Deep neural network-aided coherent integration method for maneuvering target detection

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.

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

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.

The multivariate range function of the high-speed maneuvering target induces modulations on both the envelop and phase, i.e., the range cell migration (RCM) and Doppler frequency migration (DFM) which degrade the long-time coherent integration used for detection and localization. To solve this problem, many long-time coherent integration methods have been proposed. Based on mechanisms of typical methods, this paper names two signal processing modes, i.e., processing unification (PU) mode and processing separation (PS) mode, and presents their general forms. Thereafter, based on the principle of the PS mode, a novel long-time coherent integration method, known as the generalized dechirp-keystone transform (GDKT), is proposed for radar high-speed maneuvering target detection and localization. The computational cost, energy integration, peak-to-sidelobe level (PSL), resolution, and anti-noise performance of the GDKT are analyzed and compared with those of the maximum likelihood estimation (MLE) method and keystone transform-dechirp (KTD) method. With mathematical analyses and numerical simulations, we validate two main superiorities of the GDKT, including (1) the statistically optimal anti-noise performance, and (2) the low computational cost. The real radar data is also used to validate the GDKT. It is worthwhile noting that, based on closed analytical formulae of the MLE method, KTD method, and GDKT, several doubts in radar high-speed maneuvering target detection and localization are mathematically interpreted, such as the blind speed sidelobe (BSSL) and the relationship between the PU and PS modes.

High-speed, low-observable, and maneuvering target detection is always the difficult problem for the early warning and detection of space target, ballistic target, and passive radar signal processing. The high-order motion information of maneuvering target is employed in this paper, such as acceleration and jerk. Accordingly, several long-time coherent integration methods are demonstrated and illustrated, i.e., Radon-fractional Fourier transform (RFRFT), Radon fractional ambiguity function (RFRAF), Radon-linear canonical ambiguity function (RLCAF), and phase differentiation-Radon-Lv's distribution (PD-RLVD). These methods can compensate the across range unit (ARU) and Doppler frequency migration (DFM) effects simultaneously during the long-time integration. The background clutter and noise can be well suppressed with higher integration gain. Experimental results using real radar data show the superiority of the proposed methods.

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.

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.

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.

Coherent integration is a conventional approach to improve detection ability in radar applications, whereas its performance is decreased by migration through range cell due to the motion of target, limiting the time of integration. This problem becomes more severe in terahertz band. This paper introduces Keystone transform to terahertz radar in order to realize long-time coherent integration, aiming to get a successful detection of targets. Moreover, doppler ambiguity is resolved based on intra-pulse interference processing. A simulation is conducted to demonstrate the effective improvement for target detection using Keystone transform in terahertz radar.

This paper introduces a new concept of focus-before-detect (FBD) with long-time coherent integration to improve detection of low-SNR and high-speed radar target. By modeling the target range migration function with limited motion and position parameters, the target's echo energy can be focused and projected into a low-dimensional parameter space via the proposed FBD method. Compared to the existing Doppler filter bank and track-before-detect (TBD) method, the proposed FBD method may obtain higher SNR gain and effectively overcome the non-desired effects of across range unit and across Doppler unit for the long-time coherent integration. Therefore, larger coverage diagram and smaller detectable radar cross-section may be obtained for an FBD-based radar system.

Long time hybrid integration of radar rotating target

The micro-Doppler (m-D) signature can describe the motion state and structure of the target in detail. It can be considered as an effective method for ship target detection and recognition in the marine environment. In this paper, an effective strategy is proposed to simulate the m-D signature and extract the ship’s motion parameters on the time-varying sea surface. For this purpose, a ship target micro-motion model based on six degrees of freedom is first established. Then, the public domain strip (PDSTRIP) method is used to realize real-time estimation of ship motion. Next, a high-precision electromagnetic scattering model is used to generate radar echoes of a ship on the rough sea. Finally, the m-D signature can be acquired and analysed based on the obtained radar echo. The numerical results show that the instantaneous frequency and motion parameters can be estimated well from the m-D signature. At the same time, the proposed model can also be used to calibrate the Inverse Synthetic Aperture Radar (ISAR) of ship targets in the marine environment.

In this paper, we propose a novel long-time coherent integration detection method to detect an uncooperative moving target in a frequency and pulse repetition interval randomly jittering radar system based on signum coding (SC). In the proposed algorithm, an additional reference waveform is applied to eliminate the third-order harmonic influence induced by SC. Then, a generalized Keystone transform (GKT) is proposed to resolve the complex coupling among the range frequency, jittered carrier frequency, and nonuniformly sampled time. Simulation results are presented to validate the effectiveness and feasibility of the proposed method.

The phase-derived velocity measurement (PDVM) technique can achieve a high measurement accuracy at the phase level and thus has great application prospects in the field of micromotion feature extraction and target recognition. To achieve a PDVM with a low signal-to-noise ratio (SNR), a PDVM method based on the generalized Radon–Fourier transform (GRFT) is proposed in this article. The main challenges that we overcome are phase extraction and phase ambiguity resolving under the condition of a low SNR. By utilizing the GRFT to estimate the target motion parameters, the echo peak position can be reconstructed, and then the peak phase value can be extracted. In the meantime, the phase ambiguity integer can be resolved based on the rough velocity estimation results obtained by the GRFT, and the phase ambiguity resolving can be realized at a low SNR. In addition, to suppress the influence of noise on the extracted phase, a filter design method based on the target motion characteristics is proposed to further improve the accuracy of the PDVM. In the simulation, the performance of the proposed method under different motion models and different SNR conditions is analyzed, and the effectiveness of the proposed method under low-SNR conditions is verified. Compared with directly using the GRFT, the proposed method has the advantages of strong applicability to different motion models and low computational load.

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.