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In order to improve the multiple-missile cooperative attack capability and penetration capability, this paper investigates two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target for controllable thrust missiles. First, a three-dimensional nonlinear guidance model is established that does not assume small missile lead angles in the guidance process. Second, in the line-of-sight (LOS) direction of the cluster cooperative guidance strategy, the proposed guidance algorithm transforms the simultaneous attack problem into a second-order multiagent consensus problem, which effectively solves the practical problem of low guidance precision provoked by the time-to-go estimation. Then, by combining second-order sliding mode control (SMC) and nonsingular terminal SMC theory, the guidance algorithms in the normal and lateral directions to the LOS are designed, respectively, so that the multi-missile can accurately attack a maneuvering target while satisfying the impact angle constraints. Finally, by utilizing the second-order multiagent consensus tracking control in the leader-following cooperative guidance strategy, a novel leader-following time consistency algorithm is investigated to ensure that the leader and followers can attack the maneuvering target simultaneously. Moreover, the stability of the investigated guidance algorithms is proved mathematically. The effectiveness and superiority of the proposed cooperative guidance strategies are verified by numerical simulations. • This paper designs two three-dimensional impact-angle-constrained cooperative guidance strategies against maneuvering target. • This paper utilizes the relative distance and radial relative velocity as consensus variables to improve guidance precision. • This paper combines a nonsingular SMC with a second-order sliding mode control theory to improve guidance performance. • The proposed cooperative guidance algorithm has a simpler form and a more straightforward structure to avoid singularity problems. [ABSTRACT FROM AUTHOR]

• A novel DRL-based decision approach for simultaneously conducting the coordinated attack of the maneuvering target and the evasion of interceptors. • A MOMDP containing multi-step history states is constructed and further transformed into a first-order MDP with memory extraction, which integrates the spatio-temporal coupling properties among missiles, interceptors, and targets while supporting efficient sequential decision-making. • Domain-knowledge-assisted pre-training and reward functions are constructed to speed up the convergence of the training process. This paper presents an open and interesting issue for missiles, i.e., achieving collaborative parameters constrained cooperative guidance, despite the interference of pursing interceptors (INTs) and the maneuvering target, by the fact that the target-missile-interceptor (TMI) engagement induces their complex and time-varying relationships. The Memory-Extraction-based Soft-Actor-Critic (ME-SAC) approach is proposed, which enhances the collaborative performance of missiles by implicitly extracting coupling motion characteristics among TMI from historical state, achieving the joint optimization of situation awareness and strategy. Firstly, the cooperative guidance task is formulated as a multi-order Markov decision process (MOMDP) to better represent the dynamic evolution of engagement, and a memory-extraction process is introduced to alleviate the curse of dimensionality. Secondly, a memory-decision-oriented maximum entropy framework combined with memory update modules is designed for enhancing strategy search ability. Then, a domain-knowledge-based pre-training is implemented to improve convergence speed. Finally, in simulation evaluation with various scenarios, the proposed ME-SAC shows more promising than the typical DRL-based and model-based algorithms in task success rate, learning efficiency, and adaptability. [ABSTRACT FROM AUTHOR]

This paper proposes a prescribed-time cooperative guidance law (PTCGL) against maneuvering target with variable line-of-sight (LOS) angle constraint for leader-following missiles, where the convergence times of the state errors can be arbitrarily set. The leader missile against the maneuvering target is provided as the modified proportional navigation (MPN) guidance law. The proposed PTCGL for follower missiles consist of two parts, in LOS direction, the range-to-go (Rgo) is selected as a co-variable, avoiding the estimation of time-to-go (Tgo), and a novel second-order nonlinear consensus protocol is developed to design the PTCGL; in normal LOS direction, considering the variable LOS angle constraint, the cooperative guidance law is designed with the proposed prescribed-time sliding model control (PTSMC) method. Besides, the prescribed-time convergence of Rgo and LOS errors are proved. Finally, the effectiveness and superiority of the proposed PTCGL with leader-following strategy is illustrated by numerical simulation results. • The convergence time of the cooperative guidance law can be set arbitrarily. • The multi-missile surrounding attack was achieved without pre-setting the desired LOS angle. • The Range-to-go was selected as a co-variable to design the cooperative guidance law. • A prescribed time convergence sliding mode method was developed to design the cooperative guidance law. [ABSTRACT FROM AUTHOR]

