Coherent Integration for Maneuvering Target Detection Based on Radon-Lv’s Distribution

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

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

This paper considers the coherent integration problem for a low-observable maneuvering target, where the velocity and acceleration result in range migration (RM) and Doppler frequency migration (DFM) within the coherent pulse interval. A novel method based on the frequency spectrum segment processing (FSSP) and the segmental Lv's distribution (SLVD) is proposed to realize the long-time coherent integration for multiple maneuvering targets. In this method, FSSP is proposed to eliminate the RM effect by dividing the received signal into several subband signals and expanding the range resolution of the subband signals. Then SLVD is applied to achieve the coherent integration of the subband signals and accumulate the energy of all the subband signals coherently. The proposed method can realize the coherent integration for multiple maneuvering targets without any prior knowledge of the targets' motion. The simulation and experimental results demonstrate the effectiveness of the proposed algorithm.

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

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

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

The Doppler mismatch, range migration and Doppler frequency migration (DFM) correction problem for realizing the long-time coherent integration of space moving target with high-speed manoeuvring performance in passive bistatic radar is considered. A novel method based on intra-partition range-Doppler (RD) processing is proposed, where the intra-partition RD processing is first performed to achieve the pre-accumulation of target’s energy in each partition and eliminate the Doppler mismatch. Then, the generalized keystone transform is employed to correct the range curvature. After that, the residual range walk is removed with the centre frequency of the coarse Doppler filter related to the target velocity. Furthermore, matched filtering process is carried out to compensate the DFM. The advantage of the method is that it can obtain superior coherent integration and detection performance in comparison with the existing algorithms. Numerical simulations are presented to demonstrate the coherent integration and the detection performance for a high-speed target.

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.

Signal integration, as an effective method of detecting weak target, is widely used in areas of radar, sonar, etc. In previous studies of long-time coherent integration, researchers usually established a multi-pulse echo model with linear frequency modulation (LFM) signal due to its good compression performance and large Doppler tolerance. Then, perfect analytical formula can be deduced to compensate for range migration and Doppler spread, which is helpful in analyzing the mechanism of long-time coherent integration in depth. However, besides LFM, a wide variety of signal waveforms are also used in modern sonar and underwater guidance system to meet the requirements for diverse applications. For instance, continuous wave (CW) pulse is often used in signal detection, high resolution direction of arrival (DOA) estimation, and velocity estimation, while large time-bandwidth product waveforms such as modulated signal, coded signal, and pseudo-random signal are utilized for special tasks like anti-interference detection, channel matching, and active concealed detection. Therefore, the formulas and corresponding instructive conclusions deduced by LFM have no generality when other sonar waveforms are used in pulse integration. In this paper, we focus on long-time coherent integration for arbitrary signal reflected by underwater target moving with a uniform velocity and propose a motion-compensated coherent integration method for arbitrary complex envelop signal. A kind of general ambiguity function (GAF) for transmitted signal is defined to present a unified expression based on GAF for the output of the matched filter. The operation not only helps us to describe and calculate the pulse compression form of the arbitrary complex envelop by using a general mathematical model, but also provides information about the range migration and Doppler frequency shift of the multi-pulse echo, which is needed in pulse range alignment and FFT integration. For the matched filter output expressed by the GAF, Keystone transform is utilized to correct the complex envelop of the multi-pulse echo and eliminate the range walk. Then, Doppler frequency shift is compensated for by performing FFT transform, and the long-time coherent integration for arbitrary complex envelop is realized. To verify the correctness of the proposed method, we carry out the computer simulation on both signal integration and detection performance by using four sonar waveforms, i.e., CW signal, LFM signal, m-sequence phase-coded signal, and Costas frequency hop coded signal. The simulation results show that the proposed motion-compensated coherent integration method is applicable to arbitrary complex envelop signal. We also design an anechoic water tank experiment scheme which can successfully obtain the multi-pulse echoes of constant moving target. The motion-compensated coherent integration of the experimental data of the above-mentioned four waveforms further validates the effectiveness of the proposed method.

