Nonlinear Chirp Scaling Algorithm Research Articles

A Modified Frequency Nonlinear Chirp Scaling Algorithm for High-Speed High-Squint Synthetic Aperture Radar with Curved Trajectory

The imaging of high-speed high-squint synthetic aperture radar (HSHS-SAR), which is mounted on maneuvering platforms with curved trajectory, is a challenging task due to the existence of 3-D acceleration and the azimuth spatial variability of range migration and Doppler parameters. Although existing imaging algorithms based on linear range walk correction (LRWC) and nonlinear chirp scaling (NCS) can reduce the range–azimuth coupling of the frequency spectrum (FS) and the spatial variability of the Doppler parameter to some extent, they become invalid as the squint angle, speed, and resolution increase. Additionally, most of them ignore the effect of acceleration phase calibration (APC) on NCS, which should not be neglected as resolution increases. For these issues, a modified frequency nonlinear chirp scaling (MFNCS) algorithm is proposed in this paper. The proposed MFNCS algorithm mainly includes the following aspects. First, a more accurate approximation of range model (MAARM) is established to improve the accuracy of the instantaneous slant range history. Second, a preprocessing of the proposed algorithm based on the first range compression, LRWC, and a spatial-invariant APC (SIVAPC) is implemented to eliminate most of the effects of high-squint angle and 3-D acceleration on the FS. Third, a spatial-variant APC (SVAPC) is performed to remove azimuth spatial variability introduced by 3-D acceleration, and the range focusing is accomplished by the bulk range cell migration correction (BRCMC) and extended secondary range compression (ESRC). Fourth, the azimuth-dependent characteristics evaluation based on LRWC, SIVAPC, and SVAPC is completed to derive the MFNCS algorithm with fifth-order chirp scaling function for azimuth compression. Consequently, the final image is focused on the range time and azimuth frequency domain. The experimental simulation results verify the effectiveness of the proposed algorithm. With a curved trajectory, HSHS-SAR imaging is carried out at a 50° geometric squint angle and 500 m × 500 m imaging width. The integrated sidelobe ratio and peak sidelobe ratio of the point targets at the scenario edges approach the theoretical values, and the range-azimuth resolution is 1.5 m × 3.0 m.

An Improved NLCS Algorithm Based on Series Reversion and Elliptical Model Using Geosynchronous Spaceborne–Airborne UHF UWB Bistatic SAR for Oceanic Scene Imaging

Geosynchronous spaceborne–airborne (GEO-SA) ultra-high-frequency ultra-wideband bistatic synthetic aperture radar (UHF UWB BiSAR) provides high-precision images for marine and polar environments, which are pivotal in glacier monitoring and sea ice thickness measurement for polar ocean mapping and navigation. Contrasting with traditional high-frequency BiSAR, it faces unique challenges, such as the considerable spatial variability, significant range–azimuth coupling, and vast volumes of echo data, which impede high-resolution image reconstruction. This paper presents an improved bistatic nonlinear chirp scaling (NLCS) algorithm for imaging oceanic scenes with GEO-SA UHF UWB BiSAR. This methodology extends the two-dimensional (2-D) spectrum up to the sixth order via the method of series reversion (MSR) to meet accuracy demands and then employs an elliptical model to elucidate the alterations in the azimuth frequency modulation (FM) rate mismatch. Initially, the imaging geometry and signal model are introduced, and then a separation of bistatic slant ranges based on the configuration is proposed. In addition, during range processing, after eliminating linear range cell migration (RCM), the derivation process for the sixth-order 2-D spectrum is detailed and an improved filter is applied to correct the high-order RCM. Finally, during azimuth processing, the causes of the FM rate mismatch are analyzed, a cubic perturbation function derived from the elliptical model is used for FM rate equalization, and a unified sixth-order filter is applied to complete the azimuth compression. Experimental results with point targets and natural oceanic scenes validate the outstanding efficacy of the proposed NLCS algorithm, particularly in imaging quality enhancements for GEO-SA UHF UWB BiSAR.

