To deal with the problem that the block sparse Bayesian algorithm exists in grid estimation, an off-grid weighted block sparse Bayesian algorithm is proposed based on coherent accumulation. The algorithm first uses the signal characteristics to coherently accumulate the polarization-sensitive array received data to enhance the signal-to-noise ratio (SNR); then the first-order Taylor expansion of the steering vector is performed, and an off-grid real-valued model is introduced by improving the block structure; then the weighting vectors are introduced to accelerate the iteration of the algorithm and reduce the number of iterations; and finally, the solution of the off-grid parameters is achieved by iterative optimization of the parameters. Compared with the traditional block sparse Bayesian learning (BSBL) algorithm, the method iterates faster and achieves efficient joint off-grid polarization-DOA estimation. Simulation results show the effectiveness of the algorithm.

Frequency planning is of great significance which can effectively dispatch the battlefield resources of radio equipment. To enhance the efficiency of scheduling, this paper investigates the frequency planning problem (FPP) and puts forward a multi-objective approach. The proposed multi-objective model considers the coordination constraints of radio equipment alongside diverse resources, defining key points to delineate the cooperative interactions among radio equipment. The model integrates considerations of time, space, and energy, focusing on electromagnetic interference, frequency demand satisfaction and frequency occupancy as its primary optimization objectives. To improve the accuracy of the solution, this study proposes a multi-population multi-objective memetic algorithm (MPMA). This algorithm employs a segment-based coding strategy and a specialized genetic operator to facilitate the integration of global and local search techniques. Additionally, chaos initialization and a multi-population-based scheduling approach are incorporated to enhance global search performance. The experimental results demonstrate the superiority of the proposed model and MPMA in meeting the diverse scheduling needs of radio equipment across various scenarios.

Sign language recognition (SLR) can be improved by using millimeter-wave radar, which safeguards the privacy of those who are hearing-impaired. However, existing SLR methods do not fully utilize the unique features of radar echoes, resulting in limited accuracy. Sign language is composed of an individual’s poses and hand movements. To obtain these recognition features, this paper presents a multi-modal-feature-based SLR (MMF-SLR) network framework. This method first constructs a transformer-pose network to extract the human skeleton information, which represents the poses in sign language, from the radar images. Additionally, hand movement information can be represented by the range-Doppler sequence and micro-Doppler signatures. The human skeleton and hand movement information are input into a multimodal fusion network to achieve high-accuracy SLR. The experimental results demonstrate that the proposed method can enhance the recognition accuracy of the sign language with similar poses or movements compared to the traditional SLR methods.

The track association of clustered targets is a crucial step in integrating detection results from multiple sensors. Nonetheless, traditional association methods are frequently impaired by reduced accuracy due to challenges such as high-density clusters and observation mismatches. To address these issues, a dual-channel TCN-GRU network is developed which leverages temporal convolutional networks (TCN) and gated recurrent units (GRU) to capture subtle differences in track features. Furthermore, an association module based on the global nearest neighbor (GNN) approach is elaborated to refine scenario perception of the association task. Experimental findings indicate that the proposed method attains a track association accuracy of 87.16%, with a 6.29% improvement credited to the GNN module. This work signifies the novel integration of deep learning models with traditional methods in the realm of clustered targets track association, providing significant insights for the advancement of track association methodologies.

This paper proposes a three-dimensional (3D) interferometer direction-finding (DF) method to address the reduced accuracy of conventional two-dimensional (2D) interferometer DF methods in non-planar antenna configurations. First, we enhance the multi-channel soft synchronization (MCSS) technique by dynamically compensating for sampling point offsets, achieving phase estimation accuracy better than 0.01 sampling points. Second, we construct a 3D baseline model based on the 3D distribution characteristics of the antennas and introduce a 3D error allocation model to improve the system error estimation method, allowing for dynamic correction of calibration deviations. This effectively addresses the phase ambiguity issues caused by 3D mechanical errors. Finally, we develop a 3D DF algorithm and an optimized multi-pulse fusion approach utilizing the maximum-ratio combining (MFA-MRC) method to reduce DF errors and enhance system stability. Simulation experiments and flight tests demonstrate that the proposed method has a computational load of only 0.31% of the multiple signal classification (MUSIC) algorithm. When the baseline offset exceeds 10 mm, the angular accuracy improves from 0.9° to 0.3°, and the positioning accuracy is enhanced from approximately 10 km to around 1 km. The study holds significant theoretical and practical value in engineering.

