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Optimal production lot size with process deterioration under an extended inspection policy
Hu Fei, Xu Genqi & Ma Lixia
Journal of Systems Engineering and Electronics    2009, 20 (4): 768-776.  
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A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.

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Vehicle and onboard UAV collaborative delivery route planning: considering energy function with wind and payload
Jingfeng GUO, Rui SONG, Shiwei HE
Journal of Systems Engineering and Electronics    2025, 36 (1): 194-208.   DOI: 10.23919/JSEE.2025.000020
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The rapid evolution of unmanned aerial vehicle (UAV) technology and autonomous capabilities has positioned UAV as promising last-mile delivery means. Vehicle and onboard UAV collaborative delivery is introduced as a novel delivery mode. Spatiotemporal collaboration, along with energy consumption with payload and wind conditions play important roles in delivery route planning. This paper introduces the traveling salesman problem with time window and onboard UAV (TSP-TWOUAV) and emphasizes the consideration of real-world scenarios, focusing on time collaboration and energy consumption with wind and payload. To address this, a mixed integer linear programming (MILP) model is formulated to minimize the energy consumption costs of vehicle and UAV. Furthermore, an adaptive large neighborhood search (ALNS) algorithm is applied to identify high-quality solutions efficiently. The effectiveness of the proposed model and algorithm is validated through numerical tests on real geographic instances and sensitivity analysis of key parameters is conducted.

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FOLMS-AMDCNet: an automatic recognition scheme for multiple-antenna OFDM systems
Yuyuan ZHANG, Wenjun YAN, Limin ZHANG, Qing LING
Journal of Systems Engineering and Electronics    2023, 34 (2): 307-323.   DOI: 10.23919/JSEE.2023.000027
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The existing recognition algorithms of space-time block code (STBC) for multi-antenna (MA) orthogonal frequency-division multiplexing (OFDM) systems use feature extraction and hypothesis testing to identify the signal types in a complex communication environment. However, owing to the restrictions on the prior information and channel conditions, these existing algorithms cannot perform well under strong interference and non-cooperative communication conditions. To overcome these defects, this study introduces deep learning into the STBC-OFDM signal recognition field and proposes a recognition method based on the fourth-order lag moment spectrum (FOLMS) and attention-guided multi-scale dilated convolution network (AMDCNet). The fourth-order lag moment vectors of the received signals are calculated, and vectors are stitched to form two-dimensional FOLMS, which is used as the input of the deep learning-based model. Then, the multi-scale dilated convolution is used to extract the details of images at different scales, and a convolutional block attention module (CBAM) is introduced to construct the attention-guided multi-scale dilated convolution module (AMDCM) to make the network be more focused on the target area and obtian the multi-scale guided features. Finally, the concatenate fusion, residual block and fully-connected layers are applied to acquire the STBC-OFDM signal types. Simulation experiments show that the average recognition probability of the proposed method at ?12 dB is higher than 98%. Compared with the existing algorithms, the recognition performance of the proposed method is significantly improved and has good adaptability to environments with strong disturbances. In addition, the proposed deep learning-based model can directly identify the pre-processed FOLMS samples without a priori information on channel and noise, which is more suitable for non-cooperative communication systems than the existing algorithms.

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UAV cooperative air combat maneuver decision based on multi-agent reinforcement learning
Jiandong ZHANG, Qiming YANG, Guoqing SHI, Yi LU, Yong WU
Journal of Systems Engineering and Electronics    2021, 32 (6): 1421-1438.   DOI: 10.23919/JSEE.2021.000121
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In order to improve the autonomous ability of unmanned aerial vehicles (UAV) to implement air combat mission, many artificial intelligence-based autonomous air combat maneuver decision-making studies have been carried out, but these studies are often aimed at individual decision-making in 1v1 scenarios which rarely happen in actual air combat. Based on the research of the 1v1 autonomous air combat maneuver decision, this paper builds a multi-UAV cooperative air combat maneuver decision model based on multi-agent reinforcement learning. Firstly, a bidirectional recurrent neural network (BRNN) is used to achieve communication between UAV individuals, and the multi-UAV cooperative air combat maneuver decision model under the actor-critic architecture is established. Secondly, through combining with target allocation and air combat situation assessment, the tactical goal of the formation is merged with the reinforcement learning goal of every UAV, and a cooperative tactical maneuver policy is generated. The simulation results prove that the multi-UAV cooperative air combat maneuver decision model established in this paper can obtain the cooperative maneuver policy through reinforcement learning, the cooperative maneuver policy can guide UAVs to obtain the overall situational advantage and defeat the opponents under tactical cooperation.

