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A multi-source clustered targets track association method based on dual-channel TCN-GRU
Xiao LING, Zhiqi CHEN, Guangyang DU, Qinghong SHENG
Journal of Systems Engineering and Electronics    2026, 37 (2): 367-376.   DOI: 10.23919/JSEE.2026.000091
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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.

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Robust azimuth ambiguity detection method in SAR images based on non-negative matrix factorization
Jieshuang LI, Mingliang TAO, Lei CUI, Yanyang LIU, Ling WANG
Journal of Systems Engineering and Electronics    2026, 37 (3): 743-754.   DOI: 10.23919/JSEE.2026.000067
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Azimuth ambiguity significantly degrades the quality of synthetic aperture radar images. Sub-look spectral analysis (SSA) is a common ambiguity-detection method, but its performance is limited by threshold sensitivity and the high correlation of specific ambiguities across sub-looks. To overcome these specific limitations, this paper proposes an improved detection method. It first increases the number of sub-looks and constructs a high-dimensional multi-look matrix to enrich the coherence differences between targets and ambiguities. Non-negative matrix factorization is then employed to decompose this matrix, effectively separating the coherent target components from the variably coherent ambiguity components without relying on predefined thresholds. Experimental results on real data demonstrate that the proposed improvements achieve superior azimuth-ambiguity-detection performance compared with conventional SSA methods.

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An evaluation framework for equipment contribution rate to system of systems based on operation loop and improved Shapley value
Cancan HU, Yaping WANG
Journal of Systems Engineering and Electronics    2026, 37 (3): 974-992.   DOI: 10.23919/JSEE.2026.000117
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The evaluation of the equipment contribution rate to system-of-systems (CRSoS) is crucial for optimizing the armament system-of-systems structure and enhancing combat effectiveness. The traditional relative contribution rate method poses limitations by focusing on individual equipment evaluation without considering the interrelations between equipment. In response to the issue, this study proposes a framework based on operation loop and improved Shapley value (OLISV) for analysis to ananlyze the equipment CRSoS. Specifically, a multi-layer network model is first constructed based on complex heterogeneous network and operation loop theory. Next, information entropy and evidence theory are used for the edges of the functional node layer, while improving the parallel node structure within the network. Subsequently, an improved Shapley value contribution rate method based on non-efficiency influencing factors is proposed. Finally, the rationality and effectiveness of the OLISV are illustrated through a case study.

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Three-dimensional interferometric direction-finding for non-planar antenna arrays
Wangjie CHEN, Weiqiang ZHU, Zhenhong FAN, Li WU, Yi HE
Journal of Systems Engineering and Electronics    2026, 37 (2): 377-392.   DOI: 10.23919/JSEE.2025.000117
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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.

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Research on the evaluation of dynamic decision-making effectiveness of UAV’s air combat
Shulin DING, Yuhui WANG, Haodi ZHANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 534-547.   DOI: 10.23919/JSEE.2026.000060
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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.

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CONTENTS
Journal of Systems Engineering and Electronics    2025, 36 (5): 0-0.  
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Cross-domain feature fusion and classification for weak target in sea clutter based on metric learning
Shichao CHEN, Mengke DING, Feng LUO
Journal of Systems Engineering and Electronics    2026, 37 (3): 755-766.   DOI: 10.23919/JSEE.2026.000056
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Cross-domain feature fusion offers an approach to weak target recognition in complex sea environments. This paper proposes a distance metric learning-based method for weak target classification. The method first extracts three time-domain features and three frequency-domain features from radar echo signals. Then, the features are partitioned and mapped to low-dimensional subspaces using linear projection matrices. The squared Euclidean distance is used as a metric function to measure the similarity between samples, and supervised optimization is performed by introducing information from similar and dissimilar sample pairs. Next, the projection matrices of each group are jointly updated iteratively using the gradient descent method to achieve supervised feature fusion. Finally, the fused feature is input into an ensemble one-class support vector machine (EOCSVM) for classification. Verified by IPIX measured data, the proposed method can effectively improve the separability of targets and sea clutter and improve the classification ability of sea clutter and weak targets under short-time observation. The proposed method enhances the features correlation from different domains through metric learning and EOCSVM, which can effectively alleviate the sample imbalance problem between sea clutter and targets.