The synthetic-wideband and pulse repetition frequency jittering radar systems are receiving increasing attention due to the relatively low construction costs and good anti-jamming performance. However, the inter-pulse random hopping of the carrier frequency and pulse repetition frequency introduces challenges to the long-time coherent integration and motion parameter estimation of the high-speed weak targets for these radar systems. A modified generalized Radon Fourier transform for weak target detection and motion parameter estimation is proposed. The proposed method can achieve full coherent integration gain for the high-speed weak target and has a good parameter estimation accuracy. After the target motion has been well compensated, the well-focused high-resolution range profile of the target can be obtained by synthetic-wideband processing. The effectiveness of the proposed method is verified by Monte Carlo simulations. In addition, experimental data collected using an X-band radar system are processed and analyzed to illustrate the practical performance of the proposed method.

Axis rotation MTD algorithm for weak target detection

The airborne coherent multi-input multi-output (MIMO) radar benefiting from coherent integration (including intra-channel integration and inter-channel integration) of multi-channel echoes can obtain superior detection performance for high-speed maneuvering targets. However, due to the coupling motion characteristic between multiple airborne platforms and high-speed targets, the range walk (RW) and Doppler walk (DW) will occur within the intra-channel integration. Besides, the inter-channel signals also exist envelope and phase differences, which will lead to the difficulty in multi-channel integration. We make contributions towards addressing these limitations. On the one hand, we establish a three-dimensional (3-D) geometrical model for high-speed maneuvering target detection with airborne coherent MIMO radar and derive the mathematical expression of radar echoes, while the generalized Radon-Fourier transform (GRFT) is utilized to simultaneously correct the RW and DW for acquiring intra-channel integration. On the other hand, we analyze the properties of GRFT outputs and propose a GRFT-domain integration method to achieve the multi-channel coherent integration. More specifically, the proposed method first constructs a set of coupling equations for the estimation of target motion parameters (i.e., position, velocity and acceleration), then, the target's motion parameters can be estimated by Newton-Raphson method and solving the linear equations. Second, in order to settle the envelope and phase differences between multi-channel echoes, the envelope alignment and phase compensation functions of inter-channel echoes are constituted based on the estimated parameters. Finally, the coherent accumulation of multi-channel echoes can be implemented. Numerical simulations demonstrate the effectiveness of the proposed method.

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.

This paper addresses the coherent integration problem for detecting a maneuvering target with complex motions, involving range migration (i.e., range walk and range curvature) and Doppler frequency migration (DFM) within the coherent processing interval. A new method based on adjacent cross correlation function (ACCF) and fractional Fourier transform (FRFT) is proposed, where the ACCF operation is firstly employed to remove the range migration (RM) and reduce the order of DFM. After that, the FRFT is applied to achieve the coherent accumulation. Several simulation experiments are provided to demonstrate the effectiveness.

At present, a primary challenge of seismic data processing is the ability to recognize and identify first-break seismic signals with low signal-to-noise ratio (SNR) in mountainous areas. Correlation-based supervirtual interferometry (SVI) can improve the SNR of refractions and diffractions to achieve high-quality results in velocity model construction and diffraction imaging from low SNR data. However, SVI is susceptible to coherent Gaussian noise and is limited to 2-D cases. This paper develops the cumulant-based coherent integration (CCI) method to enhance the first-break signals by using cumulant functions and multiple convolutions for both 2-D and 3-D land seismic data. The 2-D synthetic data example demonstrates that CCI can suppress coherent Gaussian noise and obtain results with higher SNR than SVI. The 3-D synthetic data example demonstrates the effectiveness of the 3-D CCI. Its application to 3-D field exploration seismic data measured in the mountainous areas of western China illustrates that the SNR of the first-break signals is much higher than that obtained by bandpass filtering, which is commonly employed in commercial software today.