Second-order Keystone Transform Research Articles

Spaceborne distributed aperture radar maneuvering target detection approach with space-time 2D hybrid integration technique

Moving target detection in spaceborne distributed aperture radar (SBDAR) is a challenging task in civilian and military fields. The common issues are that the current methods suffer from the large range cell migration (RCM) and time-varying Doppler frequency modulation (DFM) problems in space-time two-dimensional (2D) domain, which is caused by distributed aperture radar detection configuration and the maneuvering characteristics of moving targets. To address these issues, a novel SBDAR moving target detection approach via space–time hybrid integration (STHI) is proposed in this paper. Compared with single or bistatic radar mode, the utilization of multiple satellites provides an improvement in moving target detection performance, together with the capabilities of localization and parameters estimation. The proposed method mainly includes the following three steps. First, the geometric and signal models of an observed maneuvering target are accurately established in a SBDAR framework, where the space-time 2D RCM and DFM are analyzed. Based on that, the second-order Keystone transform (SKT), a novel range frequency reversal process (NRFRP) and a modified scaled Fourier transform (MSCFT) are developed to correct the RCM and DFM, achieving an efficient time dimension coherent integration for maneuvering target. After that, by dividing the radar detection area, the spatial projection method is adopted to integrate the moving target energy in space dimension. Finally, the simulation results verify the effectiveness and advantages of the proposed method.

Radar fast long-time coherent integration via TR-SKT and robust sparse FRFT

Long-time coherent integration (LTCI) is an effective way for radar maneuvering target detection, but it faces the problem of a large number of search parameters and large amount of calculation. Realizing the simultaneous compensation of the range and Doppler migrations in complex clutter background, and at the same time improving the calculation efficiency has become an urgent problem to be solved. The sparse transformation theory is introduced to LTCI in this paper, and a non-parametric searching sparse LTCI (SLTCI) based maneuvering target detection method is proposed. This method performs time reversal (TR) and second-order Keystone transform (SKT) in the range frequency & slow-time data to complete high-order range walk compensation, and achieves the coherent integration of maneuvering target across range and Doppler units via the robust sparse fractional Fourier transform (RSFRFT). It can compensate for the nonlinear range migration caused by highorder motion. S-band and X-band radar data measured in sea clutter background are used to verify the detection performance of the proposed method, which can achieve better detection performance of maneuvering targets with less computational burden compared with several popular integration methods.

Integration and Detection of a Moving Target with Multiple Beams Based on Multi-Scale Sliding Windowed Phase Difference and Spatial Projection

Due to the fast scanning speed of the current phased-array radar and the moving characteristics of the target, the moving target usually spans multiple beams during coherent integration time, which results in severe performance loss for target focusing and parameter estimation because of the unknown entry/departure beam time within the coherent period. To solve this issue, a novel focusing and detection method based on the multi-beam phase compensation function (MBPCF), multi-scale sliding windowed phase difference (MSWPD), and spatial projection are proposed in this paper. The proposed method mainly includes the following three steps. First, the geometric and signal models of multiple beam integration with observed moving targets are accurately established where the range migration (RM), Doppler frequency migration (DFM), and beam migration (BM) are analyzed. Based on that, the BM is eliminated by the MBPCF, the second-order keystone transform (SOKT) is utilized to mitigate the RM, and then, a new MSWPD operation is developed to estimate the target’s entry/departure beam time, which realizes well-focusing output within the beam. After that, by dividing the radar detection area, the spatial projection (SP) method is adopted to obtain multiple-beams joint integration, and thus, improved detection performance can be obtained. Numerical experiments are carried out to evaluate the performance of the proposed method. The results show that the proposed method could achieve superior focusing and detection performances.

A Coherent Integration and Parameter Estimation Method for Constant Radial Acceleration Weak Target via SOKT-IAR-LVD