Moving target detection (MTD) is a research hotspot in radar signal processing. Generally, the time information of non-cooperative moving targets entering and leaving a radar coverage area is unknown, which would lead to severe performance loss for target parameter estimation, detection, and imaging. Unlike our previous research work, this paper addresses the motion parameters estimation and refocusing problem for a radar maneuvering target with unknown entry and departure time. A computationally efficient method that utilizes extended Kalman filtering (EKF) for phase tracking is proposed to estimate the entry and departure times. The proposed method first performs range cell migration correction (RCMC) on the pulse compression echo signal. Then, the maneuvering target signal is modeled as a polynomial phase signal (PPS) and utilizes the EKF to construct a binary state-space equation for polynomial phase tracking. Finally, by comparing the phase tracking results of the noise cell and the signal cell, one can derive estimates for the entry/departure time and motion parameters. Compared with existing methods, the proposed method avoids multi-dimension searching on the parameter space, so it has a prominent advantage in computational complexity. Moreover, the core of the proposed method lies in tracking the polynomial phase, which is not constrained by the order of target motion, and has wider applicability in practice. Both simulated and public radar data are used to validate the effectiveness of the proposed method. • A method for estimating motion parameters under unknown time information is proposed. • The devised estimator can provide satisfactory time information estimation accuracy. • Our method avoids the high-dimensional search, which has low computational cost. • The proposed method further enriches and perfects the phase tracking theory. [ABSTRACT FROM AUTHOR]

This research introduces a new approach to address the challenges related to inaccuracies in shape estimation and motion state tracking during the tracking of maneuvering extended targets. The method combines a novel neural network model with a cubature Kalman filter. Initially, the target's shape variation is represented using a second-order autoregressive model, and Bayesian filtering is employed for target contour estimation in static environments. Subsequently, the kinematic state tracking of maneuvering targets is enhanced by modifying a neural network model based on Transformer architecture. Through the effective integration of these techniques, precise tracking of maneuvering extended targets is achieved, facilitating accurate estimation of irregular contour information while tracking the targets' motion state in real-time. The efficacy of the proposed approach is further confirmed through various simulation scenarios, underscoring its suitability for tracking maneuvering extended targets. • Modeling target shape with 2nd-order AR model, initial contour via alpha-shape algorithm, refining shape with Bayesian filtering. • State transfer matrix parameter estimation via neural network model and Cubature Kalman Filter for maneuvering target kinematic state estimation. • Integration of shape estimation and kinematic state method enables real-time tracking for Maneuvering Extended Target Tracking. [ABSTRACT FROM AUTHOR]

The motion complexity of maneuvering target causes the estimation uncertainty of target motion model, resulting in state estimation error. Especially for strong maneuvering target, the drastic change of target motion models makes the tracking methods hard to adapt and provide accurate state estimation promptly. To solve the state estimation problem of strong maneuvering targets, we propose a new transformer maneuvering target tracking model based on deep learning, named TrMTT model. The TrMTT model uses a new residual mapping between the observation trajectory and the real trajectory to estimate the target states, and is composed of the encoder and decoder branches while the two have the same input of observation trajectory. The encoder extracts the self-attention information for the input at each layer while the decoder implements cross-attention extraction and fusion between features in different layers, thus providing more correlation information between states for learning the transition law of rapidly changing states. Moreover, we propose an input module before the encoder–decoder structure to code the state features of the observation trajectory, and apply two kinds of normalization layers in the input module and the encoder–decoder structure, to project the input into a feature space which facilitates extracting the correlation information between states. Simulation results show that the proposed TrMTT model is superior in performance for maneuvering target tracking compared with other existing approaches. • A new residual mapping is built for giving real states and accelerating training. • The proposed TrMTT model inserts correlation between states into state features. • An input module is proposed to code the state features of observation trajectory. • The TrMTT model can notably reduce the estimation delay. [ABSTRACT FROM AUTHOR]

