High-speed Maneuvering Target Research Articles

NU-SCGRFT-Based Coherent Integration Method for High-Speed Maneuvering Target Detection and Estimation in Bistatic PRI-Agile Radar

NU-SCGRFT-Based Coherent Integration Method for High-Speed Maneuvering Target Detection and Estimation in Bistatic PRI-Agile Radar

High-Speed Maneuvering Target Inverse Synthetic Aperture Radar Imaging and Motion Parameter Estimation Based on Fast Spare Bayesian Learning and Minimum Entropy

High-speed maneuvering target inverse synthetic aperture radar (ISAR) imaging is always a hot topic in signal processing. High-speed maneuvering targets often have high-order maneuvering characteristics, such as translational and rotational characteristics, which destroy the signal structure of stationary targets and make basic imaging processing methods such as range-Doppler (RD) algorithm no longer suitable. In this paper, a high-resolution imaging method for high-speed maneuvering targets is proposed, which uses the fast sparse Bayesian learning (SBL) algorithm and the minimum entropy algorithm for ISAR high-resolution imaging and motion parameter estimation, respectively. Because SBL makes full use of the characteristics of the target and the environment, it can obtain an ISAR high-resolution image of the maneuvering target. However, the high computational complexity caused by matrix inversion and some matrix operations in SBL iteration limit the practical application of SBL in ISAR imaging. In view of the special structure of the matrix required to be inverted, we propose a fast SBL algorithm, which uses a new decomposition method to obtain the decomposition formula of the inverse matrix. Based on the decomposition factors, the multiplication operation involving the inverse matrix can be quickly calculated using fast Fourier transform (FFT), which greatly improves the computational efficiency. Image entropy represents the sharpness and focusing degree of an image, and so the minimum entropy algorithm can estimate the motion parameters of maneuvering targets more accurately. We combine the minimum entropy algorithm with the fast SBL algorithm to realize phase error correction and high-resolution imaging, which has better noise sensitivity and can obtain the best focusing degree image. Finally, simulation results prove the effectiveness of this algorithm.

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.

Capurability analysis for arbitrarily high-speed maneuvering targets

The capturability of an arbitrarily maneuvering target featuring speed superiority over an interceptor is analyzed for Augmented Pure Proportional Navigation (APPN) and Retro-Augmented Proportional Navigation (RAPN) guidance. This paper focuses on intercepting arbitrary maneuvers to study more general interception problems. A comparative analysis of the capture region between head-on interception related to APPN and head-pursuit interception related to RAPN is proposed. The results indicate that RAPN performs better than APPN in capturability. It is concluded that increasing the target velocity, which increases the velocity ratio, significantly weakens the capturability of the interceptor, and the average acceleration and relative distance affect the location of the capture region but not its size. The analysis is based on prior knowledge of the target maneuver, which inevitably leads to deviations from actual maneuvers in practical engagement, so a deviation analysis is implemented. The effective capture region shrinks as the absolute value of acceleration deviation increases, and the RAPN has a better deviation fault tolerance compared with the APPN. The results reveal that a larger relative distance can weaken the deviation fault tolerance, and the target velocity has opposite effects on head-on and head-pursuit interception.

Adaptive Finite Time Intercept Guidance

This paper summarizes several key issues of importance related to intercept of high-speed maneuvering targets under stratospheric altitude conditions, where it is unlikely that the interceptor will have a significant speed and/or maneuverability advantage. It explains why one cannot rely on traditional proportional navigation guidance and presents simulation results for a recently developed finite time method of guidance. A simplified version of finite time intercept guidance is derived, and a modification required to allow it to be practically implemented is described. Simulation results are presented to illustrate the advantages of the simplified version.