In order to enhance the detection and parameter estimation capacity to the maneuvering target with complex motions, a low complexity coherent integration and parameter estimation method named SOKT-IAR-LVD is proposed in this paper. In SOKT-IAR-LVD, first, the second-order keystone transform (SOKT) is utilized to eliminate the range curvature induced by target acceleration. Second, improved axis rotation (IAR) is applied to regulate the linear range migration by rotating the fast time axis and the target envelope is aligned along the slow time axis with a quadratic phase characteristic. At last, the target signal is coherently integrated via the Lv’s Distribution (LVD) transform. The target motion parameters, including range, velocity, and acceleration, are estimated by the IAR and LVD results. The integration gain and computational load of SOKT-IAR-LVD are analyzed. Without needing to estimate the Doppler ambiguity number and target acceleration, the computational burden of SOKT-IAR-LVD is three orders of magnitude lower than that of the Radon-Lv’s Distribution (RLVD) method. Simulation results demonstrate that the detection performance of SOKT-IAR-LVD is almost the same as that of RLVD and that the required input SNR of SOKT-IAR-LVD is 17.4 dB lower than that of SOKT–Radon Fourier transform (SOKT-RFT) when the detection threshold is set to 12 dB.

Two-Dimensional Frequency Domain Second-Order Keystone Transform for Weak Target Integration Detection Based on Bistatic Radar Configuration

Two-Dimensional Frequency Domain Second-Order Keystone Transform for Weak Target Integration Detection Based on Bistatic Radar Configuration

Long-Time Coherent Integration for Maneuvering Target Based on Second-Order Keystone Transform and Lv’s Distribution

Maneuvering target detection is a challenging task for radar due to its maneuverability and weak energy. Long-term coherent integration can remarkably increase signal energy to improve the target detection ability. Unfortunately, high velocity and acceleration of the target will produce linear range migration (LRM), quadratic range migration (QRM), and Doppler frequency migration (DFM), which seriously degrades the coherent integration gain and further deteriorates target detection performance. To solve this problem, a method based on second-order Keystone transform (SKT) and Lv’s distribution (LVD), also combined with Radon Fourier transform (RFT), i.e., SKTLVD, is proposed in this paper. The LRM is firstly corrected by using RFT. Then, the SKT is employed to remove QRM. Finally, LVD is utilized to eliminate the DFM and achieve coherent integration. Compared with several representative methods, the SKTLVD consumes low computation and obtains good target detection performance, striking a balance between computational cost and target detection ability. Numerical simulations and real measured radar data demonstrate that the proposed method can obtain considerable coherent integral gain under acceptable computational complexity.

An Improved Ground Moving Target Parameter Estimation and Imaging Method for Multichannel High Resolution SAR

With increasing demands from both military and civilian applications, ground moving-target imaging is becoming one of the important research topics for high-resolution SAR systems. However, the existing moving-target imaging methods are not suitable for high-resolution SAR because of their low parameter estimation accuracy and high computational complexity. To solve the problem, an improved ground moving-target parameter estimation and imaging method is proposed. First, the third-order phase model of the uniformly accelerated target signal is constructed, and the Hough transform and the second-order Keystone transform (SOKT) are used to correct the range cell migration into one range cell to achieve target coherent accumulation. Secondly, a delayed cross-correlation function (DCCF) is constructed to reduce the order of the range migration phase response in the slow time domain, and the coupling degree between the cross-correlation peak position and the range migration is reduced, so that the obtained DCCF has a higher gain, which ensures the accuracy of parameter estimation. Parameter estimation is simplified to peak detection by the Shift-And-Correlation (SAC) algorithm and two-dimensional Fourier transform (2D-FFT), avoiding parameter search. Compared with the existing methods, the proposed method has better focusing effect and lower computational complexity. Finally, simulation and measured data are given to verify the effectiveness of the proposed method.

An adaptive non‐searching method for long‐time coherent integration of manoeuvring target with multiple motion models

Long-time coherent integration (LTCI) is one of the effective methods to enhance the radar detection capability of manoeuvring targets. In most existing studies, the target is assumed to move at a consistent model during the total integration time. In modern times, this point is not always true. The modern targets often possess strong manoeuvring penetration capability, which enables the presence of multiple motion models (i.e. the target's motion model is changing during the total integration time) with a high possibility, especially when the coherent integration time is long. This factor would reduce the performance of the existing LTCI methods. In this study, an adaptive non-searching method, based on the adjacent cross correlation function (ACCF)/modified ACCF (MACCF), Keystone transform (KT)/second-order KT, Hough transform and fractional Fourier transform, is proposed for LTCI of a manoeuvring target with multiple motion models. First, the motion model change points are identified. Subsequently, the adaptive case prejudgement and parameters estimation for different motion stages are completed. Finally, the LTCI of the manoeuvring target with multiple motion models is realised after motion compensation. Simulation results demonstrate the effectiveness of the proposed method.