In view of the large amount of data and dense pixel points in point cloud files, this article proposes a multiple point cloud file encryption algorithm based on principal component analysis (PCA) and fractional Fourier transform (FrFT). In this method, a point cloud data matrix (PCDM) is generated by extracting the coordinates and color information of the point cloud, then using PCA to reduce the dimension of a sequence of PCDMs, which are spliced and scrambled to produce a feature vector matrix and a dimension-reduced matrix (DRM) for encryption and reconstruction. Then using the hyperchaotic Lorenz system to generate the random phase masks and the orders of the FrFT. These two parameters will be used as keys to encrypt the point cloud feature vector matrix. The simulation results verify that the encryption algorithm can quickly encrypt multiple point cloud files, and the quality of the point cloud files obtained by decryption and reconstruction is good. The algorithm also has a large enough key space and highly sensitive keys, which means it has good security and strong robustness to different attacks.

The spaceborne inverse synthetic aperture radar (ISAR) has attracted significant attention due to its extensive observation range and imaging performance. However, the complex motion between spaceborne platform and the air target leads to complex signal modulation. The scattering anisotropy and occlusion lead to the scattering points missing problem. These problems pose a serious challenge to the traditional ISAR imaging algorithms. Aiming at the above problems, this paper proposes a joint intra-frame and inter-frame imaging algorithm based on spaceborne ISAR. In this algorithm, we divide the long coherent processing interval into several sub-apertures using the narrow-band tracking data, and each-order terms of the signal within sub-aperture is derived in detail. Then, the intra-frame algorithm based on the parametric minimized image entropy search is proposed to correct the spatial-variant phase errors caused by the complex relative motion. As to the well-focused images from different views and the rotation parameters obtained in sub-apertures, the inter-frame algorithm based on wavelet transform can perform image registration and image fusion to obtain more detailed target feature information and more complete target structure. In simulated and real-measured data experiments, the effectiveness and superiority of the proposed algorithm are validated.

The paper presents a full-exchange streaming adaptive processor architecture with nested parallel sampling covariance matrix estimation and adaptive weight computation, to achieve polarization-space-time adaptive processing (P-STAP), adaptive digital beamforming (ADBF) and multiple side-lobe canceller (MSLC) within a configurable computational framework. An effective method for real-time numerical calculation is proposed by reducing truncation errors, ensuring robust convergence, and low time complexity through the lower-diagnoal-lower transpose (LDLT) right multiplication iterative (LDLT-RMI) method. To fully implement P-STAP for high-intensity interference clutter adaptive robust suppression, a series of intellectual property (IP) cores are designed for high-order, high-condition symmetric positive definite matrix inversion. The adaptive processor can operate on a frame-structured data flow, accommodating various space-time-frequency-polarization multi-domain combinations, which supports 8 to 100 channels with a dynamic range of up to 80 dB. Even the interferences reach a high intensity of 65 dB, the adaptive processor can still work stably.

In this paper, we propose evaluation approaches for the spatial target localization precision based on the observation matrix conditional number. Three evaluation approaches for the spatial target localization precision are derived including relative condition numbers, absolute condition numbers, and volume condition numbers by properties of vectors and matrix norms. The theoretical analysis shows that the proposed methods are the upper certainty bound of the magnification of measurement error. Meanwhile, the proposed methods are able to account for variations of localization accuracy by exploiting geometric variations in the composition between the target and measurement stations. Finally, the proposed methods perform better, compared with the traditional evaluation methods. This is of great significance for the accuracy evaluation of high-precision measuring equipment, optimization of workstation layout and geometric configuration. Simulation experiments corroborate the effectiveness of the proposed methods.

