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An airborne bistatic radar working in downward-looking mode confronts two major challenges for low-altitude target detection. One is range cell migration (RCM) and Doppler migration (DM) resulting from the relative motion of the radar and target. The other is the non-stationarity characteristic of clutter due to the radar configuration. To solve these problems, this paper proposes a joint implementation method based on sub-aperture processing to achieve clutter suppression and coherent maneuvering target detection. Specifically, clutter Doppler compensation and sliding window processing are carried out to realize sub-aperture space–time processing, removing the clutter non-stationarity resulting from the bistatic geometric configuration. Thus, the output matrix of clutter suppression in the sub-aperture could be obtained. Then, the elements with the same phase of this matrix are superimposed and rearranged to achieve the reconstructed 2-D range-pluse echo matrix. Next, the aperture division with respect to slow time is conducted and the RCM correction based on modified location rotation transform (MLRT) and coherent integration (CI) are realized within each sub-aperture. Finally, the matched filtering process (MFP) is applied to compensate for the RCM/DM among different sub-apertures to coherently integrate the maneuvering target energy of all sub-apertures. The simulation and measured data processing results prove the validity of the proposed method.

Targets faced by inverse synthetic aperture radar (ISAR) are often non-cooperative, with target maneuvering being the main manifestation of this non-cooperation. Maneuvers cause ISAR imaging results to be severely defocused, which can create huge difficulties in target identification. In addition, as the ISAR bandwidth continues to increase, the impact of migration through resolution cells (MTRC) on imaging results becomes more significant. Target non-cooperation may also result in sparse aperture, leading to the failure of traditional ISAR imaging algorithms. Therefore, this paper proposes an algorithm to realize MTRC correction and sparse aperture ISAR imaging for maneuvering targets simultaneously named whale optimization algorithm–fast iterative shrinkage thresholding algorithm (WOA-FISTA). In this algorithm, FISTA is used to perform MTRC correction and sparse aperture ISAR imaging efficiently and WOA is adopted to estimate the rotational parameter to eliminate the effects of maneuvering on imaging results. Experimental results based on simulation and measured datasets prove that the proposed algorithm implements sparse aperture ISAR imaging and MTRC correction for maneuvering targets simultaneously. The proposed algorithm achieves better results than traditional algorithms under different signal-to-noise ratio conditions.

In this paper, by accounting for the angle constraint (AC) and autopilot lag compensation (ALC), a novel fixed-time convergent guidance law is developed based on a fixed-time state observer and bi-limit homogeneous technique. The newly proposed guidance law exhibits three attractive features: (1) unlike existing guidance laws with AC and ALC which can only guarantee asymptotic stability or finite-time stability, the newly proposed guidance scheme can achieve fixed-time stability. Thus, the newly proposed scheme can drive the guidance error to zero within bounded time which is independent of the initial system conditions. (2) To compensate for autopilot lag, existing guidance schemes need the unmeasurable second derivative of the range along line-of-sight (LOS) and second derivative of LOS angle or the derivative of missile’s acceleration. Without using these unmeasurable states, the newly proposed guidance law still can guarantee the fixed-time stability. (3) By using the bi-limit homogeneous technique to construct an integral sliding-mode surface, the proposed scheme eliminates the singular problem without using the commonly-used approximate method in recent fixed-time convergent guidance schemes. Finally, the simulation results demonstrate the effectiveness of the proposed scheme.

In this paper, we propose a nonlinear tracking solution for maneuvering aerial targets based on an adaptive interacting multiple model (IMM) framework and unscented Kalman filters (UKFs), termed as AIMM-UKF. The purpose is to obtain more accurate estimates, better consistency of the tracker, and more robust prediction during sensor outages. The AIMM-UKF framework provides quick switching between two UKFs by adapting the transition probabilities between modes based on a distance function. Two modes are implemented: a uniform motion model and a maneuvering model. The experimental validation is performed with Monte Carlo simulations of three scenarios with ACAS Xa tracking logic as a benchmark, which is the next generation of airborne collision avoidance systems. The two algorithms are compared using hypothesis testing of the root mean square errors. In addition, we determine the normalized estimation error squared (NEES), a new proposed noise reduction factor to compare the estimation errors against the measurement errors, and an estimated maximum error of the tracker during sensor dropouts. The experimental results illustrate the superior performance of the proposed solution with respect to the tracking accuracy, consistency, and expected maximum error.

