Doppler Frequency Migration Research Articles

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).

Coarse-to-fine coherent integration method for radar maneuvering target with complex motion

In recent years, target detection has drawn increasing attention in the field of radar signal processing. We consider the problem of coherent integration for detecting a highly maneuvering target with complex motion, involving range migration (RM), linear Doppler frequency migration, and quadratic Doppler frequency migration within the coherent interval. Owing to the different sensitivity of the envelope and phase to the target motion, the parametric and nonparametric models are, respectively, established. A coarse-to-fine integration algorithm is correspondingly proposed. Specifically, the keystone transform and fold factor searching are first utilized to remove the parametric RM and to achieve coarse integration. Then, the embedded phase gradient autofocus is applied to estimate the nonparametric nonlinear Doppler phase and realize refined integration. Compared with several representative algorithms, the proposed method could achieve a good trade-off between computational complexity and detection performance. Moreover, this method can be easily extended to detect a high-order maneuvering target. Finally, both simulations and real data experiments are presented to demonstrate the effectiveness of the proposed method.

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.

Fast long‐time coherent integration algorithm for detecting manoeuvring targets with high‐order motion parameters based on GKT and ISCPF

This study deals with the efficient correction of range migration (RM) and Doppler frequency migration (DFM) for long-time coherent integration in detecting manoeuvring targets with complex motions. A fast long-time coherent integration algorithm based on generalised keystone transform (GKT) and integrating smoothed cubic phase function (ISCPF) is proposed. In particular, GKT and blind velocity fold factor searching is performed to correct the RM. ISCPF is proposed to estimate the acceleration and jerk for correcting the DFM. Consequently, the focus of the target energy is improved. Compared with the algorithm based on generalised Radon Fourier transform, the proposed method achieves a good trade-off between the computational complexity and detection ability because the motion parameters are estimated via locating the peak of a univariate function instead of multi-dimensional searching. Furthermore, the proposed method has better performance compared with several methods based on higher-order ambiguity function and cubic phase function for multiple targets since ISCPF can effectively suppress the cross terms caused by multiple targets. Simulation results are provided to validate the effectiveness of the proposed method.

Ground moving target focusing and motion parameter estimation method via MSOKT for synthetic aperture radar

In this study, a ground moving target focusing and motion parameter estimation method based on modified second-order keystone transform (MSOKT) have been proposed for a synthetic aperture radar. Firstly, a cross-track velocity matching compensation function is derived to remove range walk migration and estimate the cross-track velocity of the moving target. Secondly, an MSOKT is proposed to remove the range curvature and Doppler frequency migration simultaneously. Lastly, a well-focused result of the moving target is obtained, and the motion parameters of the moving target are estimated. Compared with the traditional KT-based method, the proposed method works well in situations where Doppler centre blur and Doppler spectrum ambiguity are present. The computational complexity of the proposed method is considerably lower than that of the traditional optimum method, such as Radon-Lv's distribution. Simulation and real data processing results validate the effectiveness of the proposed method.

A new coherent integration method for weak maneuvering target with jerk motion

In radar systems, prolonging the integration time helps to improve the detection and estimation performance of weak target. However, in a long integration time, target's high-order motion is non-ignorable, which causes high-order range migration (RM) and Doppler frequency migration (DFM) problems. The RM and DFM defocus the integration result and lead to detection and estimation performance loss. In this paper, a new coherent integration method is proposed for maneuvering radar target with jerk motion. First, we define a new cross correlation function basing on non-uniformly resampling technique. By using this function, we eliminate the range migration (RM) and Doppler frequency migration (DFM) caused by target's velocity and acceleration. Then, matched filtering process is performed to compensate the phase error caused by target's jerk motion. Finally, the integration is achieved by summing signal data in different range frequency cells and performing a two-dimensional fast Fourier transform (FFT). The proposed method is applicable for low signal-to-noise ratio (SNR) environment. Compared with the GRFT algorithm, the proposed method has a close integration performance and a lower computational complexity. The effectiveness is validated by simulations and real-data processing results.

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.