In environments with complex electromagnetic characteristics, signals from active repeater mainlobe deception jamming are closely aligned with radar emissions, significantly impairing radar functionality. This paper explores the efficacy of frequency diverse array (FDA) radar in combating active mainlobe jamming. Initially, the signal model for FDA multi-input multi-output (FDA-MIMO) radar is introduced. Building on this, a frequency offset optimization approach for FDA radar using the differential artificial bee colony (DEABC) algorithm is developed. Following this, the steepest descent linear minimum variance distortionless response beamforming algorithm is implemented in an FDA early warning radar to mitigate mainlobe jamming. Simulations are conducted to validate the effectiveness of the proposed strategies. The results from these simulations demonstrate that the methodologies can create a focused beam aimed at the target while effectively neutralizing jamming signals within the mainlobe area.

This paper proposes a space target attitude estimation method with inverse synthetic aperture radar (ISAR) images to address the challenges of difficult feature extraction, low estimation accuracy, and inefficiency in the attitude estimation of space targets. This method relies on ISAR contour projection plane alignment. Unlike traditional contour matching methods, this approach introduces an image plane alignment algorithm for different radar lines of sight (LOS). The algorithm aligns image planes from various frames, defined by their corresponding LOS and rotation axis, with those of a reference template library. This alignment resolves attitude mismatches during template matching caused by differences in image planes. The attitude estimation method first uses the Hausdorff distance as the contour matching criterion to enhance matching speed. Second, the contour projection plane alignment algorithm outputs the actual attitude for each frame. Third, the multi-solution attitude problem is addressed by combining the actual attitudes of each frame using the minimum distance method. Finally, an optimization algorithm is employed to improve estimation accuracy. This method demonstrates higher accuracy and efficiency compared to traditional approaches in scatter point imaging and electromagnetic simulation experiments.

The launch process of a multi-stage launch vehicle is significantly influenced by uncertain parameters, including air density, aerodynamic parameters, and engine thrust, which often exhibit deviation. Predicting the trajectory range of the launch vehicle under the influence of uncertainty is essential before launch, and uncertainty quantification serves as a crucial method to address this challenge. In traditional uncertainty quantification for launch vehicles, unknown parameters are often assigned specific distributions based on prior knowledge. However, prior knowledge is sometimes subjective, and unknown parameters are often assigned conservative ranges to meet safety margins. In addition, the flight data of the past launch is precious, especially in quantifying the uncertainty of reusable or same-type launch vehicles. This paper utilizes flight data to estimate parameters base on Bayesian methods and integrates the estimation results with prior knowledge, which can more objectively set the distribution of uncertain parameters. Reasonable distribution has a positive impact on uncertainty quantification, which can avoid control strategies that are not robust enough or overly redundant. Therefore, the uncertainty quantification for launch vehicles is discussed under different information sources. In addition, the algorithm is accelerated based on Gaussian process regression and polynomial chaos expansions.

To predict the ranking of the country’s innovation capability in the world in real-time, this study designs a two-phased prediction model based on the pairwise comparison. Data from the global innovation index (GII) reports are employed in this study. Countries with different income levels have shown different development inertias, the two-phased prediction model is thus proposed. In the first phase, the GII data from the previous year are applied to predict the ranking of innovation capability for high-income countries. In the second phase, more years of historical data are adopted to predict the innovation ranking for other countries. The global innovation rankings for all countries and economies are thus obtained. Experiments have proved that the model requires only a few indicators to get accurate results. The model provides real-time decision support for decision-makers to formulate innovative development policies.

Resolving conflict and achieving consensus among social groups with diverse opinions becomes a critical issue in today’s extensively connected society. Despite the ubiquitous heterogeneity of connection or contact patterns, the study of how topological characteristics of network structure affect opinion convergence is still insufficient. Based on Deffuant and colleagues’ bounded confidence model and the transformable network structure between random network and typical complex network types, including small-world network and scale-free network, we analyze the critical factors affecting continuous opinion convergence. We find that the network density plays a crucial role in the aggregated process of opinions in the social group, followed by the modularized level and the average shortest path length of the social network. However, the structural features have little impact on the consensus phase transition threshold. The further simulation experiments under real networks can be well understood based on the interplay of these three main factors. These findings confirm the paramount importance of creating a high-frequency and widely communicated atmosphere to mitigate conflict and efficiently reach consensus.

