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Optimization of the frequency offset increment of FDA-MIMO based on cuckoo search algorithm
Bo WANG, Yu ZHAO, Yonglin LI, Rennong YANG, Junjie XUE
Journal of Systems Engineering and Electronics    2026, 37 (1): 157-170.   DOI: 10.23919/JSEE.2026.000001
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Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar has gained considerable research attention due to its ability to effectively counter active repeater deception jamming in complex electromagnetic environments. The effectiveness of interference suppression by FDA-MIMO is limited by the inherent range-angle coupling issue in the FDA beampattern. Existing literature primarily focuses on control methods for FDA-MIMO radar beam direction under the assumption of static beampatterns, with insufficient exploration of techniques for managing nonstationary beam directions. To address this gap, this paper initially introduces the FDA-MIMO signal model and the calculation formula for the FDA-MIMO array output using the minimum variance distortionless response (MVDR) beamformer. Building on this, the problem of determining the optimal frequency offset for the FDA is rephrased as a convex optimization problem, which is then resolved using the cuckoo search (CS) algorithm. Simulations confirm the effectiveness of the proposed approach, showing that the frequency offsets obtained through the CS algorithm can create a dot-shaped beam direction at the target location while effectively suppressing interference signals within the mainlobe.

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Joint beamforming design for low probability of intercept in transmit subaperturing MIMO radar
Jiale WU, Chenguang SHI, Zhifeng WU, Jianjiang ZHOU
Journal of Systems Engineering and Electronics    2026, 37 (1): 94-103.   DOI: 10.23919/JSEE.2025.000098
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In this paper, the joint design of transmit and receive beamformers for transmit subaperturing multiple-input-multiple-output (TS-MIMO) radar is investigated, aiming to enhance its low probability of intercept (LPI) capability. The main objective is to simultaneously minimize the transmission power, suppress the transmit sidelobe levels, and minimize the probability of intercept, thus bolstering the LPI performance of the radar system while maintaining the desired target detection performance. An alternative optimization method is proposed to jointly optimize the transmit and receive beamformers, yielding an unified LPI optimization framework. Particularly, the proposed iterative algorithm based on the Lagrange duality theory for transmit beamforming is more efficient than the conventional convex optimization method. Numerical experiments highlight the effectiveness of the proposed approach in sidelobe suppression and computational efficiency.

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λ-return-based aircraft maneuvering for terminal defense and positioning guidance strategies
Shijie DENG, Yingxin KOU, Maolong LYU, Zhanwu LI, An XU
Journal of Systems Engineering and Electronics    2025, 36 (6): 1692-1708.   DOI: 10.23919/JSEE.2025.000112
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Aiming at the terminal defense problem of aircraft, this paper proposes a method to simultaneously achieve terminal defense and seize the dominant position. The method employs a λ-return based reinforcement learning algorithm, which can be applied to the flight assistance decision-making system to improve the pilot’s survivability. First, we model the environment to simulate the interaction between air-to-air missiles and aircraft. Subsequently, we propose a λ-return based approach to improve the deep Q learning network (DQN), deep advantageous actor criticism (A2C), and proximity policy optimization (PPO) algorithms used to train manoeuvre strategies. The method employs an action space containing nine manoeuvres and defines the off-target distance at the end of the scene as a sparse reward for algorithm training. Simulation results show that the convergence speed of the three improved algorithms is significantly improved when using the λ-return method. Moreover, the effect of the fetch value on the convergence speed is verified by ablation experiments. In order to solve the illegal behavior problem in the training process, we also design a backtracking-based illegal behavior masking mechanism, which improves the data generation efficiency of the environment model and promotes effective algorithm training.

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Adversarial robustness evaluation based on classification confidence-based confusion matrix
Xuemei YAO, Jianbin SUN, Zituo LI, Kewei YANG
Journal of Systems Engineering and Electronics    2026, 37 (1): 184-196.   DOI: 10.23919/JSEE.2026.000053
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Evaluating the adversarial robustness of classification algorithms in machine learning is a crucial domain. However, current methods lack measurable and interpretable metrics. To address this issue, this paper introduces a visual evaluation index named confidence centroid skewing quadrilateral, which is based on a classification confidence-based confusion matrix, offering a quantitative and visual comparison of the adversarial robustness among different classification algorithms, and enhances intuitiveness and interpretability of attack impacts. We first conduct a validity test and sensitive analysis of the method. Then, prove its effectiveness through the experiments of five classification algorithms including artificial neural network (ANN), logistic regression (LR), support vector machine (SVM), convolutional neural network (CNN) and transformer against three adversarial attacks such as fast gradient sign method (FGSM), DeepFool, and projected gradient descent (PGD) attack.