In this paper, a new fixed-time convergence guidance law is proposed against maneuvering targets in the three-dimensional (3-D) engagement scenario. The fixed-time stability theory is used to zero the line-of-sight (LOS) angle rate, which will ensure the collision course and the impact of the target. It is proven that the convergence of the LOS angle rate can be achieved before the final impact time of the guidance process, regardless of the initial conditions. Furthermore, the convergence rate is merely related to control parameters. In theoretical analysis, the convergence rate and upper bound are compared with that of other laws to show the potential advantages of the proposed guidance law. Finally, simulations are carried out to illustrate the effectiveness and robustness of the proposed guidance law.

Long-time coherent integration works to significantly increase the detection probability for maneuvering targets. However, during the observation time, the problems that often tend to occur are range cell migration (RCM) and Doppler frequency cell migration (DFCM), due to the high velocity and acceleration of the maneuvering target, which can reduce the detection of the maneuvering targets. In this regard, we propose a new coherent integration approach, based on the product scale zoom discrete chirp Fourier transform (PSZDCFT). Specifically, by introducing the zoom operation into the modified discrete chirp Fourier transform (MDCFT), the zoom discrete chirp Fourier transform (ZDCFT) can correctly estimate the centroid frequency and chirp rate of the linear frequency-modulated signal (LFM), regardless of whether the parameters of the LFM signal are outside the estimation scopes. Then, the scale operation, combined with ZDCFT, is performed on the radar echo signal in the range frequency slow time domain, to remove the coupling. Thereafter, a product operation is executed along the range frequency to inhibit spurious peaks and reinforce the true peak. Finally, the velocity and acceleration of the target estimated from the true peak position, are used to construct a phase compensation function to eliminate the RCM and DFCM, thus achieving coherent integration. The method is a linear transform without energy loss, and is suitable for low signal-to-noise (SNR) environments. Moreover, the method can be effectively fulfilled based on the chirp-z transform (CZT), which prevents the brute-force search. Thus, the method reaches a favorable tradeoff between anti-noise performance and computational load. Intensive simulations demonstrate the effectiveness of the proposed method.

In this paper, a novel cooperative and predictive guidance law is proposed to intercept high-speed and high-maneuverability targets with inferior interceptors. The purpose of guidance is cooperatively covering the most-probable locations where the target may be in the future. To fulfill this purpose, predicted target states in the form of a probability density function were obtained using limited target information, i.e., noisy position data for one case and maneuverability limits for the second case, at first. Next, the likelihood of the reachable set of interceptors was computed over the predicted target state. Then, to increase the probability of interception in a finite time, the interceptors’ trajectories were adjusted collaboratively depending on the likelihood values. An extensive Monte Carlo study, with practically applicable simulation parameters, was used to demonstrate the effectiveness of the proposed methods against targets in challenging maneuvering modes.

This paper addresses the issue of a complex three-dimension (3-D) terminal guidance process that is used against maneuvering targets while considering both the terminal impact angle (TIA) and field-of-view (FOV) angle constraints. According to the highly coupled and nonlinear 3-D terminal guidance model, an adaptive back-stepping sliding-mode guidance law algorithm is proposed in order to guarantee the stability and robustness of the guidance system. Considering the explicit expression of the line-of-sight (LOS) angle in the kinematics and dynamics of the terminal guidance process, the TIA constraint is transformed into an LOS constraint based on their well-known relationship. In view of the challenges in obtaining the motion information of maneuvering targets, an adaptive law design is introduced in order to estimate and compensate for external disturbances caused by the maneuvering of the target and modeling uncertainty. In addition, because the FOV angle represented by the overall leading angle is not a state variable in the sliding-mode guidance system, it is decoupled into two partial leading angles based on a specific transformation relation, so the 3-D terminal guidance control problem is converted into separate tracking system control issues in the pitch and yaw planes. Then, the Lyapunov stability theory is utilized to substantiate the stability of the guidance system, where the Lyapunov functions in both of the subsystems consist of the LOS and partial FOV state error terms. Finally, a series of simulations of various motion states of maneuvering targets under different terminal cases were carried out. It was proved that the terminal guidance design based on the strategies presented above was able to obtain the desired LOS constraints with satisfying the FOV limitation, and the simulation results verified the effectiveness, universality, and significance for practical applications of the proposed guidance design method.

