Linear Range Migration Research Articles

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.

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.

A Novel Coherent Integration Algorithm for Maneuvering Target Detection Based on Symmetric Instantaneous Autocorrelation Function

Detection and parameter estimation of maneuvering targets having a jerking motion are some of the challenging problems for modern radar systems. Such targets usually introduce range migration (RM) and Doppler frequency migration (DFM) problems leading to serious performance degradation in detection. To address these problems, a novel coherent integration (CI) algorithm is proposed based on a new symmetric instantaneous autocorrelation function (NSIAF), which can be utilized to reduce the order on the slow time and to eliminate the linear range migration (LRM) first. Then, the jerk and acceleration of the target are estimated after applying the keystone transform (KT) and the scaled Fourier transform (SFT); both of these are then used to construct the reference function for matched filtering. Finally, CI and target detection can be accomplished by the scaled inverse Fourier transform (SCIFT) after matched filtering. Both simulation data (this work) and practical radar experiment data (data set of others) were processed to validate the proposed algorithm. Compared with other representative algorithms, our algorithm can achieve a good balance between computational complexity and detection performance.

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.

Coherent detection and parameter estimation for ground moving target based on MLRT-IDCFT

In a synthetic aperture radar system, long-time coherent integration for ground moving targets suffers from the complex range migrations (RMs) and Doppler frequency migration (DFM), which lead to a serious degradation of the target detection. To address these problems and obtain the motion parameters of the moving target, a new algorithm based on modified location rotation transform (MLRT) and improved discrete chirp Fourier transform (IDCFT), i.e., MLRT-IDCFT, is proposed in this paper. More concretely, the matched filtering function is first utilized to remove the range curvature (RC) for improving the computational efficiency. After that, the MLRT-IDCFT corrects the residual linear range migration (LRM) through rotating coordinate locations of the echo trajectory and achieves the coherent integration as well as the motion parameter estimation via the IDCFT. The IDCFT exploits the prior information to adaptively adjust the parameter estimation range, which not only improves the parameter resolution but also guarantees the validity of the parameter estimation. Due to the linear transform property, the proposed method can work well under the low signal-to-noise ratio (SNR) environment. Additionally, it has a relatively low computational complexity since the exhaustive searching for acceleration is avoided. Several simulations are provided to demonstrate the effectiveness of the proposed algorithm.

Long-time coherent accumulation algorithms for reflected signal with non-zero higher derivatives of the range to radar target in the spectral domain

The purpose of the article is to present computationally economical algorithms for long-term coherent accumulation of signals reflected from a point target with compensation for range and frequency migration and accumulation of signals in the spectral region. The algorithms include intra-period processing with simultaneous correction of range and frequency migration and inter-period processing with coherent accumulation of signals at the output of intra-period processing. In the first variant of the algorithm, intra-period processing is implemented by calculating the spectra of the received signals in each repetition period, multiplying the samples of the spectra by the samples of the amplitude-phase-frequency characteristic of the matched filter of a single signal and correcting phase coefficients determined by the number of the repetition period and the values of the range derivatives, and the inverse Fourier transform of the transformed spectra. The difference between the second version of the algorithm at the stage of intraperiod processing is the correction of only the quadratic and subsequent components of the range and frequency migration and the use of the keystone transformation, which eliminates the linear range migration. Coherent accumulation for both variants is realized due to the fast Fourier transform of the signal samples over the repetition periods for all samples over the range. The concept of “rough speed resolutionˮ is introduced, which determines the arrangement of channels when compensating for range migration. The uncertainty function in the coordinates “velocity–acceleration” is obtained. The equivalence of the two variants of the algorithm is shown and estimates for the required number of receiver channels are given. The simulation results confirming the operability of the proposed algorithms are presented.