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Multiple point cloud encryption based on principal component analysis and fractional Fourier transform
Xinze LI, Lei YU, Jiafa NIE, Yan SUN
Journal of Systems Engineering and Electronics    2026, 37 (2): 393-411.   DOI: 10.23919/JSEE.2026.000092
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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.

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Three-dimensional path planning algorithm for UAV based on obstacle envelopes
Yuzhen ZHOU, Yao LIU, Jincai HUANG, Jianmai SHI
Journal of Systems Engineering and Electronics    2026, 37 (3): 1042-1058.   DOI: 10.23919/JSEE.2026.000126
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In this paper, a three-dimension envelope-based path planning algorithm (3DE-PP) is proposed to automatically generate a collision-free trajectory for unmanned aerial vehicle (UAV). Firstly, focusing on the defects of low efficiency of obstacle modelling representation and large search space, an elliptical envelope-based obstacle modelling method is proposed to facilitate the generation of obstacle avoidance waypoints and improve the search efficiency. Then, considering safety and aiming at minimum energy consumption, waypoint generation strategies based on tangent guidance and minimum deviation are designed. Meanwhile, aiming at the UAV motion constraint, a three-dimension (3D) path construction method based on improved Dubins is proposed. Finally, combined with the main path generation algorithm based on saving algorithm, a safe and feasible 3D flight path is constructed by considering the power constraint of UAV and the access of charging stations comprehensively. The proposed 3DE-PP is compared with four algorithms (SAS, Dubins-RRT*, APF, 3D-TG) by 15 examples generated from five typical environments, and the computational results confirm its advantages. Furthermore, a real-world case is introduced, and the key factors influencing path planning are analyzed.

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A game theoretic model and a double oracle algorithm for the heterogeneous weapon target assignment problem
Yingying MA, He LUO, Guoqiang WANG, Waiming ZHU, Xiaoxuan HU
Journal of Systems Engineering and Electronics    2026, 37 (2): 548-566.   DOI: 10.23919/JSEE.2026.000065
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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.

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Odd-even dimension RUNge Kutta optimization algorithm and its application
Lin WANG, Yingying PI, Xuerui WANG
Journal of Systems Engineering and Electronics    2026, 37 (3): 878-896.   DOI: 10.23919/JSEE.2026.000115
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This research proposes an odd-even dimension RUNge Kutta algorithm (ODRUN) to solve global optimization and a well-known NP-hard problem in inventory management. The rpoposed algorithm integrates odd-even dimensional, fourth-order Runge-Kutta method, and neighbor search strategies. This hybrid approach significantly improves population diversity, avoids local optima, and enhances convergence accuracy. To validate the performance of the proposed algorithm, a widely recognized benchmark function suit from CEC2022 is first employed. Results confirm that ODRUN achieves an overall effectiveness ratio of 66.67% across three statistical indicators (best, mean, and standard deviation) for 12 benchmark functions. The test shows this algorithm is ranked first compared to seven state-of-the-art metaheuristic algorithms. Furthermore, ODRUN is applied to the joint replenishment problem with imperfect items and trade credit. Numerical examples from 600 randomly generated large-scale instances highlight that the algorithm’s performance remains unaffected by an increase in problem scale. The significant cost savings brought by the ODRUN algorithm, with the maximum improvement ratio in average cost and best-found total cost ranging from 14.81% to 19.5%, are achieved in comparison to other algorithms. In conclusion, ODRUN is an effective and robust tool for complex optimization problems.

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High-dimensional robust nested parallel streaming adaptive processor
Gang WU, Zhongping HUANG, Zhiyong LEI
Journal of Systems Engineering and Electronics    2026, 37 (2): 431-444.   DOI: 10.23919/JSEE.2025.000042
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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.