Long-Time Coherent Integration Algorithm for Radar Maneuvering Weak Target With Acceleration Rate

In this paper, we propose a long-time coherent integration method for a maneuvering target with the first-, second-, and third-order range migrations, and the complex Doppler frequency migration. In this method, after range compression, the echo signal is first transformed into the range-frequency and Doppler domain based on series reversion, and then an azimuth matched filtering procedure is implemented in the 2-D frequency domain. It can eliminate the coupling effects between range and azimuth jointly caused by the radial velocity, radial acceleration, and radial acceleration rate of a moving target. Due to the linear transform property, the proposed method can work well under low signal-to-clutter and noise ratio. In addition, the Doppler ambiguities, when target azimuth spectrum either is within a pulse repetition frequency (PRF) or spans over neighboring PRF bands, can be well solved. Both simulated and real synthetic aperture radar data processing results are provided to validate the effectiveness of the proposed algorithm.

High-order RM and DFM correction method for long-time coherent integration of highly maneuvering target

The high-order range migration (RM) and Doppler frequency migration (DFM) induced by the high-order motion parameters will lead to severe performance loss for long-time coherent integration of highly maneuvering target. Therefore, in this paper, a high-order RM and DFM correction method is proposed. To be specific, an auto-correlation function (ACF) is first presented to correct the RM. Then, the residual high-order and linear DFM are eliminated by the polynomial-phase transform (PPT) and Lv’s distribution (LVD), respectively. Besides, the motion parameters of the maneuvering target can also be obtained based on the peak location after LVD. The computational complexity of the proposed method is low. Meanwhile, compared with the adjacent cross correlation function (ACCF)-based methods which have comparable computational cost, the proposed method can achieve RM correction without any restriction and can obtain high motion parameter resolution. Simulations are provided to evaluate the performance of the proposed method from computational complexity, coherent integration ability and detection performance. Additionally, the real experiment with X-band radar is also conducted to verify the effectiveness.

STGRFT for Detection of Maneuvering Weak Target With Multiple Motion Models

Long time coherent integration (LTCI) technique enhances radar detection of maneuvering weak targets. Unfortunately, range migration (RM) and Doppler frequency migration (DFM) would occur during the integration period. Existing LTCI methods are all based on the assumption that the target is of single motion model (i.e., the target's motion model is fixed) during the long integration time. However, with increasing target's maneuverability and long observation time (needed to detect weak targets), the target's motion model is often changing (i.e., target is of multiple motion models) during the integration time, which would reduce the performance of existing LTCI methods significantly. In this paper, we address the LTCI problem for detecting a maneuvering weak target with multiple motion models, where the target signal model is first established. Thereafter, the short-time generalized Radon Fourier transform (STGRFT) based LTCI algorithm is proposed. The STGRFT method could not only eliminate RM and DFM but also estimate the model-changing point (i.e., the time when target's motion model changes) and accumulate the target energy distributed in different motion stages (corresponding to different motion models). Finally, numerical and real-data experiments are carried out to demonstrate its effectiveness. The results confirm that in terms of integration gain, input–output signal-to-noise ratio performance and detection ability, STGRFT-based method is superior to the existing popular LTCI algorithms.

Fast implementation of ground maneuvering target focusing

Ground maneuvering target detection is a hot topic in the applications of synthetic aperture radar (SAR), whereas its focusing performance is severely deteriorated by range migration and Doppler frequency migration during a long integration time. This paper proposes a novel method to image the target and estimate its parameters via performing two independent 2-dimensional (2-D) searches after a parameter separation operation. In order to improve the search speed, we set the limited search ranges and propose local mapping sparse Fourier transform (LMSFT) to replace fast Fourier transform (FFT). Compared with the traditional algorithms, the proposed method can realize fast coherent integration of multiple maneuvering targets via compensating the high-order range migration and Doppler frequency migration. In addition, the proposed method is stable under noise. Several simulation results have validated the effectiveness of the proposed method.

Fast parameter estimation method for maneuvering target by using non-uniformly resampling reducing order technique

Abstract In radar systems, prolonging the integration time can improve the performance of motion parameter estimation for weak targets. However, when the target is maneuvering, the long integration time may lead to rang migration (RM) and Doppler frequency migration (DFM) problems. In traditional methods, multi-dimensional search of motion parameters is often used, but the computational cost is high. In this paper, a fast long-time coherent integration method for maneuvering target is proposed. By using a newly defined cross correlation function based on a non-uniform resampling technique, we eliminate the high-order RM and DFM simultaneously in the range frequency-slow time domain. Then, the target energy is integrated efficiently by performing inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) along the range and azimuth directions. The proposed method has lower computational complexity than traditional methods, because it uses FFT and IFFT instead of direct multi-dimensional search. In addition, the proposed method is applicable for multi-targets and fast moving target with ambiguities. The simulations and theoretical analysis are provided to demonstrate the effectiveness of the proposed 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.