Refocusing of Ground Moving Targets with Doppler Ambiguity Using Keystone Transform and Modified Second-Order Keystone Transform for Synthetic Aperture Radar

Ground moving targets will typically be defocused because of the range migration (RM) and Doppler frequency migration (DFM) caused by the unknown relative motions between the platform of synthetic aperture radar (SAR) and the ground moving targets. The received signal of the ground moving target easily exhibits the Doppler ambiguity, and the Doppler ambiguity leads to the refocusing difficulty of ground moving targets. To address these problems, a SAR refocusing method of ground moving targets with Doppler ambiguity based on modified second-order keystone transform (MSOKT) and keystone transform (KT) is presented in this paper. Firstly, the second-order phase is separated by the time reversing process. Secondly, MSOKT is performed to compensate the range curvature migration and DFM, and then the coefficient of the second-order phase is estimated. Finally, a well-refocused result of the moving target is achieved after KT and the estimated Doppler ambiguity number are used to eliminate residual range walk migration. The proposed method can accurately remove RM and DFM and effectively focus the moving targets without residual correction errors. Moreover, the effects of Doppler ambiguity (including Doppler center blur and spectrum split) and blind speed sidelobe are further avoided. On the basis of the analysis of cross-term for the multiple target case, the identification strategy of spurious peak of cross-term is proposed. Additionally, the developed method can be sped up by nonuniform fast Fourier transform without the interpolation operation. The effectiveness of the proposed method is verified by both airborne and spaceborne real data processing results.

Robust detection and motion parameter estimation for weak maneuvering target in the alpha-stable noise environment

This paper focuses on the weak maneuvering target detection problem in the alpha-stable noise (ASN) environment. A novel coherent integration framework is proposed, where the range migration (RM) is first removed via approximate linear methods to make the noise distribution character remain unchanged, and then the ASN suppression, Doppler frequency migration (DFM) compensation, and coherent integration are simultaneously achieved in the proper transform domain. Based on this framework, a robust detection method is developed. First, the second-order keystone transform (SoKT) is employed to correct the range curve (RC) induced by the target's acceleration. Thereafter, the centroid axis rotation (CAR) is presented to remove the residual range walk (RW) by rotating the slow time axis parallel to the RW line in the fast-time and slow-time domain. Finally, the phase fractional lower-order Lv's distribution (PFLOLVD) is proposed to compensate the DFM and realize the energy accumulation of the target in the ASN environment. Furthermore, the performance of proposed algorithm in aspects of coherent integration time, computational complexity, and multiple targets detection are analyzed in detail. Compared with the existing coherent integration detection methods, the proposed method is both robust for ASN environments and superior in the detection performance.

Noise-Resistant Estimation Algorithm for TDOA, FDOA and Differential Doppler Rate in Passive Sensing

This paper addresses the joint time difference of arrival (TDOA), frequency difference of arrival (FDOA) and differential Doppler rate estimation problem for high-speed maneuvering targets in passive location systems, involving linear range migration (LRM), quadratic range migration (QRM) and linear Doppler frequency migration (LDFM) within observation time. A noise-resistant estimation algorithm based on second-order keystone transform (SKT) and non-uniform fast Fourier transform (NUFFT) is proposed. After QRM correction via SKT, a phase compensation function is constructed to eliminate LRM and estimate the FDOA. Then, NUFFT is used to remove LDFM and realize the joint estimation of TDOA and differential Doppler rate. Comparisons with several relatively new algorithms indicate that the proposed algorithm can obtain a good trade-off between computational cost and estimation performance. Extensive numerical examples, analysis of computational complexity and estimation performance can validate the effectiveness of the proposed method.

Ground Maneuvering Targets Imaging for Synthetic Aperture Radar Based on Second-Order Keystone Transform and High-Order Motion Parameter Estimation