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Improved simulated annealing algorithm for UAV path planning with uncertain flight time
Xiaoduo LI, He LUO, Guoqiang WANG, Youlong YIN
Journal of Systems Engineering and Electronics    2026, 37 (1): 272-286.   DOI: 10.23919/JSEE.2026.000010
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Efficient multiple unmanned aerial vehicles (UAVs) path planning is crucial for improving mission completion efficiency in UAV operations. However, during the actual flight of UAVs, the flight time between nodes is always influenced by external factors, making the original path planning solution ineffective. In this paper, the multi-depot multi-UAV path planning problem with uncertain flight time is modeled as a robust optimization model with a budget uncertainty set. Then, the robust optimization model is transformed into a mixed integer linear programming model by the strong duality theorem, which makes the problem easy to solve. To effectively solve large-scale instances, a simulated annealing algorithm with a robust feasibility check (SA-RFC) is developed. The numerical experiment shows that the SA-RFC can find high-quality solutions within a few seconds. Moreover, the effect of the task location distribution, depot counts, and variations in robustness parameters on the robust optimization solution is analyzed by using Monte Carlo experiments. The results demonstrate that the proposed robust model can effectively reduce the risk of the UAV failing to return to the depot without significantly compromising the profit.

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Optimal competitive resource assignment in two-stage Colonel Blotto game with Lanchester-type attrition
Weilin YUAN, Shaofei CHEN, Zhenzhen HU, Xiang JI, Lina LU, Xiaolong SU, Jing CHEN
Journal of Systems Engineering and Electronics    2026, 37 (1): 242-256.   DOI: 10.23919/JSEE.2023.000165
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In strategic decision-making tasks, determining how to assign limited costly resource towards the defender and the attacker is a central problem. However, it is hard for pre-allocated resource assignment to adapt to dynamic fighting scenarios, and exists situations where the scenario and rule of the Colonel Blotto (CB) game are too restrictive in real world. To address these issues, a support stage is added as supplementary for pre-allocated results, in which a novel two-stage competitive resource assignment problem is formulated based on CB game and stochastic Lanchester equation (SLE). Further, the force attrition in these two stages is formulated as a stochastic progress to consider the complex fighting progress, including the case that the player with fewer resources defeats the player with more resources and wins the battlefield. For solving this two-stage resource assignment problem, nested solving and no-regret learning are proposed to search the optimal resource assignment strategies. Numerical experiments are taken to analyze the effectiveness of the proposed model and study the assignment strategies in various cases.

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Prelaunch rolling suppression for maritime rockets using RF-AdaBoost
Deng WANG, Wenhao XIAO, Jianshuai SHAO, Yi JIANG
Journal of Systems Engineering and Electronics    2026, 37 (1): 197-210.   DOI: 10.23919/JSEE.2026.000048
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Prelaunch rolling of maritime rockets threatens the reliability of launch in rough sea conditions. In order to suppress the prelaunch rolling, this study introduces advanced smart prediction designed especially for maritime rockets. The suggested approach introduces a hybrid model that combines random forest (RF) and Adaptive boosting (AdaBoost) methods to describe the coupling mechanism of factors affecting rocket rolling and to suppress the rolling. This combination improves forecast accuracy. Thereafter, the dimensionality reduced response surfaces are used to visually present the coupling between rocket rolling and influencing factors, which reveals the prelaunch rolling mechanism. When angle between the launch device and the ship’s bow is within 80°?100°, the dynamic friction coefficient between adapters and guideways is 0.4, and the dynamic friction coefficient between the rocket and launchpad is within 0?0.15 or 0.5?0.7, the prelaunch rolling of rocket during one motion cycle of the ship is less than 0.065°, originally 0.27°, reduced by 75.93%, effectively suppressing the prelaunch rolling. This study improves the prelaunch stability of maritime rockets in rough sea conditions and establishes a mapping relationship between the factors affecting rocket rolling and the structure of the sea launch system, guiding the optimization of future sea launch systems.

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Collaborative scheduling problem pertaining to launch and recovery operations for carrier aircraft
Fang GUO, Wei HAN, Yujie LIU, Xichao SU, Jie LIU, Changjiu LI
Journal of Systems Engineering and Electronics    2026, 37 (1): 287-306.   DOI: 10.23919/JSEE.2026.000043
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The proliferation of carrier aircraft and the integration of unmanned aerial vehicles (UAVs) on aircraft carriers present new challenges to the automation of launch and recovery operations. This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft, where launch and recovery tasks are conducted concurrently on the flight deck. The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft. To tackle this challenge, a multiple population self-adaptive differential evolution (MPSADE) algorithm is proposed. This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity, an asynchronous updating scheme, an individual migration operator, and a global crossover mechanism. Additionally, comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm. Ultimately, a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.

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Pseudo-spectrum based track-before-detect for bistatic radar network
Tao HAN, Gongjian ZHOU
Journal of Systems Engineering and Electronics    2026, 37 (1): 127-136.   DOI: 10.23919/JSEE.2025.000046
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This paper addresses weak target detection problem for bistatic radar via a pseudo-spectrum (PS) based track-before- detect (TBD). Generally, PS-TBD estimates target position and velocity by means of pseudo-spectrum construction in the discrete measurement space and accurate energy accumulation in mixed coordinates. However, the grids within the polar sensing region of the receivers in the bistatic radar are not aligned. Traditional PS-TBD can not directly process these measurements. In this paper, a PS-TBD method for bistatic radar is proposed to overcome this problem. Each cell in the measurement space of the receivers is mapped to the aligned Cartesian coordinates and predicted to the integration frame according to the assumed filter velocity. A PS is formulated centered on the predicted Cartesian position. Then the samples of the pseudo-spectra are accumulated to the nearest cell around the predicted Cartesian position. The procedure of the energy integration is derived in detail. Simulation results validate the efficacy of the proposed method in terms of detection accuracy and parameter estimation.