Ground moving target indication and parameter estimation algorithm using deramp space-time adaptive processing

Deramp space-time adaptive processing (Deramp-STAP) algorithm has been validated in its effectiveness in reducing the required channels to enable ground moving target indication (GMTI) for multi-channel synthetic aperture radar (SAR) systems. However, the parameter estimation for the moving target, including the critical radial velocity, is not accurate enough, and the radial velocity is always approximated by the equivalent velocity obtained by the Deramp operation. For the indication and imaging of ground moving targets, the accurate estimation of the radial velocity is of importance to improve the signal-clutter-noise-ratio of STAP and estimate the initial azimuth position of the moving target. A method for GMTI and the corresponding parameter estimation using Deramp-STAP is proposed. Compared with the traditional Deramp-STAP algorithms, the proposed algorithm utilizes the equivalent velocity estimated by Radon transform to remove the linear range migration before STAP and figure out where the moving target is located in the azimuth frequency domain. To estimate the radial velocity more accurately, the fast Fourier transform along the spatial direction is performed on the pixel where the moving target is located in the azimuth frequency domain after the Deramp operation, and then the radial velocity can be obtained through the spatial spectrum analysis. Finally, the estimated radial velocity is applied to construct the azimuth compression function for the moving target imaging, and then the initial azimuth position can be estimated. Several simulation experiments have been implemented to validate the effectiveness of the proposed algorithm.

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.

Long-Time Coherent Integration for Maneuvering Target Detection Based on ITRT-MRFT

Long-time coherent integration can effectively improve the radar detection ability of a maneuvering target. However, with the increasing of integration time, radial velocity and radial acceleration of the moving target result in linear range migration (LRM), range curvature (RC), and Doppler frequency migration (DFM) of the received signal. These may degrade detection performance seriously. To solve these problems, an efficient coherent accumulation method based on improved time reversal transform (ITRT) and modified radon Fourier transform (MRFT) is proposed in this paper. Different from conventional methods, this approach firstly eliminates the acceleration effects by ITRT. It can remove RC and DFM simultaneously via multiplying its slow-time reversed conjugate data in range-frequency and azimuth-time domains. Then by employing a new Doppler filter bank (DFB), MRFT realizes the echoes spatial temporal decoupling as well as the coherent integration in searching-velocity and Doppler-frequency domains. The major advantages of the proposed method are that RC and DFM can be rectified without parameter estimation, and computational complexity can be optimized by the new FFT-based filter bank. In addition, due to the nonlinearity of ITRT operation, the influence of cross terms of multiple targets on detection performance is also discussed. Several simulations are provided to demonstrate the effectiveness of our approach.

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 method for random pulse repetition interval radar based on non‐uniform keystone transform and non‐uniform fast Fourier transform

In order to achieve weak target detection, the range migration and Doppler frequency spread induced by the target motion within the coherent processing interval should be compensated to focus the target energy in a certain range-Doppler cell. This article proposes a new integration method based on non-uniform Keystone transform and non-uniform fast Fourier transform (NUFFT) for random pulse repetition interval (PRI) radar. In this method, non-uniform Keystone transform is applied to correct the linear range migration. After that, the acceleration is estimated by dechirp process and the Doppler frequency spread is compensated. Finally, the target energy is accumulated coherently via NUFFT. Compared with the random PRI generalised Radon-Fourier transform (RPRI-GRFT) and the moving target detection method for random PRI radar, the proposed algorithm achieves a good balance between the detection performance and the computational cost. Simulation results are provided to demonstrate the effectiveness of the proposed method.

A Fast Coherent Integration Algorithm for Maneuvering Target Detection

This paper investigates the coherent integration problem in the maneuvering target detection. We propose a new coherent integration algorithm based on the short-time Fourier transform (STFT) and the cubic phase function (CPF), i.e., STFT-CPF. First, the STFT is employed to construct a special compensation function for the linear range migration. Then, the CPF is applied to estimate the target’s acceleration and jerk, thereby compensating the linear Doppler frequency migration and the quadratic Doppler frequency migration. After that, the coherent integration can be achieved by the FT. The proposed algorithm involves only 1-D search. It reaches a good balance between the computational cost and detection performance in a certain range of acceleration and jerk. Simulations and real data demonstrate the effectiveness of the proposed algorithm.

Ground-Based Radar Detection for High-Speed Maneuvering Target via Fast Discrete Chirp-Fourier 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.