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Integrated modeling for civil aircraft PHM and maintenance support based on DoDAF and MBSE
Jie CHEN, Gaofei ZHANG, Ke GAO, Bijiang LV, Chen LI, Chang SUN
Journal of Systems Engineering and Electronics    2026, 37 (3): 904-920.   DOI: 10.23919/JSEE.2026.000116
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Integrating prognostics and health management (PHM) with the existing maintenance support system of systems plays an important role in implementing reliability-centered maintenance (RCM). However, the increasing complexity and integration of civil aircraft systems pose challenges for conventional document-based systems engineering (DBSE) practice. Aiming at the specific problems of poor modeling degree, weak traceability between problem and solution domains, and insufficient integration in civil aircraft PHM development, a model-based systems engineering (MBSE) approach is adopted to overcome the limitations of DBSE method. This paper proposes a structured integrated modeling method to facilitate PHM functional integration with other aircraft systems. An MBSE modeling method based on traceable requirements, functional, logical, and physical models, is applied in the integration process. Additionally, a multi-viewpoint analysis method within the Department of Defense Architecture Framework (DoDAF) is introduced to illustrate the modeling elements and processes from a multi-dimensional perspective. The modeling logic and architecture are subsequently presented, followed by examples of requirements, functional flows, and resource flows models using the systems modeling language (SysML). Finally, a preliminary logic simulation verification is conducted as a case study of typical PHM functional integration with maintenance support. The case study results demonstrate that the proposed method enhances information traceability and consistency, which can offer theoretical support and technical reference for the development of maintenance support system.

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Joint intra-frame and inter-frame imaging algorithm for spaceborne ISAR imaging of air target
Yichen ZHOU, Yong WANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 412-430.   DOI: 10.23919/JSEE.2025.000014
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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.

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MMF-SLR: a sign language recognition method based on multi-modal feature using millimeter-wave radar
Chang CUI, Guiyan WEI, Xichao DONG, Cheng HU, Jianping WANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 357-366.   DOI: 10.23919/JSEE.2026.000061
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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.

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Hierarchical random networks for optimizing communication complexity of consensus-based networks
Yuqi WANG, Yun ZHANG, Yunze CAI
Journal of Systems Engineering and Electronics    2026, 37 (2): 636-651.   DOI: 10.23919/JSEE.2025.000152
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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.

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Research on anti-active mainlobe interference methods for frequency diverse array radar
Bo WANG, Yonglin LI, Gang WANG, Rennong YANG, Yu ZHAO
Journal of Systems Engineering and Electronics    2026, 37 (2): 455-466.   DOI: 10.23919/JSEE.2025.000058
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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.

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Evaluation approaches for spatial targets localization precision based on observation matrix condition number
Xinyong ZHANG, Zhangming HE, Xuanying ZHOU, Huiyu CHEN, Jiongqi WANG, Haiyin ZHOU
Journal of Systems Engineering and Electronics    2026, 37 (2): 445-454.   DOI: 10.23919/JSEE.2025.000049
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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.

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CONTENTS
Journal of Systems Engineering and Electronics    2025, 36 (6): 0-0.  
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On-orbit servicing launch dynamics and multi-objective optimization of impulsive rendezvous
Weikang LI, Ju JIANG, Yue BIAN, Yanhua HAN
Journal of Systems Engineering and Electronics    2026, 37 (2): 697-711.   DOI: 10.23919/JSEE.2025.000123
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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.

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Two-phase pairwise comparison-based model for the ranking prediction of global innovation capability
Ruijing CUI, Jianbin SUN, Kewei YANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 504-520.   DOI: 10.23919/JSEE.2025.000018
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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.