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Scattered field calculation and angular glint analysis in near-field region
Bin CHEN, Tongxin DANG, Kaibin ZHAGN, Yiming LI
Journal of Systems Engineering and Electronics    2026, 37 (1): 104-111.   DOI: 10.23919/JSEE.2025.000056
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The theoretical implementation aspects of scattered field prediction and angular glint calculation in near-field region are proposed in this work. First of all, a more refined expression of the Green function is developed. In this representation, an expansion center is adopted within the neighborhood of the sources. Then a high-frequency electromagnetic scattering evaluation algorithm is formulated, combining the refined physical optics (PO) and equivalent edge current (EEC) algorithm. The modified method not only retains the conciseness and efficiency of the standard code but also can be directly used in the near field (NF) scattering estimation. Afterwards, two basic concepts of the angular glint are briefly introduced and formulated. The proposed procedure makes preparation for the computation of NF linear deviation. Numerical examples demonstrate the accuracy and efficiency of the NF scattering prediction algorithm. The angular glint characteristics in near-field scenarios are also presented and analyzed in the final section.

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Enhancing convolution for Transformer-based weakly supervised semantic segmentation
Yu LIU, Diaoyin TAN, Wen ZHOU, Huaxin XIAO
Journal of Systems Engineering and Electronics    2026, 37 (1): 84-93.   DOI: 10.23919/JSEE.2025.000165
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Weakly supervised semantic segmentation (WSSS) is a tricky task, which only provides category information for segmentation prediction. Thus, the key stage of WSSS is to generate the pseudo labels. For convolutional neural network (CNN) based methods, in which class activation mapping (CAM) is proposed to obtain the pseudo labels, and only concentrates on the most discriminative parts. Recently, transformer-based methods utilize attention map from the multi-headed self-attention (MHSA) module to predict pseudo labels, which usually contain obvious background noise and incoherent object area. To solve the above problems, we use the Conformer as our backbone, which is a parallel network based on convolutional neural network (CNN) and Transformer. The two branches generate pseudo labels and refine them independently, and can effectively combine the advantages of CNN and Transformer. However, the parallel structure is not close enough in the information communication. Thus, parallel structure can result in poor details about pseudo labels, and the background noise still exists. To alleviate this problem, we propose enhancing convolution CAM (ECCAM) model, which have three improved modules based on enhancing convolution, including deeper stem (DStem), convolutional feed-forward network (CFFN) and feature coupling unit with convolution (FCUConv). The ECCAM could make Conformer have tighter interaction between CNN and Transformer branches. After experimental verification, the improved modules we propose can help the network perceive more local information from images, making the final segmentation results more refined. Compared with similar architecture, our modules greatly improve the semantic segmentation performance and achieve 70.2% mean intersection over union(mIoU) on the PASCAL VOC 2012 dataset.

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Research on comprehensive evaluation of six properties of equipment product with relevant attributes based on DEMATEL-ANP-ELECTRE
Jian QIN, Wenhui MEI
Journal of Systems Engineering and Electronics    2026, 37 (1): 318-326.   DOI: 10.23919/JSEE.2026.000007
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The comprehensive evaluation of six properties for equipment product is an important basis for their quality control, and their correlative relationship among six properties will affect their quality level. To understand their correlative relationship among six properties, this paper firstly combines group evaluation with decision-making trial and evaluation laboratory (DEMATEL) model, and develops the optimization model based on group consensus to form six influent relationship matrices. Secondly, group consensus matrix is used to design super network hierarchy matrix, and the weights of six properties with relevant environment is also proposed. Thirdly, the elimination and choice translating reality (ELECTRE) model is used to make comprehensive evaluation, and an example is used to compare the results under two kinds of conditions, and illustrate the effect of the weights of six properties on the priority of equipment products.

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Miniaturized two-photon microscopy system for extreme shock and vibration environment
Bosong YU, Junjie WANG, Yizhou LIU, Conghao WANG, Honghao MA, Lishuang FENG, Aimin WANG
Journal of Systems Engineering and Electronics    2025, 36 (6): 1658-1664.   DOI: 10.23919/JSEE.2025.000086
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Two-photon fluorescence microscopy, based on the principles of two-photon excited fluorescence and second harmonic generation, enables real-time non-invasive in vivo imaging of skin and cells, providing a means to assess human health status. In this paper, a miniaturized two-photon imaging system is designed and fabricated to withstand extreme vibration and shock environments. The mechanical stability of the optical and structural components of the miniaturized probe is evaluated under random vibration and shock vibration tests using finite element simulation methods and ray tracing techniques. During the environmental testing, the maximum stress on the probe is 11.5 MPa, which is well below the threshold for structural failure. The largest structural displacement occurs at the collimator, where random vibrations produce an offset of 10.9 μm. This offset is analyzed by using geometric optics and point spread functions. Under the maximum collimator offset, the theoretical resolution, as calculated by the point spread function, shifted from 463.28 nm to 463.48 nm. Additionally, a lateral offset of 127 nm is observed at the center position, which does not significantly impact the imaging performance. Finally, environmental and imaging performance tests are conducted. The system’s measured resolution after the environmental tests is 530 nm, consistent with its resolution prior to testing. Imaging tests are also performed on the skin’s stratum corneum, granular layer, spinous layer, and basal cell layer, revealing clear cellular structural information. These results confirm the device’s potential for applications in extreme shock and vibration environments.