Refocusing and Motion Parameter Estimation for Ground Moving Targets Based on Improved Axis Rotation-Time Reversal Transform

In this paper, a new algorithm is presented to image ground moving targets and estimate their motion parameters in a synthetic aperture radar system based on improved axis rotation-time reversal transform (IAR-TRT). In this algorithm, the second-order Keystone transform) is applied to correct the range curvature, where the Doppler ambiguity caused by a fast-moving target is considered. Then, residual linear range migration and Doppler frequency migration are eliminated by IAR-TRT, which performs an improved axis rotation transform to correct the range walk and subsequently realizes the coherent integration based on time reversal transform. Finally, a ground moving target is well focused. Additionally, the proposed method has a relatively low computational complexity since the exhaustive searching for Doppler chirp rate estimation is avoided. The effectiveness of the proposed algorithm is validated by both simulated and real data.

A New Nonlinear Chirp Scaling Algorithm for High-Squint High-Resolution SAR Imaging

Among high-squint high-resolution (HSHR) synthetic aperture radar imaging algorithms, nonlinear chirp scaling algorithm (NLCSA) and its extensions, such as extended NLCSA (ENLCSA), have a common drawback in that they all neglect the spatial variations of linear range migration (LRM) and Doppler centroid, and thus, only targets in a specific central slant range plane can be strictly focused. In this letter, we show that by using a new NLCSA, targets can be focused in the ground plane under HSHR conditions. Based on a more accurate 2-D spectrum, the new NLCSA outperforms the ENLCSA by introducing a new range–Doppler domain interpolation to correct residual range migration and a new perturbation function to remove the dependence of Doppler phase on azimuth. The coefficients of the new perturbation function are numerically calculated and then smoothed by polynomial fitting. Though the outputs of the numerical calculation are somewhat unstable at the current stage, it has been demonstrated to perform better than the algorithms neglecting the spatial variations of LRM and Doppler centroid, such as the ENLCSA, by point target simulations.

Detection of constant radial acceleration weak target via IAR-FRFT

A novel coherent integration algorithm, improved axis rotation fractional Fourier transform (IAR-FRFT), is proposed to detect the weak targets with a constant radial acceleration. IAR-FRFT could eliminate the linear range migration and alleviate the nonlinear range migration via an improved axis rotation transform and realize coherent integration via fractional Fourier transform. Numerical experiments verify the performance of IAR-FRFT on four aspects: coherent integration time, coherent integration gain, computational complexity, and multitarget detection.

Axis rotation MTD algorithm for weak target detection

Weak targetʼs range migration often happens for long time integration in radar detection. To compensate for linear range migration and detect weak targets effectively, a novel coherent integration detection algorithm, axis rotation moving target detection (AR-MTD), is proposed. The AR-MTD eliminates the linear range migration by rotating two-dimensional echoes data plane, and realizes coherent integration via moving target detection (MTD). As the targetʼs resident time in a single range cell increases, the integration gain is improved clearly. Numerical experiments are presented to verify the reduction in the computational complexity of AR-MTD by selecting the velocity variation regions. Also, it is shown that the detection probability of AR-MTD is improved by nearly 20% when input signal-to-noise ratio (SNR) is −40 dB.

A novel spaceborne SAR wide-swath imaging approach based on Poisson disk-like nonuniform sampling and compressive sensing

Since the range swath width in the conventional single channel spaceborne synthetic aperture radar (SAR) is restricted by the system parameters, there is a trade-off between the azimuth resolution and the swath width in order to satisfy the Nyquist sampling criterion. In this paper, we propose a novel spaceborne SAR wide-swath imaging scheme based on compressive sensing (CS) for the sparse scene. The proposed method designs a Poisson disk-like nonuniform sampling pattern in the azimuth direction, which meets the demand of wider swath by restricting the smallest time interval between any two azimuth samples, with the conventional sampling pattern preserved in the range direction. By a similar way to the processing procedure of spectral analysis (SPECAN) algorithm, the linear range migration correction (RMC) is realized while carrying out range compression, which can meet the demand for focusing with middle level resolution. To reduce the computation load of CS reconstruction, we propose a novel fast reconstruction algorithm based on nonuniform fast Fourier transform (NUFFT), which greatly reduces the computation complexity from O(2MN) to O(4N logN). Experiment results validate the effectiveness of the proposed methods via the point target simulation and the Radarsat-1 raw data processing in F2 mode.