An Efficient Approach for Coherent Integration Detection of High-speed Maneuvering Targets with Arbitrary-Order Doppler Frequency Migrations

In radar detection applications, high-speed maneuvering targets (HSMTs) are commonly encountered. Given the range cell migration (RCM) and arbitrary-order Doppler frequency migrations (DFMs) induced by the complex relative motions between the HSMT and radar, they usually present a great challenge for target detections. In addition, the complex Doppler ambiguity will further aggravate the difficulty in focusing of HSMT. To address these issues, an efficient approach for coherent integration detection of HSMTs is proposed. First, inspired by the symmetrical feature of range frequency, a new range frequency reversal transform is introduced to correct complex arbitrary-order DFMs simultaneously. After that, by exploiting the advantage of range-azimuth joint processing, a modified two-dimensional scaled Fourier transform is developed to remove the residual RCM and a well-focused result is thus achieved. Furthermore, a discrimination procedure is proposed to remove the spurious peak for cross terms of targets with the same parameters. The proposed method has an extremely low computational cost and does not need to know the target motion order a priori because the operations of multidimensional search and parameter estimation are avoided. It also handles complex arbitrary-order DFMs, blind speed sidelobe, and complex Doppler center blur and spectrum ambiguity. The experiments using real data also validate the performance of the proposed method.

Signal Accumulation Method for High-Speed Maneuvering Target Detection Using Airborne Coherent MIMO Radar

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.

Radar Moving Target Detection Method Based on SET2 and AlexNet

Aiming at the nonstationary characteristics of echo signal for a high-speed maneuvering target, a signal feature extraction method is proposed by combining the time-frequency analysis and convolution neural network, and then the automatic detection of radar moving target in a noisy environment is realized. Firstly, the echo signal is modelled as a more accurate Gaussian modulation-linear frequency modulation (GM-LFM) signal and converted into the time-frequency image by a second-order synchroextracting transform (SET2). Then, ridge extraction is applied to extract the maximum energy ridge from the time-frequency distribution, and the data set is constructed by the maximum energy ridge. Finally, the data set is input into AlexNet for training, and the deep-level features of echo signal are extracted to realize the automatic moving targets detection. Simulation results show that SET2 and RE can effectively enhance the time-frequency characteristics of echo signal under the noisy environment, and the detection accuracy and noise robustness of the proposed method are better than that of SET1 and smooth pseudo-Wigner–Ville distribution (SPWVD).

ISAR Imaging Method for High-speed Maneuvering Target Based on MFT-UNET3+ Network

When inverse synthetic aperture radar (ISAR) images a high-speed maneuvering target, the imaging results of traditional methods are blurred and defocused in the range and azimuth directions because of the high speed and acceleration of the target. The existing imaging methods of maneuvering targets have poor imaging effects or low efficiency, and can’t eliminate the migration through range cells (MTRC) of far points on the target. Given that the existing methods can’t meet the imaging requirements of high-speed maneuvering targets, a new method by combing the UNET3+ convolution neural network (CNN) to machting Fourier transform (MFT) imaging process is proposed in this paper. Overcoming the limitations of the existing imaging methods, the proposed method can realize fast and accurate imaging for high-speed maneuvering targets. Experiments show that the novel MFT-UNET3+ method can achieve a good focus even under the condition of a low signal-to-noise ratio and down-sampling.

Vortex-electromagnetic-wave-based ISAR imaging for high-speed maneuvering targets

Vortex electromagnetic wave (VEMW) carrying orbital angular momentum (OAM), which is expected to introduce additional degrees of freedom in inverse synthetic aperture radar(ISAR) imaging. However, the current research about maneuvering targets is based on the "stop go" hypothesis, which does not apply to high-speed motion scenarios due to the intrapulse movement of the target. To improve the imaging quality, this letter proposes a VEMW-based high-speed maneuvering targets imaging method. Firstly, the ISAR imaging scenario of high-speed target is established. According to the spatial geometric relationship between radar and maneuvering target, the vortex echo is deduced and its characteristics are analyzed. Subsequently, a frequency modulation rate estimation method considering both calculation efficiency and high precision is proposed to realize the accurate estimation of target speed. Then, an adaptive azimuth image compensation method based on minimum entropy is proposed. Through the setting of threshold, the number of component signals in linear frequency modulation (LFM) signal is determined and compensated successively. Finally, the range profile and azimuth profile are combined to reconstruct the three-dimensional information. The simulation results demonstrate that this work can effectively eliminate the influence of high-speed motion on range and azimuth profile, also benefit the development of ISAR imaging technique of high-speed maneuvering targets.