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High-precision calibration of binocular camera with super-resolution technology
Ting SUN, Chao MA, Tian SUN, Shanshan PEI, Qian LONG
Journal of Systems Engineering and Electronics    2026, 37 (3): 844-860.   DOI: 10.23919/JSEE.2026.000105
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The calibration of parameters for onboard stereo cameras is crucial for achieving efficient visual-assisted driving. However, in practical scenarios, low-resolution images often result in inaccuracies in feature point extraction, thereby affecting the accuracy of camera parameter calibration. To address this issue, this paper proposes a self-calibration method for stereo cameras based on joint de-noising, de-mosaic, de-ringing, and super-resolution network (JDDDSN) super-resolution reconstruction. By reconstructing images into higher-resolution images with richer details, feature points are extracted for extrinsic calibration of stereo cameras. For real-world driving scenarios, the reconstructed images achieve noise and ringing artifact reduction while obtaining clearer high-resolution images. This study further investigates the impact of the super-resolution reconstruction network on target area calibration at various distances. Additionally, it highlights the significant role of super-resolution in enhancing stereo camera calibration accuracy by removing dynamic points and focusing on static regions. Through a series of experiments, this paper validates the effectiveness and practicality of the JDDDSN super-resolution reconstruction network in improving stereo camera calibration accuracy, demonstrating its application value in the field of stereoscopic vision.

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Uncertainty quantification for the ascent phase of launch vehicles using Bayesian inference
Tao CHAO, Xiaonan LI, Xiaobing SHANG, Ping MA, Ming YANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 485-503.   DOI: 10.23919/JSEE.2026.000063
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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.

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The effect of network structure on bounded confidence opinion dynamics
Miao DU, Jianfeng CAI
Journal of Systems Engineering and Electronics    2026, 37 (2): 521-533.   DOI: 10.23919/JSEE.2026.000057
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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.

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Attitude estimation of space target based on ISAR contour projection plane alignment
Dan LIU, Yuzhe FAN, Lin’gang FAN, Chengzeng CHEN, Yan DAI
Journal of Systems Engineering and Electronics    2026, 37 (2): 467-484.   DOI: 10.23919/JSEE.2026.000055
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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.

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Cooperative guidance method for seeker-less missile and beacon aircraft
Zhengxin TAO, Shifeng ZHANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 687-696.   DOI: 10.23919/JSEE.2026.000094
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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.

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Structured robust principal component analysis for infrared small target detection
Yongqiang ZHANG, Yongji LI, Meng CAI, Ye ZHANG, Yong TAN
Journal of Systems Engineering and Electronics    2026, 37 (3): 779-787.   DOI: 10.23919/JSEE.2026.000093
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Extracting infrared small targets from heterogeneous backgrounds remains a challenging task, as these targets lack salient texture and morphological features while the backgrounds are cluttered with noise. Therefore, effectively extracting discriminative features is essential for achieving complete and accurate detection. To address this issue, this paper proposes an algorithmic framework based on robust principal component analysis (RPCA), specifically designed for infrared small target detection in complex backgrounds. First, infrared small target detection is formulated as a generalized RPCA problem. A discriminative and reconstructive dictionary is constructed using supervised learning. Next, by introducing an ideal regularization term, the infrared image is reconstructed without losing structural information, yielding a discriminative principal component representation with respect to the learned dictionary. Finally, the structural features of infrared small targets are reconstructed via sparse coding, thereby enabling the extraction of infrared small targets. Extensive experimental results demonstrate the effectiveness of the proposed method.

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Dual-frequency aperiodic planar scanning array with diversified radiation elements
Hailing JIANG, Ke DU
Journal of Systems Engineering and Electronics    2026, 37 (3): 861-866.   DOI: 10.23919/JSEE.2026.000109
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A dual-frequency aperiodic planar scanning array with diversified radiation elements is proposed. The proposed element consists of an elliptic patch and two parasitic rectangular patches, which can work both at 5.28?5.33 GHz with difference radiation beam and 5.78?5.83 GHz with sum radiation beam. A four equivalent magnetic currents model has been established to explain the radiation principle of the proposed element. Compared to the beamwidth of the sum beam, the 3 dB beamwidth of the difference beam is broadened about 30% and the radiation gain of the sum beam is obviously improved about 48%. A 64-element aperiodic array with diversified radiation elements is constructed. The array can scan at a wide angle of ±70° with no grating lobes at difference radiation mode and can scan in the range of ±60° with high gain at sum radiation mode.