The evaluation of air combat decision-making has garnered significant attention due to its potential to effectively mitigate losses resulting from erroneous decisions. However, existing research primarily focuses on static evaluation methods. Therefore, this paper proposes a dynamic multi-round decision evaluation method based on the characteristics of multi-round unmanned aerial vehicle air combat under opponent’s optimal strategy. In order to determine objective weights, an improved multi-attribute decision making method is proposed, which incorporates the proximity as a correction coefficient for evaluation indicators, utilizing the cosine similarity instead of Euclidean distance, and incorporating both actual and theoretical objective weights to prevent data mutations. Subsequently, the game theory is employed to reasonably adjust subjective and objective weights to obtain comprehensive weights. To address the issues related to the ambiguity and randomness during the evaluation process, a reverse cloud generator is utilized to determine the center of gravity of the cloud model using comprehensive weights while employing the weighted deviation degree for evaluating air combat decision-making effectiveness. By activating the cloud generator through the cloud model, the optimal strategies for each round of air combat are determined, thereby completing the dynamic evaluations for multi-round sequential decision-making processes. Finally, the feasibility and effectiveness of the proposed method are verified through simulations.

Weapon target assignment (WTA) problem is a critical problem in multiplatform confrontation. This paper studies a static WTA problem with heterogeneous weapons in multi-platform air combat scenarios, called heterogeneous WTA (HWTA) problem. Heterogeneous indicates that the engagement platforms carry multiple kinds of weapons for different tactical purposes. The targets assigned and the weapons used by one side’s platforms will affect the survival probability and capability of the other side’s platforms. The goal of each side in HWTA is to find a solution to determine the kind of weapon used and the target assigned for each platform, so as to maximize their combat effectiveness. The problem is formulated as a two-player noncooperative game model with considering the conflicts between the engaged sides. The Nash equilibrium is an effective solution to the game in which no player has an incentive to deviate. However, the number of pure strategies in HWTA increases exponentially with the engagement platforms. To improve computing efficiency, a double oracle algorithm with constructive heuristic (DOCH) is developed, within which the constructive heuristic is embedded to solve the oracle subproblems efficiently. Numerical experiments are conducted to verify the effectiveness of the DOCH. The results show that the DOCH can find effective strategies for platforms to improve combat effectiveness. Moreover, the DOCH can find high-quality solutions in seconds, significantly outperforming the state-of-the-art algorithms in terms of computational efficiency, especially for large-scale problems.

Multi-domain competition is developing for disintegrating the component of the opponent’s operational system and winning advantage in decision space. Island air defense is a typical multi-domain security problem, which dramatically increases the complexity of decision-making by considering different factors such as multi-stages decisions, multi-domain settings, imperfection information, and uncertain events. However, current research on island air defense security problems is sparse and lacks consideration of key factors. To provide support for assisting human commanders to take wise decisions in a complex environment, we build a multi-domain multi-state island air defense model and propose responding solving algorithms. We study the whole progress of island air defense and propose a multi-domain, multi-stage imperfection information security game that formulates critical characters in the adversarial scenario of island air defense. In addition, considering a bounded rational opponent’s possible strategies, we propose an opponent-aware Monte Carlo counterfactual regret minimization algorithm for learning a robust defensive strategy in the security game. We evaluate our methods in various adversarial scenarios. The results show that our equilibrium learning method can effectively play against an opponent with bounded rationality and significantly outperform some advanced algorithms.

To address the problem of sea ice collisions threatening offshore drilling operations in polar regions, this paper proposes a Bayesian network–based collision risk assessment model for drillships. The model integrates large ice floe/iceberg conditions, natural environmental factors, and geometric factors derived from the ship’s shape, size, distance, and azimuth. Using iceberg routes, scenario simulations are conducted to evaluate collision probabilities and provide time-dependent risk values. Results demonstrate that the method yields reasonable and consistent assessments of drillship–ice interactions. The proposed method enables automatic collision risk assessment and can be applied to unattended management systems to enhance the safety of polar drilling operations.

