Quadratic Range Migration Research Articles

Long-time coherent integration algorithm for high-speed maneuvering target detection

Detection of high-speed maneuvering targets along with motion parameters estimation (MPE) are some of the challenging problems for modern radar systems. Such targets usually induce linear range migration (LRM), quadratic range migration (QRM), and Doppler frequency migration (DFM) problems in signal processing, resulting in severe performance degradation, especially when long time integration is needed for weak target detection. We propose an algorithm for coherent integration and MPE by combining the techniques of generalized dechirp (GD) and new axis rotation moving target detection (NAR-MTD), i.e., the GD-NAR-MTD algorithm, to solve the above problems. Specifically, the GD and NAR approaches can not only correct LRM, QRM, and DFM simultaneously with reduced rotation error in coordinate system transformation but also can abate the computational burden via frequency-domain implementation with rounding and complex addressing operations avoided, so the target’s echo energies can be well accumulated by MTD finally. Both simulation and practical radar experiments are conducted to validate the proposed algorithm. At the same time, the results by the other six typical algorithms are compared for demonstrating the superior performance of the proposed algorithm on detection and MPE. In addition, the equivalence between the practical radar experiment and the simulation experiment is analyzed by comparing the induced RMs and DFMs, which shows that the scaled equivalent experiment is persuasive in algorithm validation.

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.

Longtime Coherent Integration Algorithm for High-Speed Maneuvering Target Detection Using Space-Based Bistatic Radar

A space-based bistatic radar system, typically composed of a satellite as transmitter and an aircraft as receiver, has a larger surveillance area, stronger resistance to damage, and more superior early warning capability for high-speed targets when compared with monostatic radar system. However, the echo signal is more challenging to process because of the high speed of both receiver and transmitter. There are two main problems to be solved in space-based bistatic radar signal processing: constructing geometric model in line with the actual situation to derive the echo signal model and improving detection ability on the basis of the longtime coherent integration algorithm. This article addresses the problem of space-based bistatic radar echo signal modeling and coherent integration for detecting high-speed maneuvering targets. A novel algorithm based on generalized second-order keystone transform and modified product cubic phase function (GSKT-MPCPF) is proposed. First, the bistatic radar system model is constructed and the signal scattered from the moving target is derived. Aiming at seeking a general algorithm which is suitable for space-based bistatic radar system, the GSKT-MPCPF is presented to correct the linear range migration (LRM), the quadratic range migration (QRM), and the Doppler frequency migration (DFM), and estimate the motion parameters of targets simultaneously. The simulations of mono-target and multitargets validate the proposed method. Furthermore, we perform comparisons with several relative algorithms and results show that the proposed algorithm has superior performance.

Efficient coherent detection of maneuvering targets based on location rotation transform and non-uniform fast Fourier transform

Long-term coherent integration can remarkably improve the ability of detection and motion parameter estimation of radar for maneuvering targets. However, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration within the coherent processing interval seriously degrade the detection and estimation performance. Therefore, an efficient and noise-resistant coherent integration method based on location rotation transform (LRT) and non-uniform fast Fourier transform (NuFFT) is proposed. QRM is corrected by the second-order keystone transform. Using the relationship between the rotation angle and Doppler frequency, a novel phase compensation function is constructed. Motion parameters can be rapidly estimated by LRT and NuFFT. Compared with several representative algorithms, the proposed method achieves a nearly ideal detection performance with low computational cost. Finally, experiments based on measured radar data are conducted to verify the proposed algorithm.

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.

Coherent Detection and Parameter Estimation for Radar High-Speed Maneuvering Target Based on FAF–LVD

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.

Coherent Integration for Radar High-Speed Maneuvering Target Based on Frequency-Domain Second-Order Phase Difference

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.

Radar maneuvering target detection based on two steps scaling and fractional Fourier transform

• The problems of quadratic range migration and Doppler frequency migration for the maneuvering target are addressed. • A method based on TSS-FrFT is proposed to achieve the coherent integration and it has superior detection performance and low computational complexity. • The acceleration matched filter is presented to remove the DFRC caused by the sudden change of targets acceleration. This paper considers the detection problem of radar maneuvering target with the range migration (RM) and Doppler frequency migration (DFM) and proposes an coherent integration method based on two steps scaling and fractional Fourier transform, i.e., TSS-FrFT. To be specific, this method corrects the quadratic RM (QRM) and DFM based on FrFT and a scaling processing of the rotation angle firstly. Then, it eliminates the coupling between the range frequency variable and FrFT domain (FrFD) variable via a second scaling processing. In the end, the coherent integration is achieved by the inverse Fourier transform (IFT) with respect to the range frequency variable. Compared with the existing methods, the proposed TSS-FrFT method has superior detection performance and low computational complexity. Moreover, considering the sudden change of the target acceleration within the coherent integration interval, this paper also presents an acceleration matched filter (AMF) to remove the Doppler frequency rate change (DFRC) caused by this acceleration change. Computer simulation results are also given to demonstrate the effectiveness of the proposed method from different aspects, i.e., computational complexity, coherent integration for a single target and multiple targets and detection performance for a uniform acceleration and non-uniform accelerations.

New Approach for SAR Imaging of Ground Moving Targets Based on a Keystone Transform

We propose here a new approach for synthetic aperture radar (SAR) imaging of ground moving targets. The unique characteristic of this approach is that range curvature (i.e., quadratic range migration) can be corrected by a simple processing step. A keystone transform is used to correct range walk (i.e., linear range migration) for all targets without knowing their velocities, and the range curvature is corrected in the range-Doppler domain. The advantage of this approach is that it is simple to implement and can correct range curvature for all targets in one processing step, so that it is computationally efficient. Simulation and experimental SAR data processing results are presented to demonstrate the validity of the proposed approach.

New applications of nonlinear chirp scaling in SAR data processing

New applications of nonlinear chirp scaling (NLCS) have been found in processing monostatic and bistatic SAR data acquired in the strip-map mode. When the effects in impulse response broadenings due to quadratic range migration are negligible for short radar wavelengths, a time domain range cell migration correction (RCMC) can be applied. After the correction, the FM rates of targets confined in a range gate will differ from each other. A nonlinear chirp perturbation function can be applied to each range gate to equalize the targets' FM rates before azimuth compression. This algorithm is analyzed in the paper and is supported by point target simulation experiments.

SAR imaging of moving targets

A method of forming synthetic aperture radar (SAR) images of moving targets without using any specific knowledge of the target motion is presented. The new method uses a unique processing kernel that involves a one-dimensional interpolation of the deramped phase history which we call keystone formatting. This preprocessing simultaneously eliminates the effects of linear range migration for all moving targets regardless of their unknown velocity. Step two of the moving target imaging technique involves a two-dimensional focusing of the movers to remove residual quadratic range migration errors. The third and last step removes cubic and higher order defocusing terms. This imaging technique is demonstrated using SAR data collected as part of DARPA's Moving Target Exploitation (MTE) program.