A fast ground moving target focusing method based on first-order discrete polynomial-phase transform

Detection of high-speed maneuvering targets has attracted a great deal of attention recently. There are two main problems to be solved: improving detection ability under the condition of complicated range migration and Doppler frequency migration effects, and reducing computational load. Different from most existing fast algorithms which are at the cost of detection ability, this paper devises a computationally attractive method with excellent detection performance. First, the keystone transform is carried out to remove linear range migration. Thereafter, a fast discrete chirp-Fourier transform (FDCFT) based on radix-4 decomposition is proposed to compensate the undersampled linear Doppler frequency migration and quadratic Doppler frequency migration. Because of exploiting inherent symmetry and periodicity as in the fast Fourier transform (FFT), the FDCFT can largely reduce the computational complexity without performance loss. The novelty of the proposed algorithm lies in combining linear transform with the concept of decimation-in-time FFT, which avoids the demanding multi-dimensional search and severe performance loss via introducing nonlinear transforms. It is shown that the proposed method has an approximately optimal detection performance but with relatively low computational cost.

HighlightsWhat are the main findings?This paper presents a high-order phase compensation and parameter estimation algorithm designed for maneuvering targets, which effectively balances detection performance and computational efficiency.The proposed method achieves precise compensation of high-order range migrations without the need for exhaustive parameter search, thereby circumventing the blind speed sidelobe effect. Futhermore, the incorporation of a time-delay variable significantly improves the anti-noise capability of the approach.What is the implication of the main finding?This algorithm introduces a novel motion compensation technique to address the challenges of range migration, Doppler frequency migration, and Doppler ambiguity in detecting weak maneuvering targets. It achieves precise range migration compensation with enhanced accuracy and robustness, forming a vital preprocessing step for high-quality SAR imaging.The algorithm supports simultaneous multi-target processing and holds promising application potential in fields such as airborne radar detection, maritime moving target indication, cooperative observation by UAV formations, and other fields.This study focuses on the key challenges in detecting and estimating motion parameters of ground maneuvering targets for airborne radar sensors. The complex unknown motion states of the ground maneuvering target, including velocity, acceleration, and jerk, result in range migrations (RMs) and Doppler frequency migrations (DFMs). These effects severely degrade the long-time coherent accumulation performance of the airborne radar, thereby limiting the reliable detection and precise parameter estimation of maneuvering targets. To address this issue, a new detection and motion parameter estimation method based on the range frequency reversal transform (RFRT) and searching Lv’s distribution (SLVD), i.e., RFRT-SLVD, is proposed. Specifically, the third-order RM (TRM) and quadratic DFM (QDFM) are considered. The proposed method operates as follows: First, RMs are eliminated simultaneously via the RFRT operation, which multiplies the echo by its reversed data in the range frequency and slow-time domains, leveraging the symmetric equal-interval sampling property of the range frequency. Subsequently, a phase compensation function (PCF) related to the jerk is constructed to compensate the QDFM. Finally, the LVD is performed to remove residual DFMs and achieve effective signal energy accumulation. Additionally, the case of a fast-moving target with Doppler ambiguity is analyzed, and a method for estimating three motion parameters is provided. A key advantage of the proposed technique is its ability to directly compensate the RMs without requiring prior knowledge of the maneuvering target, while also avoiding the blind speed sidelobe (BSSL) effect. In comparison with existing algorithms, RFRT-SLVD achieves a balanced trade-off between parameter estimation performance and computational efficiency. Numerical analyses and experiments are conducted to validate the method, assessing its detection capability for ground maneuvering targets, Doppler ambiguity resolution in parameter estimation, computational complexity, and method applicability in multi-target scenarios.

This study considers the coherent integration problem for detecting a manoeuvring target, involving range migration (RM) and Doppler frequency migration (DFM) within the coherent processing interval. An efficient coherent integration method based on keystone transform (KT) and Lv's distribution (LVD) is proposed. It can not only correct the RM effect by KT and fold factor phase compensation, but also remove the DFM effect and achieve the coherent accumulation via LVD. Compared with the moving target detection, Radon‐Fourier transform, and Radon‐fractional Fourier transform algorithms, the proposed method can obtain better detection ability under low signal‐to‐noise ratio environment. Finally, several simulations are provided to demonstrate the effectiveness.