With the improvement of the informatization and intelligence level of logistics equipment, the interactive and collaborative relationships between equipment entities become complex, and the uncertainty problems emerge in the equipment system-of-systems. Herein, a heterogeneous network model is built to describe logistics equipment system-of-systems, which considers the heterogeneity and complex connections of different logistics equipment nodes. Next, the topological structure properties of this model are analyzed. On this basis, the experiments on the logistics equipment system-of-systems under attack strategies including degree attacks, betweenness centrality attacks and random attacks are taken to assess the changes of structural invulnerability. Results show that the logistics equipment system-of-systems heterogeneous network has similar topological structure characteristics of typical complex networks, namely small-world effect and scale-free characteristics, indicating that the flow, sharing, and synchronization between logistics equipment entities in the network are relatively easy. Meantime, the key logistics equipment nodes with large values such as degree, closeness centrality, and betweenness centrality should be protected in the logistics equipment system-of-systems heterogeneous network against deliberate attacks. The current work provides a perspective for demonstration and affords the theoretical support for development and decision-making of logistics equipment system-of-systems.

To overcome the limitations of traditional force aggregation methods, this paper proposes a novel clustering model integrating the self-adaptive tent chaos search ant lion optimizer (SATC-ALO) and the self-organizing map (SOM) network. The model introduces a hybrid distance calculation method to measure inter-target distances and enhances the ant lion optimization algorithm through tent chaos sequences, adaptive tent chaos search, tournament selection, and logistic chaos sequences. Aggregation accuracy is evaluated using minimum quantization error and confidence value for the SOM neural network. The model is resolved using SATC-ALO and SOM independently, with experiments demonstrating that SOM achieves fast and accurate grouping, while SATC-ALO offers higher precision but requires longer computational runtime, making it more suitable for hybrid approaches. Both methods are validated as practical solutions for force aggregation tasks.

Deep reinforcement learning algorithms are revolutionizing intelligent decision-making in air combat, drawing widespread attention and extensive research. However, air combat agents trained with these algorithms face significant challenges, such as limited decision-making capacities due to adversarial training against relatively fixed and singular expert strategies, and a lack of interpretability and reliability in their decision-making processes. To tackle these issues, this paper proposes a self-play training mechanism based on policy switching and opponent selection, allowing air combat agents to refine their capabilities via engaging with previous versions of themselves. Additionally, an explainable decision tree model is developed to clarify the decision logic of these agents. Simulations and results demonstrate that the proposed self-play training approach significantly enhances the decision-making abilities of air combat agents, with late-stage agents showing a 38% improvement over early-stage agents in confrontations with an expert strategy. Moreover, the explainable decision tree model effectively elucidates the decision logic and achieves an 86% win rate against the expert strategy, comparable to the 88% win rate of the air combat agents.

The consensus mechanism in multi-agent networks has attracted considerable attention in both control and computer science. However, current advancements in consensus-based control theory lack a general framework to optimize the communication complexity required to reach consensus. This gap highlights the necessity of robust analytical frameworks to advance the field. Our proposed method, termed hierarchical random networks, decomposes the entire network into multiple random sub-swarms and constructs a hierarchical structure among these sub-swarms. First, we establish a simplified condition to ensure the connectivity of hierarchical random networks. Further, we prove that the expected number of network connections in hierarchical random networks can be reduced to its lower bound as the size of sub-swarms approaches the square root of the total number of agents. At the end of the paper, we validate the effectiveness of the proposed network topology through simulation case studies on maneuvering target tracking. The results demonstrate that combining hierarchical random networks with consensus-based filters can achieve maneuvering target tracking while reducing communication complexity.

This paper investigates the six degree-of-freedom (6DOF) relative kinodynamic motion planning problem for spacecraft close approach operations, wherein a controlled chaser spacecraft is required to approach a noncooperative space target at a close range under both dynamic constraints and motion constraints. An enhanced version of the bidirectional rapidly-exploring random tree* (BiRRT*) algorithm based on flight zoning (FZ-BiRRT*) is proposed to generate safe, feasible, and near-optimal relative motion trajectories. In the proposed algorithm, the space surrounding the space target is zoned in a spherical coordinate system based on the collision probability so that specific designs can be made for different phases of the approaching. Subsequently, based on the flight zone, dynamic constraints, and experiential knowledge, a series of modifications are made to the classic BiRRT* algorithm, and a postprocessing step is designed to accelerate convergence and promote search efficiency. Furthermore, a general regression neural network is introduced to fit a smooth and applicable final motion trajectory. Finally, the feasibility of the generated motion trajectory and the superiority of the proposed algorithm is demonstrated by means of numerical simulations