Field-to-View Constrained Integrated Guidance and Control for Hypersonic Homing Missiles Intercepting Supersonic Maneuvering Targets

An integrated guidance and control (IGC) scheme considering the field-of-view (FOV) constraint is proposed in this paper for hypersonic skid-to-turn (STT) missiles with a strapdown seeker intercepting a high-speed maneuvering target, which is based on the backstepping control (BC), barrier Lyapunov function (BLF), sliding mode control (SMC), dynamic surface control (DSC), and reduced-order extended state observer (ESO). First, a fifth-order strict feedback IGC model considering the rudder delay dynamics is derived, which also considers the drag effect on the axial velocity. Second, the missile guidance control system based on the BC consists of seeker, guidance, angle-of-attack, attitude, and rudder subsystems. The seeker subsystem was designed based on the BLF, and the other four subsystems were designed based on the SMC. The system-lumped disturbances, including unknown target maneuvers, unmodeled parts, perturbations caused by aerodynamic parameter variations, and external disturbances, were estimated and compensated for using the reduced-order ESO. The DSC prevented the “differential explosion” caused by virtual control commands introduced by the BC. Subsequently, the stability of the closed-loop system was strictly proven using the Lyapunov theory, and the boundedness of the FOV angle was strictly derived. Finally, the simulation results demonstrated the effectiveness and robustness of the proposed IGC scheme.

Application of two spectrum refinement methods in frequency estimation

Considering the limitation of FFT frequency estimation method in resolution, this paper briefly introduces the complex modulation ZOOM-FFT and Chirp-Z transform spectrum zooming methods. The simulation results show that the ZOOM-FFT method has better anti spectrum leakage and interference effect. Furthermore, the two methods are applied to the frequency estimation of underwater high-speed maneuvering target, and it is found that Chirp-Z transform method can obtain smoother and stable frequency history, and has more flexible frequency resolution.

Computational efficient segmented integration method for high-speed maneuvering target detection

Long-time integration can improve the radar detection performance of the moving targets. However, the high speed maneuvering targets (HSMT) would cause range migration (RM) and Doppler Spread (DS) during the long integration process, which would lead to the failure of traditional moving target detection (MTD) method. The existed Generalized Radon-Fourier transform (GRFT) method can achieve a good integration and detection performance using multi-dimensional searching among the target parameter space, but the computational burden is too large. We propose a computational efficient segmented integration method for the HSMT detection, which could reduce the computational cost with slight integration performance loss. First, the echo signal is segmented based on the criterion that the RM and DS caused by the acceleration in each sub-segment can be ignored. After that, the proposed method obtains the integration of each sub-segment through Frequency bin Randon Fourier transform (FBRFT), while FBRFT can be quickly realized through Chirp-z transform (CZT). Subsequently, by analyzing the amplitude characteristics and phase characteristics of the FBRFT output, a matched accumulation method is presented to coherently integrate the energy among different sub-segments to further improve the signal-to-noise ratio (SNR). Finally, the performance of the proposed algorithm is analyzed through simulation experiments.

Guidance law of interceptors against a high-speed maneuvering target based on deep Q-Network

This paper proposes a novel guidance law for intercepting a high-speed maneuvering target based on deep reinforcement learning, which mainly includes the interceptor–target relative motion model and value function approximation model based on deep Q-Network (DQN) with prioritized experience replay. First, a method called prioritized experience replay is applied to extract more efficient samples and reduce the training time. Second, to cope with the discrete action space of DQN, a normal acceleration is introduced to the state space, and the normal acceleration rate is chosen as the action. Then, the continuous normal acceleration command is obtained using numerical integral method. Third, to make the line-of-sight (LOS) rate converge rapidly, the reward function whose absolute value tends to zero has been constructed. Finally, compared with proportional navigation guidance (PNG) and the Q-Learning-based guidance law (QLG), the simulation experiments are implemented to intercept high-speed maneuvering targets at different acceleration policies. Simulation results demonstrate that the proposed DQN-based guidance law (DQNG) can obtain continuous acceleration command, make the LOS rate converge to zero rapidly, and hit the maneuvering targets using only the LOS rate. It also confirms that DQNG can realize the parallel-like approach and improve the interception performance of the interceptor to high-speed maneuvering targets. The proposed DQNG also has the advantages of avoiding the complicated formula derivation of traditional guidance law and eliminates the acceleration buffeting.