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Model construction and topology analysis of logistics equipment system-of-systems heterogeneous network
Fanghua YANG, Cong JIN, Zihan ZHAO, Yanjing LU, Pei LI
Journal of Systems Engineering and Electronics    2026, 37 (2): 594-603.   DOI: 10.23919/JSEE.2026.000078
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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.

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Trajectory tracking near asteroids using relaxed Lyapunov-based model predictive control
Zhitong YU, Haibin SHANG, Zichen ZHAO, Xuefen ZHANG
Journal of Systems Engineering and Electronics    2026, 37 (2): 670-686.   DOI: 10.23919/JSEE.2026.000098
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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.

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DOA estimation via a Newton-like method under unknown mutual coupling
Jihui LYU, Shuai LIU, Ming JIN, Fenggang YAN, Lizhong SONG
Journal of Systems Engineering and Electronics    2026, 37 (3): 826-835.   DOI: 10.23919/JSEE.2026.000110
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As is well known, mutual coupling between array elements has a significant negative impact on direction of arrival (DOA) estimation. To achieve DOA estimation under unknown mutual coupling, this paper proposes a low computational complexity Newton-like method. Firstly, a block sparse model based on the signal subspace is established, and the Lagrangian function is established according to the block sparse model. Secondly, since the Hessian matrix of the Lagrangian function cannot always ensure positive definiteness and the computational complexity of the inverse matrix of the Hessian matrix is enormous, the Newton method is no longer applicable. Therefore, this paper proposes a Newton-like method to achieve DOA estimation under mutual coupling and reduce the computational complexity by matrix inversion lemma. Finally, compared with existing methods of DOA estimation under array mutual coupling, the simulation results validate the effectiveness of the proposed method.

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Multi-stage forest UAV route design based on multi-strategy GA
Wangying XU, Naiming XIE
Journal of Systems Engineering and Electronics    2026, 37 (3): 964-973.   DOI: 10.23919/JSEE.2026.000119
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Forest fires are characterized by their abrupt onset and highly destructive nature, resulting in significant annual property losses. Hence, regular surveillance is imperative for forest fire prevention and mitigation. The fundamental challenge in patrolling is akin to the problem of helicopter route planning. Conventional unmanned aerial vehicle (UAV) path planning commonly entails single-trip missions. Considering the extensive and complex forest environments, we advocate a multi-stage UAV reconnaissance strategy to address the daily inspection route planning conundrum. This approach facilitates UAVs to conduct round-trip flights between designated surveillance points and the base station at diverse time intervals, effectively satisfying the requirements for multi-tiered, hierarchical reconnaissance. Furthermore, we develop an advanced multi-strategy genetic algorithm (MSGA) to optimize the multi-stage reconnaissance model. Experimental outcomes underscore the superior performance of the enhanced MSGA, achieving a reduction of nearly 20% in total flight path length relative to the traditional genetic algorithm. This methodology significantly enhances the efficacy of daily forest patrols.

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Application of self-play reinforcement learning and explainable decision tree in intelligent air combat
Jingbo WANG, Liaoyuan ZHU, Shaojie XIA, Huibin LIU, Jing LIU, Chongxiao QU, Zhihuan SONG
Journal of Systems Engineering and Electronics    2026, 37 (2): 616-635.   DOI: 10.23919/JSEE.2026.000079
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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.