In recent years, target detection has drawn increasing attention in the field of radar signal processing. In this paper, we address the problem of coherent integration for detecting high-speed maneuvering targets, involving range migration (RM), quadratic RM (QRM), and Doppler frequency migration (DFM) within the coherent processing interval. We propose a novel coherent integration algorithm based on the frequency-domain second-order phase difference (FD-SoPD) approach. First, we use the FD-SoPD operation to reduce the signal from three to two dimensions and simultaneously eliminate the effects of QRM and DFM, which leads to signal-to-noise ratio improvement in the velocity-acceleration domain. Next, we estimate the target motion parameters from the peak position without the need for a search procedure. We show that this algorithm can be easily implemented by using complex multiplications combined with fast Fourier transform (FFT) and inverse FFT (IFFT) operations. We perform comparisons with several representative algorithms and show that the proposed technique can be used to achieve a good trade-off between computational complexity and detection performance. We present both simulated and experimental data to demonstrate the effectiveness of the proposed method.

Long-time coherent integration using frequency hopping signals is a challenging problem for passive bistatic radar due to its frequency hopping characteristics. Apart from range walk, range curve, and Doppler frequency migration, Doppler diffusion caused by frequency hopping characteristics occurs within the observation time, which also lowers the detection performance. To deal with this problem, a novel coherent integration method for frequency hopping signals based on passive bistatic radar is proposed in this paper. In this novel method, range curve and range walk are eliminated by applying generalized Keystone transform. Then, Doppler frequency migration caused by the target's acceleration is compensated for by a parameter search with a designed search scope. Finally, Doppler frequency migration caused by frequency hopping characteristics is compensated for by designing a new acceleration compensation function and a revised rotation factor for Fourier transform. Since migration effects caused by frequency hopping characteristics are considered and compensated for when using frequency hopping signals, the weak target echo can be better integrated in the observation time compared to when using the existing methods. The simulation results and performance analysis illustrate the effectiveness of the proposed method.

When multiple targets are within the same radar antenna beam and cannot be separated in the range dimension, the conventional imaging methods cannot be directly used to obtain a focused radar image. In this study, a new joint estimation algorithm for multi-targets' motion parameters is proposed. In this method, the first-order Keystone transform is first applied to correct the range walk of multiple targets simultaneously, and then the Lv's transform is used to estimate the motion parameters of targets including velocity and acceleration. The signal-to-noise ratio threshold for the proposed method is also given. The proposed method is fast and can obtain the accurate parameter estimation without knowing the number of targets and their motion information. Experimental results demonstrate the performance of the proposed algorithm. Comparisons between the proposed method and other methods, the maximum-likelihood method, fractional Fourier transform and discrete polynomial transform, are performed, which show that the proposed method can efficiently obtain the accurate parameter estimation with low computational burden.

In SAR/ISAR imaging, estimation of motion parameters of moving objects is needed in order to compensate for translational motion that causes image blurring. Phase parameter estimation from signals corresponding to one scatterer buried in complex white Gaussian noise is a problem for which various successful techniques have been devised. For multicomponent signals, it is difficult to use these parametric methods. Isolating the signal's components in order to do the estimation can help. The authors have previously proposed the isolation of scatterers for instantaneous frequency estimation. This process allows not only the extraction of components but also the manipulation of each object separately. In this paper, we study the use of time-frequency filtering on parameter estimation for a complex exponential signal with polynomial phase modulation. Our study is limited to the use of the Discrete Polynomial- Phase Transform (DPT) of Peleg and Friedlander. Our approach is to simplify the problem of parameter estimation from multicomponent signals by isolating them and then performing the estimation on each one separately. The process of isolating components is also shown to be improved by applying superresolution in the computation of the time- frequency representation. We also formulate an approach using the DPT for motion parameter estimation on a signal model for stepped-frequency ISAR returns from a scatterer.