A wide-beam NCS algorithm for multi-receiver SAS based on azimuth spectrum superposition

The existing multi-receiver synthetic aperture sonar (SAS) imaging algorithms are suitable for narrow-beam width, which will lead to a decrease in imaging quality under wide-beam condition and are not in line with the development needs of SAS. We propose a non-linear chirp scaling algorithm (NCSA) for wide beam multi-receiver SAS. Firstly, the point target reference spectrum (PTRS) of each receiver is obtained by the Lagrange inversion theorem (LIT), and then the under-sampled signal in the azimuth frequency domain is obtained through azimuth spectrum extension; Then, considering the cubic term of range frequency in the PTRS and the linear variation of equivalent frequency modulation slope with range, each receiver is imaged using the NCSA, and coherent superposition is performed in the azimuth frequency domain to eliminate spectrum aliasing caused by azimuth spectrum extension; Finally, the azimuth inverse transform is performed on the superimposed signal to obtain the focusing imaging. Computer simulation experiments and field data verify that this method is superior to the existing SAS imaging algorithm, improving the quality of wide-beam imaging, avoiding the interpolation operation of the traditional range-Doppler algorithm, and saving computation cost.

A Monostatic Forward-Looking Staring Spotlight SAR Raw Data Generation and Hybrid-Domain Image Formation Modifications Based on Extended Azimuth Nonlinear Chirp Scaling Autofocusing

Forward-looking staring spotlight synthetic aperture radar (FSS-SAR) offers operational advantages over conventional squinted SAR counterparts. However, due to its complex observation configuration, pixel anomalies occur when processing raw data. For instance, in the forward-looking geometry, symmetrically distributed point scatterers along the flight path have the same Doppler history, resulting in azimuth ambiguities, whereas staring observation narrows and skews the 2D received spectrum, reducing signal orthogonality and causing spectral folding. As a result, not only is the Doppler frequency gradient too small to be precisely measured in the FSS-SAR mode, limiting the ability to achieve high azimuth angular resolution, but it also suffers from azimuth ambiguities when forming an image. To overcome such azimuth-variant characteristics known as inherent resolutional anomalies, a hybrid-domain image formation algorithm (IFA) based on azimuth scaling is modified here. As an approach, radiometric bias correction (RBC) techniques in conjunction with an extended azimuth nonlinear chirp scaling (ANCS) algorithm capable of equalizing range space variance in the azimuth direction, which benefits from an embedded autofocusing step, have been designed for raw data processing. Given the fact that the platform experiences trajectory deviations under a real-flight condition compared to an ideal trajectory, a pre-processing motion compensation (MOCO) step based on Kalman filtering is included within the IFA. The entire proposed IFA solution tackled the inherent resolutional anomalies of FSS-SAR and succeeded in reconstructing the focused image without azimuthal anomalies. To further assess the IFA, a modified Cartesian back-projection (BP) algorithm was developed along with other objective evaluation scenarios, all of which confirm that the proposed hybrid-domain extended ANCS algorithm is valid for the FSS-SAR application.

A Modified NLCS Algorithm for High-Speed Bistatic Forward-Looking SAR Focusing with Spaceborne Illuminator

The coupling and spatial variation of range and azimuth parameters is the biggest challenge for bistatic forward-looking SAR (BFSAR) imaging. In contrast with the monostatic SAR and translational invariant bistatic SAR (TI-BSAR), the range cell migration (RCM), and Doppler parameters of high-speed bistatic forward-looking SAR (HS-BFSAR) have two-dimensional spatial variation characteristics, which makes it difficult to obtain SAR images with satisfactory global focusing. Firstly, based on the configuration of the spaceborne illuminator and high-speed forward-looking receiving platform, the accurate range-Doppler domain expression of the echo signal is derived in this paper. Secondly, using this analytical expression, a range nonlinear chirp scaling (NLCS) is proposed to equalize the RCM and equivalent range frequency modulation (FM) rate so that they can be uniformly processed in the two-dimensional frequency domain. Next, in the azimuth processing, the proposed method decomposes the Doppler contribution of the transmitter and receiver, respectively. Then, an azimuth NLCS is used to eliminate the spatial variation of the azimuth FM rate. Finally, a range-dependent azimuth filter is constructed to achieve azimuth compression. Simulation results validate the efficiency and effectiveness of the proposed algorithm.