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Performance improvement method of new R&D institutions considering Bayesian network
Jianjun ZHU, Lin JIANG
Journal of Systems Engineering and Electronics    2026, 37 (1): 257-271.   DOI: 10.23919/JSEE.2026.000022
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A performance improvement model of research and development (R&D) institutions based on evolutionary game and Bayesian network is proposed. First, the nature and performance factors of new R&D institutions are systematically analyzed, the appropriate factor model is found, and the sharing of performance benefits between institutions and employees, the change in distribution proportion, and the risk of institutional improvement and employee cooperation are considered. Second, based on the mechanism improvement and employee cooperation, the payment matrix is given and evolutionary game analysis is carried out to obtain a stable and balanced institutional improvement probability and employee cooperation probability. These two probability values are substituted into the Bayesian network model of performance improvement of new R&D institutions, and the posterior probability of performance improvement is predicted by Bayesian network reasoning and diagnosis to find effective improvement measures. Finally, practical case analysis is given to verify the effectiveness and practicability of the proposed method.

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CONTENTS
Journal of Systems Engineering and Electronics    2026, 37 (1): 0-0.  
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Specific emitter identification based on frequency and amplitude of the signal kurtosis
Yurui ZHAO, Xiang WANG, Liting SUN, Zhitao HUANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 333-343.   DOI: 10.23919/JSEE.2023.000054
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Extensive experiments suggest that kurtosis-based fingerprint features are effective for specific emitter identification (SEI). Nevertheless, the lack of mechanistic explanation restricts the use of fingerprint features to a data-driven technique and further reduces the adaptability of the technique to other datasets. To address this issue, the mechanism how the phase noise of high-frequency oscillators and the nonlinearity of power amplifiers affect the kurtosis of communication signals is investigated. Mathematical models are derived for intentional modulation (IM) and unintentional modulation (UIM). Analysis indicates that the phase noise of high-frequency oscillators and the nonlinearity of power amplifiers affect the kurtosis frequency and amplitude, respectively. A novel SEI method based on frequency and amplitude of the signal kurtosis (FA-SK) is further proposed. Simulation and real-world experiments validate theoretical analysis and also confirm the efficiency and effectiveness of the proposed method.

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Mission capability assessment of UAV swarms based on UAF and interval-valued spherical fuzzy ANP
Minghao LI, An ZHANG, Wenhao BI, Qiucen FAN, Pan YANG
Journal of Systems Engineering and Electronics    2026, 37 (1): 225-241.   DOI: 10.23919/JSEE.2026.000017
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For mission-oriented unmanned aerial vehicle (UAV) swarms, mission capability assessment provides an important reference in the design and development process, and is a precondition for mission success. For this multi-criteria decision-making (MCDM) problem, the current literature lacks a way to unambiguously present criteria and the popular fuzzy analytic network process (ANP) approaches neglect the hesitancy of subjective judgments. To fill these research gaps, an MCDM method based on unified architecture framework (UAF) and interval-valued spherical fuzzy ANP (IVSF-ANP) is proposed in this paper. Firstly, selected viewpoints in UAF are extended to construct criteria models with standardized representation. Secondly, interval-valued spherical fuzzy sets are introduced to ANP to weight interdependent criteria, handling fuzziness and hesitancy in pairwise comparisons. A method of adjusting weights of experts based on their decision similarities is also included in this process to reduce ambiguity brought by multiple experts. Next, performance characteristics are non-linearly transformed regarding to expectations to get final results. This proposition is applied to assess the mission capability of UAV swarms to search and strike surface vessels. Comparative analysis shows that the proposed method is valid and reasonable.

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CONTENTS

Journal of Systems Engineering and Electronics    2025, 36 (2): 0-0.  
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MAV-UAV combat organization’s force formation plan generation based on NSGA-III
Yun ZHONG, Lujun WAN, Jieyong ZHANG
Journal of Systems Engineering and Electronics    2026, 37 (1): 307-317.   DOI: 10.23919/JSEE.2026.000008
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Manned aerial vehicle-unmanned aerial vehicle (MAV-UAV) combat organization is a MAV-UAV combat collective formed from the perspective of organization design theory and methodology, and the generation of force formation plan is a key step in the organizational planning. Based on the description of the problem and the definition of organizational elements, the matching model of platform-target attack wave is constructed to minimize the redundancy of command and decision-making capability, resource capability and the number of platforms used. Based on the non-dominated sorting genetic algorithm III (NSGA-III) framework, which includes encoding/decoding method and constraint handling method, the generation model of organizational force formation plan is solved, and the effectiveness and superiority of the algorithm are verified by simulation experiments.