Highlights • A new motion parameters estimation method for maneuvering target is proposed. • A cross correlation function is defined to eliminate the high-order range and Doppler frequency migrations, and transform the signal into a two-dimensional complex sinusoid. • An IFFT and an FFT are performed to integrate target energy. • After obtaining the targets' peak locations, the motion parameters are estimated by solving a set of linear equation. 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. [ABSTRACT FROM AUTHOR]

Highlights • A computationally efficient coherent detection and parameter estimation algorithm via SAF-SFT is proposed. • The proposed algorithm could remove the range cell migration and Doppler spread effects without parameter-searching process. • SAF-SFT method could strike a good balance between computational cost and detection probability as well as the estimation performance. Abstract In this paper, a computationally efficient coherent detection and parameter estimation algorithm via symmetric autocorrelation function (SAF) and scaled Fourier transform (i.e., SAF-SFT) is proposed, involving range cell migration (RCM) and Doppler spread (DS) within the coherent integration (CI) time. In particular, the first SAF and SFT operations are applied to achieve the range and velocity estimations after the generalized keystone transform. With the estimations, the remaining RCM induced by target's velocity could be removed and the target signal could be extracted along the range cell. Then the second SAF and SFT operations are performed on the extracted signal, where the target energy could be coherent integrated and the acceleration estimation can be obtained. Cross term of SAF-SFT is also analyzed and its characteristic indicates the applicability in the scenario of multi-targets. Detailed comparisons of SAF-SFT with several typical algorithms with respect to computational cost, detection probability and parameter estimation ability show that the SAF-SFT could strike a balance between computational cost and detection probability as well as the estimation performance. Simulation results and real test experiment are given to verify the SAF-SFT based approach. [ABSTRACT FROM AUTHOR]

Most existing three-dimensional (3D) impact angle guidance laws against maneuvering target focus on terminal-angle-constrained guidance without considering the field-of-view (FOV) limit. In this study, a 3D nonsingular FOV-constrained guidance strategy with the desired impact angles is proposed. The analytical expression between the desired impact angles and terminal light-of-sight angles is derived by integrating the transition matrix in the interception time with the collision triangle theory. A novel fixed-time sliding mode surface is presented and, based on it, guidance commands are generated. The radial basis function neural networks are combined with composite intelligent learning to improve the approximation precision of target maneuvering. Furthermore, a barrier Lyapunov function is used in the pitch plane to satisfy the FOV constraint. For the capturability analysis, the analytical achievable impact sets are calculated. Simulations are demonstrated to verify the effectiveness and robustness of the proposed guidance strategy. [ABSTRACT FROM AUTHOR]

This paper explores performance of various methods for state estimation of radar tracking models. A coordinated turn case study of maneuvering target in the presence of non-Gaussian noise is of particular interest. We aim at evaluating the estimation potential of recently presented filters grounded in the Maximum Correntropy Criterion (MCC). Various investigations confirm the outstanding performance of such filters for treating stochastic systems disturbed with impulsive (shot) and mixed-Gaussian noises. However, those filters are intended for linear models, and the success of the MCC-based state estimation in a nonlinear continuous-time stochastic environment, which often underlies radar tracking modeling, is still debatable. First, we extend the MCC-based filters, which are designed presently for linear discrete-time stochastic models, to nonlinear continuous-discrete systems. We devise the conventional (non-square-root) filtering and its square-root version as well. Second, we fulfil a comprehensive examination of these new methods in severe conditions of tackling a seven-dimensional radar tracking problem, where an aircraft executes a coordinated turn, in the presence of both impulsive (shot) and mixed-Gaussian noises. In addition, the novel MCC-based filters are compared to various contemporary extended, cubature and unscented Kalman-like state estimators. [ABSTRACT FROM AUTHOR]