Improved ship imaging algorithm for geosynchronous synthetic aperture radar (SAR) featured by subaperture time window selection optimization and inverse SAR translational compensation

An inverse synthetic aperture radar processing-based algorithm is improved for ship imaging in geosynchronous synthetic aperture radars (GEO SARs) to solve the technical challenges including long accumulation time and complex target motion characteristics. The improvement on the existing algorithm mainly involves four aspects. First, the formula for calculating the appropriate time length of subaperture is derived, according to the principle that the accumulated power of the ship’s echo corresponding to the subaperture duration ensures that the signal-to-noise ratio satisfies the requirement of GEO SARs. The derived formula solves the problem that how long the subaperture length should be taken with regards to a long accumulation time of GEO SAR when imaging ships. Second, we propose an optimization criterion for determining the appropriate subaperture time window by ensuring that the maximum number of ship pixels is detected in the subaperture image. The proposed criterion is used to optimize the location of the subaperture time window in the long accumulation time. Third, the SPECAN algorithm used in the scene imaging process is replaced by an improved nonlinear chirp scaling (NLCS) algorithm to improve the imaging accuracy of the scene. Our improvement on the traditional NLCS algorithm focuses on improving precisions of some of the formulas in the traditional algorithm. Furthermore, a translational compensation algorithm is proposed by considering the influence of spatial variance of slant range history of GEO SARs. The proposed translational compensation algorithm improves the compensation accuracy since the spatial variance of different scatterers in the scene is considered. A series of simulation experiments related with ship imaging in GEO SARs were carried out to verify the correctness of the proposed algorithm and the improvement on the imaging quality compared with that of the existing algorithm.

Focusing of Wide-Swath Range Sweep SAR With Extended Wide Nonlinear Chirp Scaling Algorithm

Multi-channel, DBF-based high-resolution wide swath SAR (HRWS-SAR) is dedicated to acquiring large observation width and high resolution in a single pass. However, the existing HRWS-SAR imaging modes are difficult to cover effectively for the coastline area not parallel to the satellite orbit. Combined with the beam direction changing, variable PRI and distance-oriented DBF techniques, the wide-swath range sweep SAR (WRS-SAR) can image the wide coastline area not parallel to the satellite orbit at high resolution in a single-pass. In this study, an extended wide nonlinear chirp scaling (E-WLNCS) algorithm is proposed, which mainly consists of: a time-domain blind range sample reconstruction algorithm combined with phase variation estimation, a non-uniform resampling algorithm combined with Doppler variation correction, and the effectiveness of the proposed modified E-WLNCS algorithm is demonstrated through point target and surface target simulations.

Focus Improvement of Spaceborne-Missile Bistatic SAR Data Using the Modified NLCS Algorithm Based on the Method of Series Reversion

The speed and direction of a missile shifts sharply in the dive phase, making the azimuth frequency modulation (FM) rate change with the azimuthal position, leading to azimuth ambiguities and image distortion. To solve this problem, a modified nonlinear chirp scaling (NLCS) algorithm was adopted to compensate for the azimuth FM rate. First, the geometric configuration and echo signal model of the spaceborne missile bistatic synthetic aperture radar (SAR) were built, and then the Doppler frequency correction was performed, and the 2-D spectrum of the signal was derived by the method of series reversion. Next, range migration correction and range compression were finished in the 2-D frequency domain. Following this, a modified NLCS algorithm was proposed to solve the space variance of Doppler phase problem. After compensating for the azimuth FM rate, the azimuth compression focusing was completed and the imaging result was obtained. Finally, by comparing the calculation amount, imaging effect, and performance index with the traditional NLCS algorithm, it can be concluded that the algorithm reduced the calculation amount by 1.0128 × 108 floating point operations per second (FLOPs) compared with the traditional NLCS algorithm, and the azimuth focusing effect of the edge point was greatly improved. Its resolution, peak sidelobe ratio (PSLR), and integrated sidelobe ratio (ISLR) were improved by 0.87 m, 3.32 dB, and 1.79 dB, respectively, which proved the effectiveness and feasibility of this method.

Research on Configuration Constraints of Airborne Bistatic SARs.

Based on the analysis of the airborne bistatic synthetic aperture radar (SAR) imaging geometric mode, an extended nonlinear chirp scaling algorithm is employed to simulate and verify the imaging effect of the bistatic SARs. A gradient theory-based two-dimensional resolution bistatic SAR model is proposed, and the constraints of the multi-platform flight trajectory parameters meeting the imaging accuracy of the bistatic SAR are analyzed. Finally, through the bistatic SAR imaging simulation of cooperative flight trajectories under various situations, the spatial configuration constraint envelope between the flight vehicles to achieve the optimal resolution is revealed. The results of this paper will provide a theoretical reference for the SAR application in formation flight control.