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Temperature error compensation method for fiber optic gyroscope based on a composite model of k-means, support vector regression and particle swarm optimization
Yin CAO, Lijing LI, Sheng LIANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 510-522.   DOI: 10.23919/JSEE.2025.000023
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As the core component of inertial navigation systems, fiber optic gyroscope (FOG), with technical advantages such as low power consumption, long lifespan, fast startup speed, and flexible structural design, are widely used in aerospace, unmanned driving, and other fields. However, due to the temperature sensitivity of optical devices, the influence of environmental temperature causes errors in FOG, thereby greatly limiting their output accuracy. This work researches on machine-learning based temperature error compensation techniques for FOG. Specifically, it focuses on compensating for the bias errors generated in the fiber ring due to the Shupe effect. This work proposes a composite model based on k-means clustering, support vector regression, and particle swarm optimization algorithms. And it significantly reduced redundancy within the samples by adopting the interval sequence sample. Moreover, metrics such as root mean square error (RMSE), mean absolute error (MAE), bias stability, and Allan variance, are selected to evaluate the model’s performance and compensation effectiveness. This work effectively enhances the consistency between data and models across different temperature ranges and temperature gradients, improving the bias stability of the FOG from 0.022 °/h to 0.006 °/h. Compared to the existing methods utilizing a single machine learning model, the proposed method increases the bias stability of the compensated FOG from 57.11% to 71.98%, and enhances the suppression of rate ramp noise coefficient from 2.29% to 14.83%. This work improves the accuracy of FOG after compensation, providing theoretical guidance and technical references for sensors error compensation work in other fields.

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Design of wide-scanning array with reactive splitter network and metasurface
Haiying LUO, Fulong JIN, Xiao DING, Wei SHAO
Journal of Systems Engineering and Electronics    2025, 36 (2): 323-332.   DOI: 10.23919/JSEE.2024.000005
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In this paper, the reactive splitter network and metasurface are proposed to radiate the wide-beam isolated element pattern and suppress mutual coupling (MC) of the low-profile phased array with the triangular lattice, respectively. Thus, broadband wide-angle impedance matching (WAIM) is implemented to promote two-dimensional (2D) wide scanning. For the isolated element, to radiate the wide-beam patterns approximating to the cosine form, two identical slots backed on one substrate integrated cavity are excited by the feeding network consisting of a reactive splitter and two striplines connected with splitter output paths. For adjacent elements staggered with each other, with the metasurface superstrate, the even-mode coupling voltages on the reactive splitter are cancelled out, yielding reduced MC. With the suppression of MC and the compensation of isolated element patterns, WAIM is realized to achieve 2D wide-angle beam steering up to ± 65° in E-plane, ± 45° in H-plane and ± 60° in D-plane from 4.9 GHz to 5.85 GHz.

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Deep unfolded amplitude-phase error self-calibration network for DOA estimation
Hangui ZHU, Xixi CHEN, Teng MA, Yongliang WANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 353-361.   DOI: 10.23919/JSEE.2024.000099
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To tackle the challenges of intractable parameter tuning, significant computational expenditure and imprecise model-driven sparse-based direction of arrival (DOA) estimation with array error (AE), this paper proposes a deep unfolded amplitude-phase error self-calibration network. Firstly, a sparse-based DOA model with an array convex error restriction is established, which gets resolved via an alternating iterative minimization (AIM) algorithm. The algorithm is then unrolled to a deep network known as AE-AIM Network (AE-AIM-Net), where all parameters are optimized through multi-task learning using the constructed complete dataset. The results of the simulation and theoretical analysis suggest that the proposed unfolded network achieves lower computational costs compared to typical sparse recovery methods. Furthermore, it maintains excellent estimation performance even in the presence of array magnitude-phase errors.

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Factor graph method for target state estimation in bearing-only sensor network
Zhan CHEN, Yangwang FANG, Ruitao ZHANG, Wenxing FU
Journal of Systems Engineering and Electronics    2025, 36 (2): 380-396.   DOI: 10.23919/JSEE.2024.000122
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For target tracking and localization in bearing-only sensor network, it is an essential and significant challenge to solve the problem of plug-and-play expansion while stably enhancing the accuracy of state estimation. This paper proposes a distributed state estimation method based on two-layer factor graph. Firstly, the measurement model of the bearing-only sensor network is constructed, and by investigating the observability and the Cramer-Rao lower bound of the system model, the preconditions are analyzed. Subsequently, the location factor graph and cubature information filtering algorithm of sensor node pairs are proposed for localized estimation. Building upon this foundation, the mechanism for propagating confidence messages within the fusion factor graph is designed, and is extended to the entire sensor network to achieve global state estimation. Finally, groups of simulation experiments are conducted to compare and analyze the results, which verifies the rationality, effectiveness, and superiority of the proposed method.