An adaptive long time integration method based on dynamic programming (DP) is proposed for the detection of high speed maneuvering fluctuating targets. The proposed method is aimed at detecting a target with an unpredictable range migration and fluctuating echoes by jointly applying three main ideas: the improved DP procedure that could search the maneuver position and velocity at each frame; the multi-pulse integration that could suppress the influence of fluctuation; and the adaptive step with fading factor that could allow the integration time to be suitable for each searching velocity. Compared with the existing methods, the target energy could be integrated along its trajectory using the proposed method without estimating the specific motion parameters, which makes the proposed method applicable to a target with arbitrary motion. Simulation results and performance comparisons show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

In allusion to the coupling relationship among radial velocity variation, range migration and Doppler spread of a maneuvering target, a dynamic programming (DP) based long time coherent integration (DPCI) detection method is proposed. The energy of the target of high velocity and strong maneuver could be integrated along its trajectory by the proposed DPCI method with high efficiency. The main idea of the DPCI is the joint execution of two operations: the modified DP procedure that could search the current position and velocity of the target, and the improved coherent integration that could calibrate the Doppler shift during the entire process with any large phase spread. The proposed method is applicable to a target with arbitrary motion without estimating its specific movement parameters. Simulation results and performance comparisons show the accuracy and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on designing a novel homing missile guidance law applicable to intercepting maneuvering target while considering time and field-of-view (FOV) constraints. To realize accurate zero miss-distance and time control, a sliding mode manifold consisting of the range-to-go, expected impact time and two newly-defined weighting functions is constructed based on a nonlinear model, which can guarantee the interception at a prescribed impact time once the sliding mode has reached. Then, an overall guidance command is derived by taking both finite time convergence of sliding mode manifold and non-singularity into consideration. A new guidance strategy with boundary conditions is proposed to satisfy FOV requirement. Furthermore, the feasibility for intercepting maneuvering target is demonstrated via a Lyapunov-like approach. Numerical simulations validate the performance of the proposed guidance law, and a comparative study indicates that the proposed method is superior to relative guidance laws in terms of maneuvering target interception. [ABSTRACT FROM AUTHOR]

• The generation method of digital camouflage image is studied based on several background images. • The K-harmonic means clustering algorithm is combined with the color histogram to optimize the clustering algorithm. • The edge contour of regular hexagon digital camouflage basic unit is more blurred and broken. Since the digital camouflage generation method based on fixed single background image cannot fully meet the hidden need of maneuvering targets. In this paper, a method of generating digital camouflage image based on several background images is proposed. Firstly, according to the active range of the maneuvering target, several background images are collected. Secondly, in order to resolve the problem that the clustering algorithm is sensitive to the initial clustering center and easy to fall into local optimum, K-harmonic means (KHM) clustering algorithm is introduced and initial clustering center is determined based on color histogram. Again, KHM clustering is used to extract color features from several background images, the first clustering is extracted from a single background image, and the second clustering is extracted with several color features sets extracted from the first clustering of background images as input. Finally, the regular hexagon is used as the basic unit of the digital camouflage image to construct the spot template, and the digital camouflage image is generated by the lowest horizontal line algorithm. Example verification and camouflage effect detection show that the digital camouflage image generated by this method can effectively realize the concealment of maneuvering targets and has good camouflage effect. [ABSTRACT FROM AUTHOR]