Efficient imaging method for multireceiver SAS

With the Loffeld's bistatic formula, the point target reference spectrum (PTRS) of multireceiver synthetic aperture sonar (SAS) can be decomposed into the quasi monostatic term and bistatic deformation (BD) term. The former term is analogous to the monostatic SAS PTRS while the latter one describes the bistatic phase introduced by the bistatic displacement between the transmitter and receiver. The multireceiver SAS echo signal can be transformed into monostatic SAS equivalent data after correcting the BD term. Based on the range sub-block processing method, this data transformation is conducted by using the preprocessing step. Then, fast imaging processors based on monostatic SAS system can be directly exploited to process the monostatic SAS equivalent data. In this paper, the authors mainly focus on the application of non-linear chirp scaling algorithm. At last, the simulations and real data are used to validate the presented method. The processing results show that the imaging performance of presented method is nearly close to that of traditional method. Besides, the imaging efficiency is highly improved compared to the phase centre approximation (PCA) method.

Focusing Highly Squinted SAR Data of a Short-Range Wide-Swath Region Using Azimuth-Dependent High-Order RCMC and Frequency Extended Nonlinear Chirp Scaling Based on Equidistant Sphere Model

Focusing highly squinted synthetic aperture radar (SAR) data of a short-range wide-swath (SRWS) region is a challenging task because the reference range linear range cell migration correction (LRCMC) and the inherent range-dependent squint angle produce two-dimensional (2-D) spatial-variant RCM and azimuth-dependent Doppler parameters. In this paper, a two-step imaging algorithm (strategy) based on a novel equidistant sphere model (ESM) is proposed to accommodate these issues. The ESM, which is used for depicting the spatial-variant property of the echo data, is established by an investigation into the property of the origin range after the keystone transform (KT) operation and the reference range RCMC. Based on the ESM, an azimuth-dependent high-order RCMC (ADH-RCMC) method is adopted in the first step to implement the residual azimuth-dependent RCMC. In the second step, a frequency extended nonlinear chirp scaling (FENLCS) algorithm is introduced to achieve the highly varying residual Doppler centroid correction and the azimuth-dependent high-order Doppler parameter equalization. Simulation results in the case of SRWS SAR demonstrate the superior performance of the proposed algorithm.

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.

Focusing highly squinted missile-borne SAR data using azimuth frequency nonlinear chirp scaling algorithm

Focusing highly squinted missile-borne SAR data using azimuth frequency nonlinear chirp scaling 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.

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.

A novel AFNCS algorithm for super-resolution SAR in curve trajectory

With the improvement of SAR resolution, super-resolution SAR imaging is more and more widely used in the all-time and all-weather video surveillance and remote sensing imaging. One implementation of super-resolution SAR is that radar works in the spotlight mode. In the case with highly squinted angle and acceleration, the azimuth space variance and the coupling between range and azimuth will become serious in super-resolution imaging. Thus, an azimuth frequency nonlinear chirp scaling algorithm is proposed to solve this problem. Based on the acceleration model, the accurate 2-D spectrum is performed by adopting the method of series reversion. The space-variance of missile-borne SAR in curved flight path is analyzed and an azimuth polynomial phase filter is constructed to make the coefficients of the perturbation function has sufficient flexibility to eliminate the spatial-variant couple terms between range and azimuth. In addition, the gradient operation is used to expand the space-variant coefficients of azimuth modulation term, and the perturbation function is applied to eliminate the space-variant in azimuth direction. The proposed focusing method can process the missile-borne SAR data obtained in spotlight mode in highly squinted angle with high efficiency. The simulation results verify the effectiveness of the proposed imaging approach. The integration of the research in this paper and the deep learning will further pave the way of super-resolution SAR imaging applications in disaster monitoring, security and surveillance.