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CONTENTS
Journal of Systems Engineering and Electronics    2024, 35 (6): 0-0.  
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Multi-objective optimization framework in the modeling of belief rule-based systems with interpretability-accuracy trade-off
Yaqian YOU, Jianbin SUN, Yuejin TAN, Jiang JIANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 423-435.   DOI: 10.23919/JSEE.2024.000064
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The belief rule-based (BRB) system has been popular in complexity system modeling due to its good interpretability. However, the current mainstream optimization methods of the BRB systems only focus on modeling accuracy but ignore the interpretability. The single-objective optimization strategy has been applied in the interpretability-accuracy trade-off by integrating accuracy and interpretability into an optimization objective. But the integration has a greater impact on optimization results with strong subjectivity. Thus, a multi-objective optimization framework in the modeling of BRB systems with interpretability-accuracy trade-off is proposed in this paper. Firstly, complexity and accuracy are taken as two independent optimization goals, and uniformity as a constraint to give the mathematical description. Secondly, a classical multi-objective optimization algorithm, nondominated sorting genetic algorithm II (NSGA-II), is utilized as an optimization tool to give a set of BRB systems with different accuracy and complexity. Finally, a pipeline leakage detection case is studied to verify the feasibility and effectiveness of the developed multi-objective optimization. The comparison illustrates that the proposed multi-objective optimization framework can effectively avoid the subjectivity of single-objective optimization, and has capability of joint optimizing the structure and parameters of BRB systems with interpretability-accuracy trade-off.

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CONTENTS
Journal of Systems Engineering and Electronics    2024, 35 (3): 0-.  
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Multi-platform collaborative MRC-PSO algorithm for anti-ship missile path planning
Gang LIU, Xinyuan GUO, Dong HUANG, Kezhong CHEN, Wu LI
Journal of Systems Engineering and Electronics    2025, 36 (2): 494-509.   DOI: 10.23919/JSEE.2025.000026
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To solve the problem of multi-platform collaborative use in anti-ship missile (ASM) path planning, this paper proposed multi-operator real-time constraints particle swarm optimization (MRC-PSO) algorithm. MRC-PSO algorithm utilizes a semi-rasterization environment modeling technique and integrates the geometric gradient law of ASMs which distinguishes itself from other collaborative path planning algorithms by fully considering the coupling between collaborative paths. Then, MRC-PSO algorithm conducts chunked stepwise recursive evolution of particles while incorporating circumvent, coordination, and smoothing operators which facilitates local selection optimization of paths, gradually reducing algorithmic space, accelerating convergence, and enhances path cooperativity. Simulation experiments comparing the MRC-PSO algorithm with the PSO algorithm, genetic algorithm and operational area cluster real-time restriction (OACRR)-PSO algorithm, which demonstrate that the MRC-PSO algorithm has a faster convergence speed, and the average number of iterations is reduced by approximately 75%. It also proves that it is equally effective in resolving complex scenarios involving multiple obstacles. Moreover it effectively addresses the problem of path crossing and can better satisfy the requirements of multi-platform collaborative path planning. The experiments are conducted in three collaborative operation modes, namely, three-to-two, three-to-three, and four-to-two, and the outcomes demonstrate that the algorithm possesses strong universality.

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Cascading failure analysis of an interdependent network with power-combat coupling
Yang WANG, Junyong TAO, Yun’an ZHANG, Guanghan BAI, Hongyan DUI
Journal of Systems Engineering and Electronics    2025, 36 (2): 405-422.   DOI: 10.23919/JSEE.2024.000118
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Cutting off or controlling the enemy’s power supply at critical moments or strategic locations may result in a cascade failure, thus gaining an advantage in a war. However, the existing cascading failure modeling analysis of interdependent networks is insufficient for describing the load characteristics and dependencies of subnetworks, and it is difficult to use for modeling and failure analysis of power-combat (P-C) coupling networks. This paper considers the physical characteristics of the two subnetworks and studies the mechanism of fault propagation between subnetworks and across systems. Then the survivability of the coupled network is evaluated. Firstly, an integrated modeling approach for the combat system and power system is predicted based on interdependent network theory. A heterogeneous one-way interdependent network model based on probability dependence is constructed. Secondly, using the operation loop theory, a load-capacity model based on combat-loop betweenness is proposed, and the cascade failure model of the P-C coupling system is investigated from three perspectives: initial capacity, allocation strategy, and failure mechanism. Thirdly, survivability indexes based on load loss rate and network survival rate are proposed. Finally, the P-C coupling system is constructed based on the IEEE 118-bus system to demonstrate the proposed method.

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Impact time control guidance for moving-target considering velocity variation and field-of-view constraint
Hao YANG, Shifeng ZHANG, Xibin BAI, Chengye YANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 552-568.   DOI: 10.23919/JSEE.2025.000025
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In the existing impact time control guidance (ITCG) laws for moving-targets, the effects of time-varying velocity caused by aerodynamics and gravity cannot be effectively considered. Therefore, an ITCG with field-of-view (FOV) constraints based on biased proportional navigation guidance (PNG) is developed in this paper. The remaining flight time (time-to-go) estimation method is derived considering aerodynamic force and gravity. The number of differential equations is reduced and the integration step is increased by changing the integral variable, which makes it possible to obtain time-to-go through integration. An impact time controller with FOV constraints is proposed by analyzing the influence of the biased term on time-to-go and FOV constraint. Then, numerical simulations are performed to verify the correctness and superiority of the method.