Tracking multiple maneuvering (MM) targets is a well-known and challenging problem because of clutter and several uncertainties existing in target motion mode, target detection, and data association. An efficient solution to this problem is the Gaussian mixture probability hypothesis density (GM-PHD) filter for jump Markov system (JMS) models. However, this solution is inapplicable to circumstances where detection probability is low because the GM-PHD filter for JMS models requires a high detection probability. To address this problem, we propose a sequential multiple target (MT) Bayes filter for JMS models. To track MM targets that are switching among a set of linear Gaussian models, an implementation process of this filter for linear Gaussian jump Markov MT models is also developed. The conclusion that the novel filter is more efficient for tracking MM targets than the existing filter for JMS models in circumstances of low detection probability is validated by simulation results. [ABSTRACT FROM AUTHOR]

This paper has proposed two continuous composite finite-time convergent guidance laws to intercept maneuvering targets in the presence of autopilot lag: one is for hit-to-kill and the other is for zeroing the line-of-sight (LOS) angular rate. More specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty online while the finite-time control technique is used to fulfill the design goal in finite time. The key feature in derivation of the proposed guidance law is that two integral-type Lyapunov functions are used to avoid analytic differentiation of virtual control law encountered with traditional backstepping. The finite-time stability of the closed-loop nonlinear observer-controller system is established using finite-time bounded (FTB) function and Lyapunov function methods. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel composite integrated guidance and control (IGC) law for missile intercepting against unknown maneuvering target with multiple uncertainties and control constraint. First, by using back-stepping technique, the proposed IGC law design is separated into guidance loop and control loop. The unknown target maneuvers and variations of aerodynamics parameters in guidance and control loop are viewed as uncertainties, which are estimated and compensated by designed model-assisted reduced-order extended state observer (ESO). Second, based on the principle of active disturbance rejection control (ADRC), enhanced feedback linearization (FL) based control law is implemented for the IGC model using the estimates generated by reduced-order ESO. In addition, performance analysis and comparisons between ESO and reduced-order ESO are examined. Nonlinear tracking differentiator is employed to construct the derivative of virtual control command in the control loop. Third, the closed-loop stability for the considered system is established. Finally, the effectiveness of the proposed IGC law in enhanced interception performance such as smooth interception course, improved robustness against multiple uncertainties as well as reduced control consumption during initial phase are demonstrated through simulations. [ABSTRACT FROM AUTHOR]

This study explores the guidance law against maneuvering targets with the intercept angle constraint. The limitation of the traditional guidance law, which simply treats the unknown target acceleration as zero, has been analyzed. To reduce this limitation, a linear extended state observer is constructed to estimate the acceleration of the maneuvering target to enhance the tracking performance of the desired intercept angle. Furthermore, a nonsingular terminal sliding mode control scheme is adopted to design the sliding surface, which is able to avoid the singularity in the terminal phase of guidance. Simulation results have demonstrated that the proposed guidance law outperforms the traditional guidance law in the sense that more accurate intercept angle can be achieved. [ABSTRACT FROM AUTHOR]

• A computational efficient segmented integration method for the high speed maneuvering target detection is proposed, where 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. • 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. • Based on the amplitude characteristics and phase characteristics of the FBRFT output, the proposed method could then coherently integrate the energy among different sub-segments to further improve the signal-to-noise ratio (SNR). • The advantage of the proposed integration method is that it could achieve a better tradeoff among integration ability, detection performance and computational cost. 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. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of controlling impact time against various types of target – stationary, constant velocity, or maneuvering. Analytical expression of time-to-go, that is exact for non-maneuvering target but approximate for maneuvering ones, is first presented based on true-proportional-navigation guidance concepts. Guidance strategies are then derived, using Lyapunov theory, to meet impact time constraints, without linearizing the engagement dynamics. Hence, the proposed strategies remain effective even for large initial heading errors. Further, a cooperative guidance strategy to achieve simultaneous target interception by multiple interceptors is also proposed. Guidance commands that ensure consensus among the time-to-go values of the interceptors are utilized for this purpose. Using judicious choices of gains, the common time of target interception may be either pre-fixed, or the same may be decided cooperatively during the engagement. Stability analysis of the possible equilibria in heading angle dynamics, for different choices of parameters, is also performed. For both one-to-one and cooperative homing, simulation results are presented for various engagement scenarios to demonstrate the effectiveness of the proposed strategies. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of 3-dimensional guidance law design is considered and a new guidance law based on partial sliding mode technique is presented. The approach is based on the classification of the state variables within the guidance system dynamics with respect to their required stabilization properties. In the proposed law by using a partial sliding mode technique, only trajectories of a part of states variables are forced to reach the partial sliding surfaces and slide on them. The resulting guidance law enables the missile to intercept highly maneuvering targets within a finite interception time. Effectiveness of the proposed guidance law is demonstrated through analysis and simulations. [Copyright &y& Elsevier]