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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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Deep convolutional neural network for meteorology target detection in airborne weather radar images
Chaopeng YU, Wei XIONG, Xiaoqing LI, Lei DONG
Journal of Systems Engineering and Electronics    2023, 34 (5): 1147-1157.   DOI: 10.23919/JSEE.2023.000142
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Considering the problem that the scattering echo images of airborne Doppler weather radar are often reduced by ground clutters, the accuracy and confidence of meteorology target detection are reduced. In this paper, a deep convolutional neural network (DCNN) is proposed for meteorology target detection and ground clutter suppression with a large collection of airborne weather radar images as network input. For each weather radar image, the corresponding digital elevation model (DEM) image is extracted on basis of the radar antenna scanning parameters and plane position, and is further fed to the network as a supplement for ground clutter suppression. The features of actual meteorology targets are learned in each bottleneck module of the proposed network and convolved into deeper iterations in the forward propagation process. Then the network parameters are updated by the back propagation iteration of the training error. Experimental results on the real measured images show that our proposed DCNN outperforms the counterparts in terms of six evaluation factors. Meanwhile, the network outputs are in good agreement with the expected meteorology detection results (labels). It is demonstrated that the proposed network would have a promising meteorology observation application with minimal effort on network variables or parameter changes.

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Vegetation scattering attenuation characteristics of terahertz wave
Qingfeng JING, Zhuo DIAO, Zhongbo ZHU
Journal of Systems Engineering and Electronics    2023, 34 (6): 1501-1507.   DOI: 10.23919/JSEE.2022.000133
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A terahertz (THz) wave transmitted through vegetation experiences both absorption and scattering caused by the air molecules and leaves. This paper presents the scattering attenuation characteristics of vegetation in a THz range. The theoretical path loss model near the vegetation yields the average attenuation of THz waves in a mixed channel composed of air and vegetation leaves. Furthermore, a simplified model of the vegetation structure is obtained for generic vegetation types based on a variety of parameters, such as leaf size, distribution, and moisture content. Finally, based on specific vegetation species and different levels of air humidity, the attenuation characteristics under different conditions are calculated, and the influence of different model parameters on the attenuation characteristics is obtained.

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Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking
Boyu QIN, Dong ZHANG, Shuo TANG, Yang XU
Journal of Systems Engineering and Electronics    2023, 34 (6): 1375-1396.   DOI: 10.23919/JSEE.2023.000153
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This paper tackles the formation-containment control problem of fixed-wing unmanned aerial vehicle (UAV) swarm with model uncertainties for dynamic target tracking in three-dimensional space in the faulty case of UAVs ’ actuator and sensor. The fixed-wing UAV swarm under consideration is organized as a “multi-leader-multi-follower” structure, in which only several leaders can obtain the dynamic target information while others only receive the neighbors’ information through the communication network. To simultaneously realize the formation, containment, and dynamic target tracking, a two-layer control framework is adopted to decouple the problem into two subproblems: reference trajectory generation and trajectory tracking. In the upper layer, a distributed finite-time estimator (DFTE) is proposed to generate each UAV ’s reference trajectory in accordance with the control objective. Subsequently, a distributed composite robust fault-tolerant trajectory tracking controller is developed in the lower layer, where a novel adaptive extended super-twisting (AESTW) algorithm with a finite-time extended state observer (FTESO) is involved in solving the robust trajectory tracking control problem under model uncertainties, actuator, and sensor faults. The proposed controller simultaneously guarantees rapidness and enhances the system ’s robustness with fewer chattering effects. Finally, corresponding simulations are carried out to demonstrate the effectiveness and competitiveness of the proposed two-layer fault-tolerant cooperative control scheme.