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Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation
Zhichao XU, Faping LU, Lifan ZHANG, Dongkai YANG, Chuanhui LIU, Jiafang KANG, Qi AN, Zhilin ZHANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 311-322.   DOI: 10.23919/JSEE.2024.000044
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A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method, based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with $n $=10 subcarriers and a bit error rate of 1×10?5, spectral efficiency can be raised by roughly 12.4%.

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Fixed-time distributed average consensus tracking for multiple Euler-Lagrange systems
Guhao SUN, Qingshuang ZENG, Zhongze CAI
Journal of Systems Engineering and Electronics    2025, 36 (2): 523-536.   DOI: 10.23919/JSEE.2025.000034
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This paper investigates the sliding-mode-based fixed-time distributed average tracking (DAT) problem for multiple Euler-Lagrange systems in the presence of external disturbances. The primary objective is to devise controllers for each agent, enabling them to precisely track the average of multiple time-varying reference signals. By averaging these signals, we can mitigate the influence of errors and uncertainties arising during measurements, thereby enhancing the robustness and stability of the system. A distributed fixed-time average estimator is proposed to estimate the average value of global reference signals utilizing local information and communication with neighbors. Subsequently, a fixed-time sliding mode controller is introduced incorporating a state-dependent sliding mode function coupled with a variable exponent coefficient to achieve distributed average tracking of reference signals, and rigorous analytical methods are employed to substantiate the fixed-time stability. Finally, numerical simulation results are provided to validate the effectiveness of the proposed methodology, offering insights into its practical application and robust performance.

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CONTENTS
Journal of Systems Engineering and Electronics    2025, 36 (5): 0-0.  
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Knowledge map of online public opinions for emergencies
Shuang GUAN, Zihan FANG, Changfeng WANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 436-445.   DOI: 10.23919/JSEE.2024.000054
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With the popularization of social media, public opinion information on emergencies spreads rapidly on the Internet, the impact of negative public opinions on an event has become more significant. Based on the organizational form of public opinion information, the knowledge graph is used to construct the knowledge base of public opinion risk cases on the emergency network. The emotion recognition model of negative public opinion information based on the bi-directional long short-term memory (BiLSTM) network is studied in the model layer design, and a linear discriminant analysis (LDA) topic extraction method combined with association rules is proposed to extract and mine the semantics of negative public opinion topics to realize further in-depth analysis of information topics. Focusing on public health emergencies, knowledge acquisition and knowledge processing of public opinion information are conducted, and the experimental results show that the knowledge graph framework based on the construction can facilitate in-depth theme evolution analysis of public opinion events, thus demonstrating important research significance for reducing online public opinion risks.

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Off-grid DOA estimation based on coherent accumulation and weighted block sparse Bayesian
Ankang REN, Qi WU, Pingye LIANG, Yuanyuan XU
Journal of Systems Engineering and Electronics    2026, 37 (2): 327-336.   DOI: 10.23919/JSEE.2025.000164
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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.

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DDIRNet: robust radar emitter recognition via single domain generalization
Honglin WU, Xueqiong LI, Junjie HUANG, Ruochun JIN, Yuhua TANG
Journal of Systems Engineering and Electronics    2025, 36 (2): 397-404.   DOI: 10.23919/JSEE.2025.000053
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Automatically recognizing radar emitters from complex electromagnetic environments is important but non-trivial. Moreover, the changing electromagnetic environment results in inconsistent signal distribution in the real world, which makes the existing approaches perform poorly for recognition tasks in different scenes. In this paper, we propose a domain generalization framework is proposed to improve the adaptability of radar emitter signal recognition in changing environments. Specifically, we propose an end-to-end denoising based domain-invariant radar emitter recognition network (DDIRNet) consisting of a denoising model and a domain invariant representation learning model (IRLM), which mutually benefit from each other. For the signal denoising model, a loss function is proposed to match the feature of the radar signals and guarantee the effectiveness of the model. For the domain invariant representation learning model, contrastive learning is introduced to learn the cross-domain feature by aligning the source and unseen domain distribution. Moreover, we design a data augmentation method that improves the diversity of signal data for training. Extensive experiments on classification have shown that DDIRNet achieves up to 6.4% improvement compared with the state-of-the-art radar emitter recognition methods. The proposed method provides a promising direction to solve the radar emitter signal recognition problem.