Generalized Dechirp-Keystone Transform for Radar High-Speed Maneuvering Target Detection and Localization

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.

Fractional Sliding Mode Guidance Law for High Speed Maneuvering Targets

Fractional Sliding Mode Guidance Law for High Speed Maneuvering Targets

Detecting High-Speed Maneuvering Targets by Exploiting Range-Doppler Relationship for LFM Radar

This paper considers the problem of high-speed maneuvering target detection, which involves the processing of complex range migration (RM) and Doppler frequency migration (DFM) within the coherent processing interval (CPI). By exploiting the coupling relationship between the range frequency and the Doppler frequency, a detection algorithm is proposed for high-speed maneuvering targets. After the range compression, approximate 2-D range-frequency and Doppler-frequency expressions are derived according to the principle of stationary phase (POSP) and series inversion extension. The mathematical range-Doppler frequency relationships are then exploited to search the target's first-order motion parameters and Doppler ambiguity numbers within a predetermined parameter range, and formulate the corresponding new data from the original 2-D data matrix. Finally, Fourier transform and constant false-alarm rate (CFAR) detector are further applied to detect the targets. Simulation results show that the proposed algorithm has low complexity requirements and is suitable for low signal-to-noise ratio (SNR) scenarios. Moreover, it is not sensitive to the motion order of targets.

High-resolution imaging algorithm of high-speed maneuvering target with Doppler ambiguity removal

High-resolution imaging algorithm of high-speed maneuvering target with Doppler ambiguity removal

A New Guidance Algorithm Against High-Speed Maneuvering Target

This paper aims to propose a new guidance algorithm for intercepting a high-speed maneuvering target, such as a tactical ballistic missile that flies in a quasi-ballistic trajectory. The motivation of this study lies in the fact that the classical proportional navigation guidance (PNG) undergoes the performance degradation under the above engagement scenario due to its intrinsic property. To deal with the issue, an accurate collision course that reflects the motion characteristics of the ballistic target and missile is first analyzed. The desired look angle that leads to achieving the accurate collision course is then determined with the help of a novel time-to-go calculation method. Finally, the proposed guidance law providing the desired look angle is obtained by leveraging the concept of the biased PNG. Since the proposed method is designed to achieve an accurate collision course, it does not lead to unnecessary maneuvering near the target under the engagement scenario. This property is desirable for reserving the operational margin of maneuverability for reacting to unexpected situations during the engagement. It could improve the capturability of the target. Finally, the performance of the proposed method is verified through numerical simulations in a way to compare with the existing methods such as PNG and the augmented PNG (APNG).

Radar Maneuvering Target Motion Parameter Estimation Based on Hough Transform and Polynomial Chirplet Transform

This paper considers the problem of estimating the motion parameters of a low-observable high-speed maneuvering target with high-order motions, where the target’s complex motions will result in the range migration (RM) and Doppler frequency migration (DFM) effects within the observation time interval, which will significantly affect the radar performance. Based on the Hough transform (HT) and the polynomial Chirplet transform (PCT), a novel method for the motion parameter estimation, which we coin as HPCT, is proposed in this paper. It first employs the trajectory feature extracted from the image of range profiles by the HT to correct the first-order RM and resolve the Doppler ambiguity. Then, it compensates the residual range curvature and the DFM with the motion parameters estimated from the time-frequency ridge, which is extracted from the highly concentrated time-frequency representation (TFR) generated by the PCT. After that, the energy of radar returns can be coherently integrated along the target’s moving trajectory. In addition, we evaluate the parameter estimation performance, integration performance and computational cost of the proposed method via theoretical analysis or numerical experiments. The results show that in terms of the anti-noise ability, cross-term interference avoidance, measurement accuracy and computational complexity, the HPCT is superior to some common methods for the motion parameter estimation. Finally, we extend it to the scenario of multiple targets with different motion orders.