Although there have been numerous studies on maneuvering target tracking, few studies have focused on the distinction between unknown maneuvers and inaccurate measurements, leading to low accuracy, poor robustness, or even divergence. To this end, a noise-adaption extended Kalman filter is proposed to track maneuvering targets with multiple synchronous sensors. This filter avoids the simultaneous adjustment of the process model and measurement model without distinction. Instead, the maneuver detection based on the Dempster-Shafer evidence theory is constructed to achieve the reliable distinction between unknown maneuvers and inaccurate measurements by fusing multi-sensor information, which effectively improves the robustness of the filter. Moreover, the adaptive estimation of the process noise covariance is modeled by a Markovian decision process with a proper reward function. Deep deterministic policy gradient is designed to obtain the optimal process noise covariance by taking the innovation as the state and the compensation factor as the action. Furthermore, the recursive estimation of the measurement noise covariance is applied to modify a priori measurement noise covariance of the corresponding sensor. Finally, the fusion algorithm is developed for the global estimation. Simulation experiments are carried out in two scenarios, and simulation results illustrate the feasibility and superiority of the proposed algorithm.

A new, highly constrained guidance law is proposed against a maneuvering target while satisfying both impact angle and terminal acceleration constraints. Here, the impact angle constraint is addressed by solving an optimal guidance problem in which the target’s maneuvering acceleration is time-varying. To deal with the terminal acceleration constraint, the closed-form solutions of the new guidance are needed. Thus, a novel engagement system based on the guidance considering the target maneuvers is put forward by choosing two angles associated with the relative velocity vector and line of sight (LOS) as the state variables, and then the system is linearized using small angle assumptions, which yields a special linear time-varying (LTV) system that can be solved analytically by the spectral-decomposition-based method. For the general case where the closing speed, which is the speed of approach of the missile and target, is allowed to change with time arbitrarily, the solutions obtained are semi-analytical. In particular, when the closing speed changes linearly with time, the completely closed-form solutions are derived successfully. By analyzing the generalized solutions, the stability domain of the guidance coefficients is obtained, in which the maneuvering acceleration of the missile can converge to zero finally. Here, the key to investigating the stability domain is to find the limits of some complicated integral terms of the generalized solutions by skillfully using the squeeze theorem. The advantages of the proposed guidance are demonstrated by conducting trajectory simulations.

Inverse synthetic aperture radar (ISAR) imaging of a maneuvering target is a challenging task in the field of radar signal processing. The azimuth echo can be characterized as a multi-component polynomial phase signal (PPS) after the translational compensation, and the high quality ISAR images can be obtained by the parameters estimation of it combined with the Range-Instantaneous-Doppler (RID) technique. In this paper, a novel parameters estimation algorithm of the multi-component PPS with order three (cubic phase signal-CPS) based on the modified discrete polynomial-phase transform (MDPT) is proposed, and the corresponding new ISAR imaging algorithm is presented consequently. This algorithm is efficient and accurate to generate a focused ISAR image, and the results of real data demonstrate the effectiveness of it.