With the developments of the synthetic aperture radar (SAR) system, the long dwell time provides high resolution but at the same time it produces large range migration (RM) and Doppler frequency migration, which brings a new challenge for ground moving target imaging. To address those problems, a ground moving target refocusing method based on a novel parameter estimation algorithm, namely second-order Keystone transform (SOKT)-Radon-cubic phase function-Fourier transform (RCFT), is proposed in this work. First, the SOKT is applied to correct the range curvature. After that, the Hough transform is utilized to estimate the trajectory slope for the range walk correction and the across-track velocity acquirement. Finally, a novel coherently integrated parameter estimation method, termed as RCFT, is developed in this work to transform the azimuth quadratic frequency-modulated signal into a peak point in two-dimensional (2-D) time-frequency plane. In the process, the second- and third-order motion parameters are simultaneously obtained, which eliminates the error propagation effect. Due to 2-D coherent integration realization and its bilinear function feature, the proposed RCFT method is capable of obtaining accurate parameter estimates in low signal-to-noise ratio scenario with a relatively low computational burden. Compared with the conventional SAR imaging methods using the second-order phase model, the proposed method produces better imaging quality since the third-order Doppler frequency migration is effectively eliminated. The performance of the proposed method is demonstrated by both the simulated and real data.

A fast non-searching algorithm for radar maneuvering target detection

The detection of maneuvering targets is a challenging work for radar system. During a long integration time, the target’s complex motion will cause severe range migration and Doppler frequency migration, which greatly degrade the energy integration performance. In order to obtain a well-focused result of the maneuvering target, this paper proposes a novel and fast algorithm without any parameter searching process. In our algorithm, a parameter separation (PS) operation is conducted to isolate the target’s acceleration from other motion parameters. Then, the second-order keystone transform (SOKT) is utilized to correct range curvature and relocate the target’s energy into one range cell. Lastly, the target’s energy is integrated along the slow time axis via performing the non-uniform sparse Fourier transform (NUSFT), which is a fast implementation of Fourier transform (FT) for the input signal with unequally sampled points and frequency domain sparse representation. According to the simulation results, the proposed PS–SOKT–NUSFT method can realize multiple targets detection due to its good ability to suppress cross terms. In addition, the runtime of PS–SOKT–NUSFT (106.23 s) is much shorter than the PS–acceleration search (AS) method (2168.67 s).

A Doppler Ambiguity Tolerated Method for Radar Sensor Maneuvering Target Focusing and Detection

Maneuvering target detection is a challenging task for modern radar sensor applications. Range migration (RM) and Doppler frequency migration (DFM) lead to serious coherent integration loss, which affects the performance of maneuvering target focusing and detection. Moreover, Doppler ambiguity can easily appear due to the limitation of pulse repetition frequency; thus, maneuvering targets become difficult to focus correctly. In this paper, a new Doppler ambiguity tolerated method is proposed to focus and detect maneuvering targets with jerk motions. First, the order of RM and DFM is reduced by multiplying the signals before and after the time reversal operation. Second, generalized modified keystone transform is proposed to eliminate residual RM and DFM simultaneously. Subsequently, a well-focused result is obtained. In comparison with the traditional keystone transform (KT) or second-order KT based methods, the proposed method works well in situations wherein Doppler center blur and spectrum ambiguity appear. Moreover, the computational complexity of the proposed method is remarkably reduced in comparison with that of multidimensional parameter searching methods. These advantages show that the proposed method achieves balance between detection performance and computational load. The experiment results validate the effectiveness of the proposed method.

Focusing High-Resolution High Forward-Looking Bistatic SAR With Nonequal Platform Velocities Based on Keystone Transform and Modified Nonlinear Chirp Scaling Algorithm

This paper presents a focusing solution for high-resolution high forward-looking bistatic synthetic aperture radar with nonequal platform velocities (NPV-BFSAR). In NPV-BFSAR, due to the high-resolution SAR and high forward-looking angle, range cell migration, and two-dimensional spatial variation are more serious. To solve this problem, a modified imaging algorithm based on second-order keystone transform (KT) and modified nonlinear chirp scaling (NLCS) method are proposed. The second-order KT method can correct the linear range cell migration and reduce the strong coupling between azimuth and range. The proposed modified azimuth NLCS algorithm is more accurate than traditional NLCS algorithm on eliminating the variation of azimuth reference function that can improve the focus quality of edge targets. Finally, some simulation results confirm the efficiency of the proposed algorithm.

Fast non-searching method for ground moving target refocusing and motion parameters estimation

Ground moving targets may be smeared in a synthetic aperture radar (SAR) image due to the range migration, Doppler ambiguity and azimuth spectrum split caused by target unknown motion parameters. To handle these problems, we propose a fast non-searching method for maneuvering target refocusing and motion parameters estimation in this paper. First, the azimuth-deramp is conducted, which is capable of eliminating the azimuth spectrum splitting. In the sequel, the second-order keystone transform (SOKT) based on the scaling principle is applied to further correct the residual range curvature. Then, the phase difference (PD) is performed to eliminate the range walk and estimate the motion parameters, which does not require the prior knowledge of Doppler ambiguity number. Finally, the moving target can be well focused with the estimated parameters. This method has high computational efficiency and improved parameter estimation accuracy. Both simulated and real data are processed to demonstrate the effectiveness of the proposed method.