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Radar emitter signal recognition method based on improved collaborative semi-supervised learning
Tao JIN, Xindong ZHANG
Journal of Systems Engineering and Electronics    2023, 34 (5): 1182-1190.   DOI: 10.23919/JSEE.2023.000126
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Rare labeled data are difficult to recognize by using conventional methods in the process of radar emitter recognition. To solve this problem, an optimized cooperative semi-supervised learning radar emitter recognition method based on a small amount of labeled data is developed. First, a small amount of labeled data are randomly sampled by using the bootstrap method, loss functions for three common deep learning networks are improved, the uniform distribution and cross-entropy function are combined to reduce the overconfidence of softmax classification. Subsequently, the dataset obtained after sampling is adopted to train three improved networks so as to build the initial model. In addition, the unlabeled data are preliminarily screened through dynamic time warping (DTW) and then input into the initial model trained previously for judgment. If the judgment results of two or more networks are consistent, the unlabeled data are labeled and put into the labeled data set. Lastly, the three network models are input into the labeled dataset for training, and the final model is built. As revealed by the simulation results, the semi-supervised learning method adopted in this paper is capable of exploiting a small amount of labeled data and basically achieving the accuracy of labeled data recognition.

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Mitigation of cross-eye jamming using a dual-polarization array
Jiazhi MA, Longfei SHI, Shunping XIAO, Xuesong WANG
Journal of Systems Engineering and Electronics    2018, 29 (3): 491-498.   DOI: 10.21629/JSEE.2018.03.06
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This paper presents an approach for mitigating the cross-eye jamming using a dual-polarization array. By transmitting a sum beam and a difference beam in two orthogonal polarimetric channels, a synthesized transmitted beam with spatially varying polarization is produced, such that the polarization of the transmitted radar wave varies in azimuth or elevation. Thus, the phases of the signals received on the two antennas of a cross-eye jammer become unequal, and an additional phase difference is introduced to disrupt the 180° phase shifting in the retrodirective loop of the jammer. By means of beam scanning in a small angular range, the optimal beam steering configuration can be found to maximize the phase error for the mitigation of cross-eye jamming. As a result, the jamming performance of the cross-eye jammer degrades largely. Theoretical analysis and simulation results indicate that the proposed method is valid and feasible.

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An effective array beamforming scheme based on branch-and-bound algorithm
Xiaodong YE, Li LI, Hao WANG, Shifei TAO
Journal of Systems Engineering and Electronics    2023, 34 (6): 1483-1489.   DOI: 10.23919/JSEE.2022.000123
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In this paper, we propose an effective full array and sparse array adaptive beamforming scheme that can be applied for multiple desired signals based on the branch-and-bound algorithm. Adaptive beamforming for the multiple desired signals is realized by the improved Capon method. At the same time, the sidelobe constraint is added to reduce the sidelobe level. To reduce the pointing errors of multiple desired signals, the array response phase of the desired signal is firstly optimized by using auxilary variables while keeping the response amplitude unchanged. The whole design is formulated as a convex optimization problem solved by the branch-and-bound algorithm. In addition, the beamformer weight vector is penalized with the modified reweighted ${l_1}$-norm to achieve sparsity. Theoretical analysis and simulation results show that the proposed algorithm has lower sidelobe level, higher SINR, and less pointing error than the state-of-the-art methods in the case of a single expected signal and multiple desired signals.

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A spawning particle filter for defocused moving target detection in GNSS-based passive radar
Hongcheng ZENG, Jiadong DENG, Pengbo WANG, Xinkai ZHOU, Wei YANG, Jie CHEN
Journal of Systems Engineering and Electronics    2023, 34 (5): 1085-1100.   DOI: 10.23919/JSEE.2023.000033
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Global Navigation Satellite System (GNSS)-based passive radar (GBPR) has been widely used in remote sensing applications. However, for moving target detection (MTD), the quadratic phase error (QPE) introduced by the non-cooperative target motion is usually difficult to be compensated, as the low power level of the GBPR echo signal renders the estimation of the Doppler rate less effective. Consequently, the moving target in GBPR image is usually defocused, which aggravates the difficulty of target detection even further. In this paper, a spawning particle filter (SPF) is proposed for defocused MTD. Firstly, the measurement model and the likelihood ratio function (LRF) of the defocused point-like target image are deduced. Then, a spawning particle set is generated for subsequent target detection, with reference to traditional particles in particle filter (PF) as their parent. After that, based on the PF estimator, the SPF algorithm and its sequential Monte Carlo (SMC) implementation are proposed with a novel amplitude estimation method to decrease the target state dimension. Finally, the effectiveness of the proposed SPF is demonstrated by numerical simulations and preliminary experimental results, showing that the target range and Doppler can be estimated accurately.