The main difficulty of synthetic aperture radar (SAR)-optical image matching or registration lies in the significant heterogeneous characteristics introduced by the different imaging mechanisms between SAR and optical images. Instead of directly using the raw image pair, transforming the pair into a feature domain, where they have homogeneous feature representation, is believed more effective. Inspired by image segmentation, we develop an end-to-end deep learning model for the SAR-optical matching, based on a siamese U-net with a fast Fourier transform (FFT) correlation layer. First, the siamese U-net with sharing weights extracts the feature maps of the SAR and optical images and projects the heterogeneous images into a homogeneous space. Then, the two feature maps are cross-correlated or normalized cross-correlated by the FFT layer and a similarity heatmap is obtained. Finally, the heatmap is send into a softmax2d classifier to determine the best matching, and thus matching is converted into classification. The nonlinear mapping capability of deep learning can well tackle the intensity variation across the different imaging modals; the encoder–decoder architecture with skip connections in the U-net can take full advantage of the global information and simultaneously preserve the local resolution and position information and thus guarantees high accuracy and robustness; besides, the FFT correlation is helpful for the efficiency improvement and training with large image pairs. Experiments show that the proposed method can achieve a pixel-level matching error.

Synthetic aperture radar imaging at high resolution and highly squint angle is confronted with several difficulties, such as the spatial variance of range cell migration (RCM) and the azimuth-dependent property of high-order terms. In order to address the above-mentioned problems, an improved non-linear chirp scaling algorithm based on keystone transform (KT) and linear range walk correction (LRWC) is proposed. First, KT is applied to correct the second-order RCM in range frequency and azimuth time domain. Then the spatial variance of linear RCM (LRCM) is analysed, and range–azimuth coupling is alleviated through LRWC, in this way, azimuth-variant RCM can be removed by phase multiplication, which avoids the approximate error of RCMC in two-dimensional frequency domain. Taking both the spatial variance of LRCM and the difference of the minimum bistatic slant range caused by LRWC into consideration, high-precision approximation of azimuth-dependent coefficients for azimuth signal are deduced, based on which the Doppler centroid, azimuth FM rate and cubic phase can be equalised by selecting proper perturbation coefficients. The proposed algorithm leads to a large depth of focusing in both range direction and azimuth direction. Simulation results prove the effectiveness of the proposed method.

This paper considers the coherent integration problem for maneuvering target detection and motion parameters estimation, involving range migration (RM) and Doppler frequency migration (DFM) within the coherent pulse interval. A fast non-searching method based on adjacent cross correlation function (ACCF) and Lv's distribution (LVD) is proposed, where the adjacent correlation operation is first employed to remove the RM and reduce the order of DFM. After that, LVD is applied to realize the coherent integration, target detection and parameters estimation. In addition, at the cost of some performance loss, another fast method via ACCF iteratively is also introduced to further reduce the computational complexity and obtain the motion parameters estimation. The proposed two methods are fast in that they can be easily implemented by using complex multiplications, the fast Fourier transform (FFT) and inverse FFT (IFFT). Compared with the existing methods, the presented algorithms can obtain the motion parameters estimation without any searching procedure and can achieve a good balance between the computational cost and the detection ability as well as parameters estimation performance. Finally, several simulation experiments are provided to demonstrate the effectiveness.

Long-time coherent integration can remarkably improve the detection and motion parameter estimation ability of radar for maneuvering targets. Unfortunately, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration (DFM) within the coherent processing interval seriously degrade the target detection and parameter estimation performance. In this regard, a novel coherent integration approach based on frequency autocorrelation function (FAF) and Lv’s distribution (LVD), i.e., FAF–LVD, is proposed in this paper. The QRM is firstly removed by the second-order keystone transform. Then, the FAF with a variable delay is introduced to remove the DFM, followed by the scaled Fourier transform to achieve coherent integration. Finally, the acceleration and velocity are estimated simultaneously by LVD. Analysis demonstrates that FAF–LVD could be efficiently implemented via complex multiplications, the fast Fourier transform (FFT) and inverse FFT. Detailed comparisons with several representative methods indicate that FAF–LVD achieves a better balance among computational complexity, detection ability, and parameter estimation performance. Extensive simulations are presented to validate the effectiveness of FAF–LVD method.