Abstract: This paper addresses the problem of the pursuit of a maneuvering target by a group of pursuers distributed in the plane. This pursuit problem is solved by associating it with a Voronoi-like partitioning problem that characterizes the set of initial positions from which the target can be intercepted by a given pursuer faster than any other pursuer from the same group. In the formulation of this partitioning problem, the target does not necessarily travel along prescribed trajectories, as it is typically assumed in the literature, but, instead, it can apply an “evading” strategy in an effort to delay or, if possible, escape capture. We characterize an approximate solution to this problem by associating it with a standard Voronoi partitioning problem. Subsequently, we propose a relay pursuit strategy, that is, a special group pursuit scheme such that, at each instant of time, only one pursuer is assigned the task of capturing the maneuvering target. During the course of the relay pursuit, the pursuer–target assignment changes dynamically with time based on the (time varying) proximity relations between the pursuers and the target. This proximity information is encoded in the solution of the Voronoi-like partitioning problem. Simulation results are presented to highlight the theoretical developments. [Copyright &y& Elsevier]

Abstract: This paper aims to investigate the theoretical performance of bearings-only maneuvering target tracking when fixed measurement biases exist. Firstly, the general formulation of Cramér–Rao lower bound (CRLB) is presented when both target''s maneuver and fixed measurement biases work simultaneously in a bistatic system, and the corresponding recursive CRLB formulation is then derived. Finally, a maneuver detection method is developed to calculate the approximation of the theoretical CRLB. Numerical simulation results indicate either that the proposed or the fuzzy-neural-network-based maneuver detection method can yield a satisfying CRLB compared with the theoretical CRLB, but the proposed method is easier to implement owing to directly utilizing the target''s bearing information. [Copyright &y& Elsevier]

Particle filtering may cope with non-linear and/or non-Gaussian models. As a counterpart, this technique suffers from an heavy computation cost and cannot always satisfy the real time constraints of applications. A data parallel algorithm is proposed to achieve real-time particle filtering. Extensive results are presented in the passive SONAR tracking context for maneuvering targets. [Copyright &y& Elsevier]