Fast coherent integration for maneuvering target with high-order range migration via TRT-SKT-LVD

This paper addresses the coherent integration problem for detecting a maneuvering target with high-order range migration (RM), where the velocity, acceleration, and jerk result in, respectively, the first-order range migration (FRM), second-order range migration (SRM), and third-order range migration (TRM) within the coherent pulse interval. A fast coherent integration method based on time reversing transform (TRT), second-order keystone transform (SKT) and Lv’s distribution (LVD), i.e., TRT-SKT-LVD, is proposed. In this method, TRT operation is first presented to remove the TRM and FRM simultaneously. After that, the SKT is employed to correct the remaining SRM and then the coherent accumulation could be obtained via LVD. The proposed algorithm is simple and fast in that it can be easily implemented by using complex multiplications, the fast Fourier transform (FFT), and inverse FFT (IFFT). Compared with the existing methods, the presented method can realize the coherent integration without any searching procedure and can achieve a good balance between the computational cost and detection ability. Both simulated and real data demonstrate the effectiveness of the proposed algorithm.

Parameter estimation for maneuvering targets with complex motion via scaled double-autocorrelation transform

In this paper, a novel parameter estimation method is proposed for maneuvering targets with complex motion. In the proposed method, the second-order keystone transform (SOKT) and modified range cell migration correction (RCMC)/integration are jointly applied to overcome the velocity ambiguity and eliminate the envelope migration. Then, since the azimuth echoes of maneuvering targets with complex motion can be modeled as cubic phase (CP) signals after motion compensation, a new transform, namely, scaled double-autocorrelation transform (SCDCT), is defined. This transform can be essentially interpreted as the two-dimensional (2-D) Fourier transform (FT) of a scaled parametric instantaneous double-autocorrelation (PIDAC) function. By employing this derived transform, the estimated chirp rates and derivative of chirp rates of CP signals can be obtained simultaneously without searching operation and thus the computational burden can be reduced significantly. Furthermore, the characteristics of cross terms and anti-noise performance of SCDCT are theoretically analyzed. Compared with three other popular methods, product high-order match phase transform, TC-dechirp Clean and modified discrete chirp Fourier transform, the proposed SCDCT-based method is more computationally efficient and has better estimation performance in low signal-to-noise ratio (SNR) circumstance. Simulation results verify the effectiveness of the proposed SCDCT-based method.

An Integration Algorithm for Bistatic Radar Weak Target Detection

The bistatic radar weak target detection problem is considered in this paper. An effective way to detect weak target is the long time integration. However, range migration (RM) will occur due to the high speed. Without knowing the target motion parameters, a long time integration algorithm for bistatic radar is proposed in this paper. Firstly, the algorithm utilizes second-order keystone transform (SKT) to remove range curvature. Then the quadratic phase term is compensated by the estimated acceleration. After that, SKT is used once more and the Doppler ambiguity phase term compensation is performed. At last, the target energy is integrated via FT. Simulations are provided to show the validity of the proposed algorithm in the end.

A Doppler Ambiguity Tolerated Algorithm for Airborne SAR Ground Moving Target Imaging and Motion Parameters Estimation

This letter proposes an algorithm for airborne synthetic aperture radar (SAR) ground moving target imaging (GMTIm) and motion parameters estimation (MPE), which is applicable in situations whether the Doppler ambiguity occurs or not. To derive the algorithm, the general expression for the received signal after range compression is deduced first, in which the useless exponential term induced by the possible Doppler ambiguity is omitted. Then, the second-order keystone transform (SOKT) is used to correct the range curvature. After the SOKT, the Radon transform is employed to estimate the slope of the target trajectory, and the range walk correction follows. In the following, the scaled Fourier transform and the dechirp technique are utilized to estimate the azimuthal parameters. Finally, the target's motion parameters are obtained by solving equations according to the trajectory slope and the estimated azimuthal parameters, with which the target is focused through azimuth matched filtering. Both simulated and real airborne SAR data are processed to validate the effectiveness of the proposed algorithm.