Aiming at the application background of sliding spotlight mode Synthetic Aperture Radar (SAR) imaging processing, this paper builds a System-on-a-Programmable-Chip-based (SoPC-based) sliding spotlight mode SAR imaging verification system, which uses software and hardware collaborative design method to complete algorithm-to-hardware mapping and can quickly and truly perform in FPGA or ASIC. Finally, we analyzed the implementation of the imaging prototype system and the imaging results. For the generation of correlation factors, this paper hierarchically decomposes the factor generation operation to realize the time division multiplexing of the operation unit, in order to reduce resource consumption. At the same time, a variable point Fast Fourier Transformation (FFT) processor based on a variable radix-2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> multiplexing butterfly unit is designed and implemented. Combining these two parts with other modules enables the entire sliding spotlight mode imaging process. On the basis of keeping the error of the result small, the overall resource consumption is greatly reduced. The 1024~32768 point FFT is implemented by the top-level configurable method, and the operation delay is reduced by more than 20% compared with the Xilinx FFT IP core. The final imaging time is reduced to seconds, and the imaging results meet the requirements. Subsequent compatibility design for other SAR imaging modes also can be achieved.

A novel autofocus method for synthetic aperture radar (SAR) image is studied. Based on a quadratic model for the phase error within each sub-area (narrow strip × sub-aperture) after a wide range swath is subdivided into narrow range strips and long azimuth aperture into sub-apertures, an objective function for estimation of the error is derived through the principle of minimum entropy. There is only one unknown variable in the function. With the Chebyshev approximation, the function is approximated as a polynomial, and the unknown is then solved using the method of series reversion. Curve-fitting methods are applied to estimate phase error for an entire scene of the full-swath by full-aperture. Through simulations, the proposed method is applied to restore the defocused SAR imagery that is well focused. The restored and original images are almost identical qualitatively and quantitatively. Next, the method is implemented into an existing SAR data processor. Two sets of SAR raw data at X- and Ku-bands are processed and two images are formed. Well-focused and high-resolution images from plain and rugged terrain are obtained even without the use of ancillary attitude data of the airborne SAR platform. Thus, the studied method is verified.

For the Inverse Synthetic Aperture Radar (ISAR) imaging, the ISAR image obtained by the Range-Doppler (RD) or time-frequency analysis methods can not display the target's real shape due to its azimuth relating to the target Doppler frequency, thus the cross-range scaling is required for ISAR image. In this paper, a fast cross-range scaling method for ISAR is proposed to estimate the Rotational Angular Velocity (RAV). Firstly, the proposed method utilizes efficient Pseudo Polar Fast Fourier Transform (PPFFT) to transform the rotational motion of two ISAR images from two different instant time into translation in the polar angle direction. Then, a new cost function called integrated correction is defined to obtain the RAV coarse estimation. Finally, the optimal RAV can be estimated using the Bisection method to realize the cross-range scaling. Compared with the available algorithms, the proposed method avoids the problems of precision loss and high computational complexity caused by interpolation operation. The results of computer simulation and real data experiments are provided to demonstrate the validity of the proposed method.

The cross-range scaling is quite important for inverse synthetic aperture radar (ISAR) because the cross-range resolution cannot be acquired directly for non-cooperative targets. Its essence is to estimate the relative rotating velocity of the target to radar and calculate the cross-range resolution. Since the rotating velocity is involved in the slow-time domain of the signals and relative with the frequency-modulation rate, the problem of cross-range scaling can be considered as the task to estimate the frequency-modulation rate of the slow-time signals. Considering the common methods of this kind are always limited by the resolution of Fourier transform and cannot get good performances in the situations of slowly rotating targets, a novel method of scaling based on the iterative adaptive approach and the discrete polynomial-phase transform is proposed in this paper. The results of the simulated and real-measured data experiments verify the effectiveness of this method on scaling the ISAR images of slowly rotating targets.