The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational motion compensation (RMC) requirement. The time-varying terms, caused by rotational motion in the Doppler frequency shift, are able to be eliminated at the selected time frame. Furthermore, the processed backscattered signal is transformed to the one in the frequency domain while applying the phase retrieval to run the translational motion compensation (TMC). Phase retrieval plays an important role in range tracking, because the ISAR echo module is not affected by both radial velocity and the acceleration of the target. Finally, after the removal of both the rotational and translational motion errors, the time-invariant Doppler shift is generated, and radar returned signals from the same scatterer are always kept in the same range cell. Therefore, the unwanted motion effects can be removed by applying this approach to have an autofocused ISAR image of the maneuvering target. Furthermore, the method does not need to estimate any motion parameters of the maneuvering target, which has proven to be very effective for an ideal range⁻Doppler processing. Experimental and simulation results verify the feasibility of this approach.

As a powerful signal processing tool for imaging moving targets, placing radar on a non-stationary platform (such as an aerostat) is a future direction of Inverse Synthetic Aperture Radar (ISAR) systems. However, more phase errors are introduced into the received signal due to the instability of the radar platform, making it difficult for popular algorithms to accurately perform motion compensation, which leads to severe effects in the resultant ISAR images. Moreover, maneuvering targets may have complex motion whose motion parameters are unknown to radar systems. To overcome the issue of non-stationary platform ISAR autofocus imaging, a high-resolution imaging method based on the phase retrieval principle is proposed in this paper. Firstly, based on the spatial geometric and echo models of the ISAR maneuvering target, we can deduce that the radial motion of the radar platform or the vibration does not affect the modulus of the ISAR echo signal, which provides a theoretical basis for the phase recovery theory for the ISAR imaging. Then, we propose an oversampling smoothness (OSS) phase retrieval algorithm with prior information, namely, the phase of the blurred image obtained by the classical imaging algorithm replaces the initial random phase in the original OSS algorithm. In addition, the size of the support domain of the OSS algorithm is set with respect to the blurred target image. Experimental simulation shows that compared with classical imaging methods, the proposed method can obtain the resultant motion-compensated ISAR image without estimating the radar platform and maneuvering target motion parameters, wherein the fictitious target is perfectly focused.

In real applications, the image quality of the conventional monostatic Inverse Synthetic Aperture Radar (ISAR) for the maneuvering target is subject to the strong fluctuation of Radar Cross Section (RCS), as the target aspect varies enormously. Meanwhile, the maneuvering target introduces nonuniform rotation after translation motion compensation which degrades the imaging performance of the conventional Fourier Transform (FT)-based method in the cross-range dimension. In this paper, a method which combines the distributed ISAR technique and the Matching Fourier Transform (MFT) is proposed to overcome these problems. Firstly, according to the characteristics of the distributed ISAR, the multiple channel echoes of the nonuniform rotation target from different observation angles can be acquired. Then, by applying the MFT to the echo of each channel, the defocused problem of nonuniform rotation target which is inevitable by using the FT-based imaging method can be avoided. Finally, after preprocessing, scaling and rotation of all subimages, the noncoherent fusion image containing all the RCS information in all channels can be obtained. The accumulation coefficients of all subimages are calculated adaptively according to the their image qualities. Simulation and experimental data are used to validate the effectiveness of the proposed approach, and fusion image with improved recognizability can be obtained. Therefore, by using the distributed ISAR technique and MFT, subimages of high-maneuvering target from different observation angles can be obtained. Meanwhile, by employing the adaptive subimage fusion method, the RCS fluctuation can be alleviated and more recognizable final image can be obtained.

Tracking the target that maneuvers at a variable turn rate is a challenging problem. The traditional solution for this problem is the use of the switching multiple models technique, which includes several dynamic models with different turn rates for matching the motion mode of the target at each point in time. However, the actual motion mode of a target at any time may be different from all of the dynamic models, because these models are usually limited. To address this problem, we establish a formula for estimating the turn rate of a maneuvering target. By applying the estimation method of the turn rate to the multi-target Bayes (MB) filter, we develop a MB filter with an adaptive estimation of the turn rate, in order to track multiple maneuvering targets. Simulation results indicate that the MB filter with an adaptive estimation of the turn rate, is better than the existing filter at tracking the target that maneuvers at a variable turn rate.