Lyapunov-based model predictive control (LMPC) is an effective approach for trajectory tracking because of its well-guaranteed and easy-to-implement stability. However, traditional LMPC utilizes pre-designed auxiliary controllers to estimate the domain of attraction (DOA) and construct stability constraints, which inevitably reduces its stable domain and degrades tracking performance. For this problem, this paper proposes a relaxed LMPC (RLMPC) which is designed independently of auxiliary controllers. The control Lyapunov function (CLF) is firstly introduced to decouple the DOA and auxiliary control, alleviating the conservatism in traditional LMPC. Subsequently, a multi-resolution sampling-based search algorithm is developed to estimate the DOA, where the state space is partitioned into hyper-rectangles. A verification condition is derived to extend the verification validity of sampling points to all states within hyper-rectangles, thereby reducing DOA estimation error. Based on the auxiliary-controller-independent DOA (ACI-DOA) and CLF, stability constraints are formulated to ensure stability for RLMPC, while relaxing the stable domain of RLMPC to the entire ACI-DOA. Furthermore, a convergence rate adaptive adjustment technology is developed to enhance the convergence rate while balancing it with control effort. Through numerical simulations involving asteroid orbiting missions, the proposed method is found to significantly expand the stable domain and improve tracking performance.

To solve the problem of the precise strike for seeker-less missile, a cooperative guidance method of seeker-less missile and the beacon aircraft is proposed. Firstly, the guidance law considering the miss distance and line-of-sight (LOS) angle constraint is designed to achieve the precise strike on the target and satisfy the LOS angle constraint. On this basis, the tangential load of the beacon aircraft is designed to ensure that the remaining flight time (time-to-go) for the missile and the beacon aircraft converge to the same value within a finite time, thus the seeker-less missile can indirectly strike the target precisely. Simulation results validate the effectiveness of the proposed method in addressing the problem of cooperative strike on target, and compared with the cooperative guidance method in reference, the proposed cooperative guidance method is better in strike accuracy and demand overload.

The multi-body dynamics in the launch process of a space platform deploying a server, as well as the optimal double impulse rendezvous guidance law between the server and the target spacecraft, are studied. Firstly, the space platform enters into orbit around the target, keeping its launch tube axis aiming at it. After receiving the launch command, the server shoots out from the launch tube, flying to the target. Due to body coupling, the platform’s attitude is disturbed, preventing the server from accurately aiming at the target during separation. The server uses its small rocket engine to apply two velocity pulses: the first one to adjust its trajectory for rendezvous, and the second near the target to reduce relative velocity to zero for soft docking. A two-body dynamics model is established using the Newton-Euler method, and a virtual prototype is developed in ADAMS for validation. To solve the multi-objective optimization subject to energy consumption and flight time for rendezvous, an improved non-dominated sorting genetic algorithm II (NSGA-II) algorithm is proposed. Simulation results show that launch-induced perturbations are non-negligible, and the proposed algorithm effectively derives the optimal guidance law that balances energy use and flight time.

To address the challenge of predicting reentry glide vehicle attack intention in no-fly zone scenarios, this paper proposes a multidimensional intention fusion-based inference method. Firstly, the recursive formula for the posterior probability of the vehicle’s intention is derived using Bayes’ theorem. Secondly, the concepts of pseudo heading deviation angle and endpoint relative energy are introduced to formulate an intention cost function that incorporates both angular and energetic dimensions, and the corresponding likelihood probability is obtained by quantifying the cost of different intentions, which solves the problem that the traditional cost function cannot characterize the real intention of the vehicle in scenarios involving no-fly zones. Finally, a dynamically weighted multidimensional intention fusion model is proposed to deduce the vehicle’s attack intent in the footprints. The simulation results show that the proposed method has a higher accuracy rate of intent inference compared to the existing methods.