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FZ-BiRRT*-based 6DOF relative motion planning for spacecraft close approaching maneuver
Ruichao FAN, Kerun LIU, Ming LIU
Journal of Systems Engineering and Electronics    2026, 37 (2): 652-669.   DOI: 10.23919/JSEE.2026.000097
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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

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Fault-tolerant control of hypersonic morphing vehicle based on the predefined-time disturbance observer
Yiheng LI, Wenjie ZHANG, Mingkai WANG, Qunli XIA, Yangxin LIU
Journal of Systems Engineering and Electronics    2026, 37 (3): 1019-1029.   DOI: 10.23919/JSEE.2026.000125
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To address the attitude control problem under the uncertainty, external disturbance, and actuator failure, a predefined-time fault-tolerant control method based on a predefined time disturbance observer is proposed. First, the dynamics model of hypersonic morphing vehicle (HMV) is established, and the control system is designed as an outer-loop attitude angle control loop and an inner-loop angular rate control loop considering the actuator failure problem. Secondly, a predefined-time disturbance observer is designed to estimate the comprehensive disturbances, and compensate in the control law. By integrating back-stepping control with predefined-time theory, a predefined-time attitude tracking control method is proposed, enabling the convergence time of the attitude tracking error to be designed through a simple parameter. Rigorous Lyapunov function analysis has demonstrated that the attitude tracking error can converge to an arbitrarily small neighborhood around the origin within a predefined time, and all signals in the closed-loop system are bounded. Finally, comparative simulations validate the effectiveness of the proposed method.

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Cascaded ensemble learning for efficient and high-accuracy direction of arrival estimation
Guimei ZHENG, Liyuan XIAO, Yu ZHENG, Saiyu ZHANG
Journal of Systems Engineering and Electronics    2026, 37 (3): 800-815.   DOI: 10.23919/JSEE.2026.000101
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Aiming at the issues where traditional direction-of-arrival (DOA) estimation algorithms experience substantial performance degradation in low signal-to-noise ratio environments, and deep learning-based DOA estimation methods rely on massive training data with prolonged model training cycles, this paper proposes two efficient and high-precision DOA estimation methods based on ensemble learning. By formulating DOA estimation as a multi-label classification problem and leveraging the classification chain paradigm, data-driven models, classification chain-random forest (CC-RF) and classification chain-eXtreme gradient boosting (CC-XGBoost), are constructed, which are capable of handling multi-label classification tasks. To verify the effectiveness of the proposed methods, a multi-dimensional comparative experiment is designed to benchmark their performance against the traditional multiple signal classification (MUSIC) algorithm and a convolutional neural network (CNN) model. Experimental results indicate that in both single-source and multi-source scenarios, the proposed CC-RF algorithm exhibits excellent performance, achieving DOA estimation accuracy comparable to the MUSIC algorithm; in multi-source estimation scenarios, both proposed models demonstrate strong noise adaptability. Compared with the traditional MUSIC and CNN algorithms, the estimation error of the CC-XGBoost and CC-RF models is reduced by up to nearly 30 times while maintaining low time complexity, with the single estimation time reduced by approximately 90% compared to traditional methods. This study provides a technical pathway for DOA estimation in complex environments and holds significant application value in fields such as radar detection and wireless communication.

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Multi-scale optical convolutional neural network for target classification
Zijian YU, Lijing LI, Siyuan WANG, Yue ZHENG
Journal of Systems Engineering and Electronics    2026, 37 (3): 816-825.   DOI: 10.23919/JSEE.2026.000059
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The physical architecture of optical convolution restricts its capacity to capture multi-scale features from targets, thus impeding the precision of network recognition. In this work, we propose a multi-scale optical convolutional neural network (MS-OCNN), which uses convolution kernels with different resolutions in the convolution layer to extract different scale features, along with attention mechanism and residual structure to analyze features. By separating the training and inference platforms of the network, we facilitate the electronic training of model parameters on a computer and the optical deployment on a system equipped with a spatial light modulator, enabling efficient target classification. The proposed MS-OCNN exhibits 1% to 3% improvement in classification performance on the modified national institute of standards and technology (MNIST) and Fashion-MNIST datasets compared to single-scale optical inference models. Online experimental systems in real-world scenarios have validated the target recognition capabilities of this method, which yielded classification accuracies of 97% and 87% on the MNIST and Fashion-MNIST datasets, respectively. This work enhances the feature acquisition capabilities of optical convolutional networks, elevates network recognition accuracy, and significantly propels the application of optical computing in domains such as guidance systems, autonomous driving, and robotics.