This paper proposes integrated guidance and control design to intercept a target, which may execute various motions, at a pre-specified time of interception. The problem is addressed considering nonlinear engagement kinematics and the interceptor is steered using the combined effects of canard as well as tail configurations (dual-controlled interceptors). Different formulations of time-to-go, without the restrictive assumption of interceptor's small heading angle, have been used in deriving the guidance commands, allowing the proposed strategy to remain effective over a wide range of impact time values. A weighted effort allocation scheme, in canard and tail deflections, has been proposed to generate the required lateral acceleration. The overall design uses sliding mode control owing to its simplicity of design, while a nonlinear finite-time disturbance observer is used to estimate the target's maneuver. Finally, simulations are presented for various target motions, and time-constrained interception with an impaired actuator is also shown, vindicating the efficacy of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper proposes a three-dimensional (3-D) robust nonlinear cooperative guidance law for multiple missiles to simultaneously attack a maneuvering target at desired impact angles. Since the flight time of terminal guidance is very short, the fast convergence of guidance errors is a vital demand, especially when the initial errors are huge and the target is maneuvering. By utilizing the theory of fixed time convergence, a distributed sliding surface that only utilizes the information from adjacent missiles is first designed, whose convergence time is independent of initial conditions. In order to avoid the performance degradation due to the estimation error of time-to-go, the consensus variables of the fixed-time sliding surface are chosen as range-to-go and radial relative velocity. Then, a robust cooperative guidance law along the line-of-sight (LOS) direction is proposed to bring the multi-missile system to reach the sliding surface in finite time. Thus, the simultaneous attack to a maneuvering target can be guaranteed. Next, the guidance laws in the elevation and azimuth direction of LOS are developed to ensure the fixed-time convergence of LOS angles. The fixed-time stability is proved through the Lyapunov theory and bi-homogenous property. Simulation results indicate that the impact time of each missile under the proposed guidance law is the same, without any deviation. Compared with the state-of-the-art methods, the convergence time of LOS angles is shortened by about 30%. In addition, the miss distance and errors of LOS angles can be reduced by more than 80%. [ABSTRACT FROM AUTHOR]

A unified optimal impact angle guidance law is designed for different types of interceptors and targets. By solving a linear quadratic optimal control problem with the energy consumption weighted by an arbitrary positive function, the generalized guidance command is determined in a closed-loop feedback form. The main feature of the proposed algorithm is that it can be applied to varying-speed interceptors and targets. The weighting function also brings the command shaping capability of the proposed guidance law. To show the applicability of the proposed guidance law, several illustrative examples covering different types of interceptors and targets are provided. Numerical simulations are conducted to demonstrate the effectiveness of the proposed guidance algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a three-dimensional (3-D) robust guidance scheme for bank-to-turn (BTT) missiles against couplings and target maneuver. Firstly, the missile-target coupled relative dynamics are established. Then, a qualitative indicator (QI) is designed based on Lyapunov stability theory for both coupling and target maneuver terms to indicate whether they strengthen or weaken the system stability. Moreover, a nonlinear disturbance observer (NDOB) with fixed-time convergence is introduced to estimate the unknown target acceleration. A robust guidance scheme is proposed by synthesizing QI, sliding mode control (SMC) and NDOB. The stability of guidance system is proven via Lyapunov stability theory. Finally, numerical simulations are executed to validate the effectiveness of proposed guidance scheme. [ABSTRACT FROM AUTHOR]

• Doppler ambiguity and acceleration reduce the integration gain of conventional coherent detection methods. • The frequency scope of DFT is extended by reintroducing its redundant period to estimate the under-sampled Doppler frequency. • The scaling and product operations are used to eliminate the couplings and suppress the grating lobes. • A good balance is achieved between computational complexity and detection performance. This paper considers the coherent integration problem for Doppler-ambiguous maneuvering target. A novel method based on the product scaled periodic Lv's distribution (PSPLVD) is proposed. To be specific, the acceleration could be accurately estimated via Lv's distribution (LVD). Then, the periodic discrete Fourier transform (DFT), which periodically extends the frequency scope of DFT, is introduced to modify the LVD to estimate the unambiguous centroid frequency. Thereafter, scaling and product operations are respectively employed to eliminate the coupling and suppress the grating lobes. Finally, coherent integration is achieved after compensating off the range migration and Doppler frequency migration. Cross term analysis indicates the applicability in the scenario of multiple targets. Efficient implementation based on chirp-z transform is also presented to alleviate the computational burden and eliminate the brute force searching procedure. Detailed comparisons with several representative methods lead us to conclude that the proposed method could strike a good balance between computational cost and detection probability. Extensive simulations and real data processing results are provided to verify the proposed method. [ABSTRACT FROM AUTHOR]