An Efficient SAR Ground Moving Target Refocusing Method Based on PPFFT and Coherently Integrated CPF

The problem of ground moving target imaging and detection is difficult due to the large range cell migration (RCM) and time-varying Doppler frequency migration (DFM) in synthetic aperture radar (SAR) system. To finely refocus a moving target, motion parameters need be accurately estimated for compensating the RCM and DFM. In this work, an efficient ground moving target refocusing method based on pseudopolar fast Fourier transform (PPFFT) and coherently integrated cubic phase function (CICPF) is proposed without a priori knowledge of the motion parameters. First, based on the known radar platform motion parameters, the range curvature correction is completed, and then the range walk is corrected using the efficient PPFFT via estimating the slope of the range walk. In doing so, the energy of the moving target has been focused into the same range cell. Second, time-varying DFM parameters are obtained utilizing the proposed CICPF, and thus the well-focused result of the moving target is obtained. Compared with the existing methods, the proposed method has the advantages in computational complexity due to avoiding the searching and interpolation operation, and anti-noise performances thanks to fully exploiting the two-dimensional (2-D) coherently accumulation characteristics and the energy of all the scatterers in moving target for estimating motion parameters. Finally, both the simulated and real SAR data processing results are presented to validate the proposed method.

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.

Analysis of the Code Phase Migration and Doppler Frequency Migration Effects in the Coherent Integration of Direct-Sequence Spread-Spectrum Signals

Coherent integration of direct-sequence spread-spectrum (DSSS) signals is a commonly used technique to improve receiver performance. However, this approach is susceptible to the code phase migration (CPM) and Doppler frequency migration (DFM) effects resulting from the relative motion between transmitter and receiver. In this paper, the CPM and DFM effects are explored and characterized. To evaluate the CPM effect, a simple analytic expression for the coherent integration results under motions of arbitrary orders is developed. In addition, the theoretically derived integration loss and time synchronization error caused by CPM are quantitatively examined. The DFM effect is evaluated under the motions of arbitrary orders by Fresnel integration and numerical fitting. The obtained closed-form expressions are verified by simulation and are shown to be useful for the performance analysis and the DSSS receiver design. The theoretical and the numerical results show that when the amount of CPM is larger than about one code chip duration, the signal-to-noise ratio gain obtained by coherent integration no longer increases because of the integration loss caused by CPM. In addition, the integration loss (in decibel units) caused by DFM is approximately inversely proportional to the square of the time-bandwidth product when the time-bandwidth product is small, and it is inversely proportional to the logarithm of the time-bandwidth product when this product is large.

Manoeuvring target detection based on keystone transforms and conjugates time reversing transform

This letter investigates the coherent integration problem for the manoeuvring target with a constant acceleration. A fast coherent integration algorithm based on the keystone transform (KT) and the conjugate time reversing transform (CTRT) is proposed to mitigate the range migration (RM) and the Doppler frequency migration (DFM). Firstly, the proposed algorithm employs the KT to remove the RM efficiently. Subsequently, the CTRT is adopted to remove the DFM. Finally, the Fourier transform is conducted to achieve the coherent integration. The computation of the proposed algorithm is in the same order with the KT. Real data processing results demonstrate the effectiveness of the proposed algorithm.

Short-Time Velocity Identification and Coherent-Like Detection of Ultrahigh Speed Targets

Finding a balance between observation duration and detection rates is the ultimate goal of the detection of ultrahigh speed targets. However, short observation durations, both across range unit, and Doppler frequency migration, may severely limit the detection performance of ultrahigh speed targets. Although, traditional coherent integration methods can efficiently accumulate signal energy to produce a high signal-to-noise-ratio measurement, they often need to search for unknown motion parameters. This search is time consuming and unacceptable for the real-time detection of ultrahigh speed targets. In this paper, a coherent-like detection method is designed based on the finite-dimension theory of Wigner matrices along with velocity identification. The proposed method can efficiently integrate signal energy without rendering motion parameters. We use the distribution and mean of the eigenvalues of the constructed matrix, i.e., an additive Wigner matrix, to identify velocities and detect ultrahigh speed targets, respectively. Simulation results validate the theoretical derivation, superiority and operability 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.

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.