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High isolation dual circularly polarized antenna in gap waveguide technology for mm-Wave satellite communications
Shuanglong QUAN, Jianyin CAO, Chao HE, Hao WANG
Journal of Systems Engineering and Electronics    2026, 37 (3): 836-843.   DOI: 10.23919/JSEE.2025.000031
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A millimeter-wave (mm-Wave) dual circularly polarized (CP) antenna in gap waveguide (GWG) technology with high port isolation is proposed in this paper. It is consisted of a simplified orthomode transducer (OMT) and an improved multi-section hexagonal waveguide CP horn antenna. The OMT is composed of two metal layers without the traditional septum or iris, which makes the structure simpler. The CP horn antenna can be easily integrated with the OMT without mode conversion. The principle analysis as well as the simulated and measured results of the proposed antenna are given in this paper. The simulated and measured results agree very well with each other. The port isolation of more than 27 dB over bandwidth of 26.5?31 GHz (|S11|< ?15 dB) is achieved with relative bandwidth of 15.7%. The axial ratio (AR) lower than 2.5 dB for both left-hand and right-hand CP (LHCP and RHCP) are achieved over the bandwidth. The proposed antenna is a candidate for mm-Wave satellite communications or beyond fifth-generation (5G) communications applications.

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Heterogeneous multi-core task scheduling based on adaptive simulated annealing
Guoliang ZHU, Jinjian ZHANG, Xuan LIU, Guojun WANG, Xiaodong ZHANG, Kaiyu CHEN, Yu WANG
Journal of Systems Engineering and Electronics    2026, 37 (3): 897-903.   DOI: 10.23919/JSEE.2026.000042
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To address the energy consumption issues caused by task lengths in task scheduling on heterogeneous multi-core systems, this paper proposes an adaptive parameterized improved simulated annealing algorithm based on the directed acyclic graph task model. The algorithm employs feedback from acceptance rates to dynamically adjust the temperature and neighborhood size of the simulated annealing process. Additionally, it introduces a security mechanism to enhance convergence speed and global search capabilities. Compared against classical simulated annealing and standard heuristic algorithms, the proposed algorithm achieves reductions exceeding 54% in convergence generations, 50% in task slots, and 10% in scheduling time, providing a direction for low-power task scheduling.

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Online reentry guidance algorithm based on trajectory analytical solutions
Weibo SUN, Ping MA, Xiaonan LI, Songyan WANG, Tao CHAO
Journal of Systems Engineering and Electronics    2026, 37 (3): 1002-1018.   DOI: 10.23919/JSEE.2026.000089
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To enhance the real-time performance and accuracy of guidance command generation, we propose an online reentry guidance algorithm based on analytical solutions of the hypersonic glide trajectory (HGT). Initially, an altitude-velocity profile is designed in the longitudinal plane to satisfy both path and terminal constraints. Based on this profile, we derive analytical solutions for the flight path angle (FPA) and bank angle. Subsequently, by employing the Newton-Raphson method to linearize the reentry motion equations, analytical solutions for the latitude and heading angle are obtained. Furthermore, we introduce an improved particle swarm optimization (IPSO) algorithm to optimize the profile parameters. This approach significantly enhances the algorithm’s global convergence by narrowing the parameter optimization range and adaptively adjusting the inertia weight and cognitive factors. Finally, we present an online guidance algorithm that combines the HGT analytical solutions with the IPSO algorithm. This algorithm effectively achieves longitudinal and lateral guidance by continuously updating the altitude-velocity profile and bank angle symbol in real time. Simulation results demonstrate that the proposed algorithm is fast, efficient, accurate, and holds significant potential for broader application.

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