Advanced high-order nonlinear chirp scaling algorithm for high-resolution wide-swath spaceborne SAR

Spaceborne Synthetic Aperture Radar (SAR) is a well-established and powerful imaging technology that can provide high-resolution images of the Earth’s surface on a global scale. For future SAR systems, one of the key capabilities is to acquire images with both high-resolution and wide-swath. In parallel to the evolution of SAR sensors, more precise range models, and effective imaging algorithms are required. Due to the significant azimuth-variance of the echo signal in High-Resolution Wide-Swath (HRWS) SAR, two challenges have been faced in conventional imaging algorithms. The first challenge is constructing a precise range model of the whole scene and the second one is to develop an effective imaging algorithm since existing ones fail to process high-resolution and wide azimuth swath SAR data effectively. In this paper, an Advanced High-order Nonlinear Chirp Scaling (A-HNLCS) algorithm for HRWS SAR is proposed. First, a novel Second-Order Equivalent Squint Range Model (SOESRM) is developed to describe the range history of the whole scene, by introducing a quadratic curve to fit the deviation of the azimuth FM rate. Second, a corresponding algorithm is derived, where the azimuth-variance of the echo signal is solved by azimuth equalizing processing and accurate focusing is achieved through a high-order nonlinear chirp scaling algorithm. As a result, the whole scene can be accurately focused through one single imaging processing. Simulations are provided to validate the proposed range model and imaging algorithm.

An Improved Imaging Algorithm for High-Resolution and Highly Squinted One-Stationary Bistatic SAR Using Extended Nonlinear Chirp Scaling Based on Equi-Sum of Bistatic Ranges

The linear range walk correction (LRWC) and the inherent azimuth-variant geometric configuration in the case of one-stationary bistatic synthetic aperture radar (OS-BiSAR) imaging produce 2-D variant range cell migrations (RCMs) and azimuth-dependent Doppler parameters, which makes it more difficult to obtain high-quality image for high-resolution and highly squinted OS-BiSAR. To accommodate these issues, an improved extended nonlinear chirp scaling (ENLCS) algorithm is developed in this letter. An analytic model based on the equi-sum of bistatic ranges (ESBR) after the RCM correction is proposed to reveal the azimuth-variant property of the azimuth distributed targets. Based on this innovative model, analytic coefficients of the ENLCS are derived, and high-quality image formation for OS-BiSAR is accomplished. Simulations are conducted to demonstrate the validity of the proposed algorithm.

Focusing of Bistatic SAR With Curved Trajectory Based on Extended Azimuth Nonlinear Chirp Scaling

The focusing of bistatic synthetic aperture radar (BiSAR) data is more challenging than the traditional monostatic counterparts because of the strong range–azimuth coupling of echo signal, and the range cell migration (RCM) and Doppler frequency modulation (FM) rate, which are caused by complex geometric configuration. Although several monostatic algorithms have been modified to handle general bistatic cases, these algorithms are derived from the assumption that the flying platforms are moving along a linear trajectory with uniform velocity. In practical situation, the flight path of the spaceborne SAR platform inevitably deviates from the ideal trajectory in the long integration time. In this case, besides the influence of the inherent geometric configuration of BiSAR, the curved trajectory of the platforms also causes an additional range–azimuth coupling and the spatial variance of RCM and Doppler FM rate, which cannot be processed by the traditional algorithms. In this article, considering the curved orbit of the SAR platforms and the motion of ground targets caused by the Earth’s rotation, a high-order motion range model is proposed. Based on the range model, the spatial variance characteristic of the BiSAR with curved trajectory is analyzed. Then, an extended azimuth nonlinear chirp scaling (EANLCS) algorithm with an addition of highly varying residual Doppler centroid correction for BiSAR with curved trajectory is proposed. Simulation results show the effectiveness of the range model and the modified algorithm.

Interpolation Free Wide Nonlinear Chirp Scaling Algorithm for Spaceborne Stripmap Range Sweep SAR Imaging

The spaceborne stripmap range sweep synthetic aperture radar (SAR) (SS-RSSAR) is a new-concept SAR mode proposed to efficiently image regions of interest (ROI) squinted with respect to satellite orbit. The most distinct feature of the SS-RSSAR is the beam sweeping in the elevation for continuous squinted ROI illumination. A wide nonlinear chirp scaling algorithm (WNLCSA) has been proposed to directly implement image formation along the ROI spreading direction. However, the algorithm efficiency is limited due to its time-consuming time-domain interpolation. In this letter, a new interpolation free WNLCSA (IF-WNLCSA) is proposed for more efficient SS-RSSAR imaging by substituting the interpolation with a much faster chirp scaling approach. Different from the interpolation, the chirp scaling induces additional range migration and Doppler modulation, both of which, however, are neglected due to their weak influences on imaging. The derivation of the chirp scaling is presented in detail, followed by the analyses on the algorithm accuracy and efficiency. The presented approach is evaluated by both the point- and extended-target simulations.