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Evolution mechanism of unmanned cluster cooperation oriented toward strategy selection diversity
Zhenhai XIE, Minggang YU, Ming HE, Guoyou CHEN, Zheng ZHAI, Ziyu WANG, Lu LIU
Journal of Systems Engineering and Electronics    2025, 36 (2): 462-482.   DOI: 10.23919/JSEE.2025.000017
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When performing tasks, unmanned clusters often face a variety of strategy choices. One of the key issues in unmanned cluster tasks is the method through which to design autonomous collaboration and cooperative evolution mechanisms that allow for unmanned clusters to maximize their overall task effectiveness under the condition of strategic diversity. This paper analyzes these task requirements from three perspectives: the diversity of the decision space, information network construction, and the autonomous collaboration mechanism. Then, this paper proposes a method for solving the problem of strategy selection diversity under two network structures. Next, this paper presents a Moran-rule-based evolution dynamics model for unmanned cluster strategies and a vision-driven-mechanism-based evolution dynamics model for unmanned cluster strategy in the context of strategy selection diversity according to various unmanned cluster application scenarios. Finally, this paper provides a simulation analysis of the effects of relevant parameters such as the payoff factor and cluster size on cooperative evolution in autonomous cluster collaboration for the two types of models. On this basis, this paper presents advice for effectively addressing diverse choices in unmanned cluster tasks, thereby providing decision support for practical applications of unmanned cluster tasks.

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Fixed-time cooperative interception guidance law with angle constraints for multiple flight vehicles
Enjiao ZHAO, Xue DING, Ke ZHANG, Zengyu YUAN
Journal of Systems Engineering and Electronics    2025, 36 (2): 569-579.   DOI: 10.23919/JSEE.2025.000036
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This paper presents a fixed-time cooperative guidance method with impact angle constraints for multiple flight vehicles (MFV) to address the challenges of intercepting large maneuvering targets with difficulty and low precision. A cooperative guidance model is proposed, transforming the cooperative interception problem into a consensus problem based on the remaining flight time of the flight vehicles. First, the impact angle constraint is converted into the line of sight (LOS) angle constraint, and a new fixed-time convergent non-singular terminal sliding surface is introduced, which resolves the singularity issue of the traditional sliding surfaces. With this approach, LOS angle rate and normal overloads can converge in fixed time, ensuring that the upper bound of the system convergence time is not affected by the initial value of the system. Furthermore, the maneuvering movement of the target is considered as a system disturbance, and an extended state observer is employed to estimate and compensate for it in the guidance law. Lastly, by applying consensus theory and distributed communication topology, the remaining flight time of each flight vehicle is synchronized to ensure that they intercept the target simultaneously with different impact angles. Simulation experiments are conducted to validate the effectiveness of the proposed cooperative interception and guidance method.

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Non-singular fast terminal sliding mode control for roll-pitch seeker based on extended state observers
Bowen XIAO, Qunli XIA
Journal of Systems Engineering and Electronics    2025, 36 (2): 537-551.   DOI: 10.23919/JSEE.2025.000035
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For air-to-air missiles, the terminal guidance’s precision is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode control method, aimed at resolving the frame control problem of roll-pitch seeker tracking high maneuvering target. The sliding mode surface is structured around the principle of segmentation, which enables the control system’s rapid attainment of the zero point and ensure global fast convergence. The system’s state is more swiftly converged to the sliding mode surface through an improved adaptive fast dual power reaching law. Utilizing an extended state observer, the overall disturbance is both identified and compensated. The validation of the system’s stability and its convergence within a finite-time is grounded in Lyapunov’s stability criteria. The performance of the introduced control method is confirmed through roll-pitch seeker tracking control simulation. Data analysis reveals that newly proposed control technique significantly outperforms existing sliding mode control methods by rapidly converging the frame to the target angle, reduce the tracking error of the detector for the target, and bolster tracking precision of the roll-pitch seeker huring disturbed conditions.

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Aerial-ground collaborative delivery route planning with UAV energy function and multi-delivery
Jingfeng GUO, Rui SONG, Shiwei HE
Journal of Systems Engineering and Electronics    2025, 36 (2): 446-461.   DOI: 10.23919/JSEE.2025.000048
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With the rapid development of low-altitude economy and unmanned aerial vehicles (UAVs) deployment technology, aerial-ground collaborative delivery (AGCD) is emerging as a novel mode of last-mile delivery, where the vehicle and its onboard UAVs are utilized efficiently. Vehicles not only provide delivery services to customers but also function as mobile warehouses and launch/recovery platforms for UAVs. This paper addresses the vehicle routing problem with UAVs considering time window and UAV multi-delivery (VRPU-TW&MD). A mixed integer linear programming (MILP) model is developed to minimize delivery costs while incorporating constraints related to UAV energy consumption. Subsequently, a micro-evolution augmented large neighborhood search (MEALNS) algorithm incorporating adaptive large neighborhood search (ALNS) and micro-evolution mechanism is proposed. Numerical experiments demonstrate the effectiveness of both the model and algorithm in solving the VRPU-TW&MD. The impact of key parameters on delivery performance is explored by sensitivity analysis.

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Modeling optimal air traffic rights resource allocation
Zhishuo LIU, Yi’nan CHENG, Yanhua LI, Danyang SHEN
Journal of Systems Engineering and Electronics    2025, 36 (3): 778-790.   DOI: 10.23919/JSEE.2025.000070
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International freedom of the air (traffic rights) is a key resource for airlines to carry out international air transport business. An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport. In this paper, a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers. A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model. The results show that the optimal allocation scheme aligns with the principle of fairness, indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.

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