range-shift gradient of adjacent range profiles. The proposed approach is independent of conventional prominent point processing (PPP) and calculates the range deviation to avoid the accumulation of errors, thereby achieving high precision and efficiency. Experiments based on simulated and measured data sets validate the proposed approach.

Fast Factorized Backprojection Imaging Algorithm Integrated With Motion Trajectory Estimation for Bistatic Forward-Looking SAR

A bistatic forward-looking synthetic aperture radar (BFSAR) is increasingly in the focus of study, as it breaks through the limitations of imaging on a forward-looking terrain of a moving platform. Fast factorized backprojection (FFBP) is a reliable BFSAR imaging algorithm, with both imaging precision and efficiency being taken into consideration. In FFBP imaging, compensation of the motion errors is important to obtain a well-focused image. To accomplish an accurate motion compensation in image processing, a high-precision navigation system is needed. However, in many cases, because of the accuracy limit of such systems, motion errors are difficult to be compensated correctly, resulting chiefly in resolution decrease in the final images. To deal with such a problem, we propose an FFBP imaging algorithm integrated with motion trajectory estimation for BFSAR. First, a coarse-to-fine residual range cell migration (RCM) correction scheme is applied to ensure the residual RCM within a range resolution. Then, an optimization model with respect to motion trajectory estimation under the criterion of maximum image sharpness is built during FFBP imaging. According to the coarse-to-fine residual RCM correction scheme and the motion trajectory estimation model, a block coordinate descent technique based on steepest descent optimization method integrated with residual RCM correction is proposed to estimate the motion errors in FFBP imaging. We empirically compare the proposed method with several state-of-the-art BFSAR imaging and autofocus algorithms. Simulations on BFSAR data show that the proposed method is more accurate and has similar computational cost.

Two-Step Accuracy Improvement of Motion Compensation for Airborne SAR With Ultrahigh Resolution and Wide Swath

The motion compensation (MOCO) for the airborne SAR with ultrahigh resolution and wide swath is required to consider the range-dependent (RD) phase error. The RD phase error may cause an RD residual-range cell migration (RCM) after the correction of RCM, which can degrade the performance of phase gradient autofocus (PGA) when estimating the phase error. In addition, because the PGA estimation is based on the strong scattering point, it may wrongly estimate the phase error for some observation scenes without strong scattering point. Alternatively, to take into account the above two problems, we study a MOCO algorithm based on two-step accuracy improvement. In the algorithm, the first step is to estimate and correct the RD residual-RCM and thus improves the accuracy of PGA. The second step is to develop a prior-information-based-weighted least square (PI-WLS) to further improve the accuracy of RD phase error estimation. Processing of airborne real data validates the effectiveness of the proposed algorithm.

Improvement of non‐linear chirp‐scaling algorithm for highly squint bistatic SAR data focusing

Bistatic synthetic aperture radar (SAR) has specific advantages, e.g. weak targets detecting, reducing system vulnerability, and anti-interference with low cost and flexible working modes. However, great challenges exist in data processing procedure due to its complicated geometry and 2-D spatial variance, which become more serious when the squint angle increases. Here, an improved non-linear chirp scaling method is proposed to handle highly squint bistatic SAR data. On one hand, Keystone transform is first performed, then linear range walk is removed to deduce the residual range cell migration correction factor, which is used for range compression and removing cross-coupling terms. On the other hand, frequency modulation rates and high-order phase based on the transmitter range offset (RO) and receiver RO are derived according to the geometric configuration. Simulation results show the effectiveness of the proposed algorithm.