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Target threat estimation based on discrete dynamic Bayesian networks with small samples
Fang YE, Ying MAO, Yibing LI, Xinrui LIU
Journal of Systems Engineering and Electronics    2022, 33 (5): 1135-1142.   DOI: 10.23919/JSEE.2022.000076
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The accuracy of target threat estimation has a great impact on command decision-making. The Bayesian network, as an effective way to deal with the problem of uncertainty, can be used to track the change of the target threat level. Unfortunately, the traditional discrete dynamic Bayesian network (DDBN) has the problems of poor parameter learning and poor reasoning accuracy in a small sample environment with partial prior information missing. Considering the finiteness and discreteness of DDBN parameters, a fuzzy k-nearest neighbor (KNN) algorithm based on correlation of feature quantities (CF-FKNN) is proposed for DDBN parameter learning. Firstly, the correlation between feature quantities is calculated, and then the KNN algorithm with fuzzy weight is introduced to fill the missing data. On this basis, a reasonable DDBN structure is constructed by using expert experience to complete DDBN parameter learning and reasoning. Simulation results show that the CF-FKNN algorithm can accurately fill in the data when the samples are seriously missing, and improve the effect of DDBN parameter learning in the case of serious sample missing. With the proposed method, the final target threat assessment results are reasonable, which meets the needs of engineering applications.

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Image encryption based on a novel memristive chaotic system, Grain-128a algorithm and dynamic pixel masking
Lilian HUANG, Yi SUN, Jianhong XIANG, Linyu WANG
Journal of Systems Engineering and Electronics    2022, 33 (3): 534-550.   DOI: 10.23919/JSEE.2022.000053
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In this paper, we first propose a memristive chaotic system and implement it by circuit simulation. The chaotic dynamics and various attractors are analysed by using phase portrait, bifurcation diagram, and Lyapunov exponents. In particular, the system has robust chaos in a wide parameter range and the initial value space, which is favourable to the security communication application. Consequently, we further explore its application in image encryption and present a new scheme. Before image processing, the external key is protected by the Grain-128a algorithm and the initial values of the memristive system are updated with the plain image. We not only perform random pixel extraction and masking with the chaotic cipher, but also use them as control parameters for Brownian motion to obtain the permutation matrix. In addition, multiplication on the finite field GF(28) is added to further enhance the cryptography. Finally, the simulation results verify that the proposed image encryption scheme has better performance and higher security, which can effectively resist various attacks.

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Optimal replacement policy of products with repair-cost threshold after the extended warranty
Lijun Shang and Zhiqiang Cai
Systems Engineering and Electronics    DOI: 10.21629/JSEE.2017.04.12
A semantic-centered cloud control framework for autonomous unmanned system
Weijian PANG, Hui LI, Xinyi MA, Hailin ZHANG
Journal of Systems Engineering and Electronics    2022, 33 (4): 771-784.   DOI: 10.23919/JSEE.2022.000077
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Rich semantic information in natural language increases team efficiency in human collaboration, reduces dependence on high precision data information, and improves adaptability to dynamic environment. We propose a semantic centered cloud control framework for cooperative multi-unmanned ground vehicle (UGV) system. Firstly, semantic modeling of task and environment is implemented by ontology to build a unified conceptual architecture, and secondly, a scene semantic information extraction method combining deep learning and semantic web rule language (SWRL) rules is used to realize the scene understanding and task-level cloud task cooperation. Finally, simulation results show that the framework is a feasible way to enable autonomous unmanned systems to conduct cooperative tasks.

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Predictive cruise control for heavy trucks based on slope information under cloud control system
Shuyan LI, Keke WAN, Bolin GAO, Rui LI, Yue WANG, Keqiang LI
Journal of Systems Engineering and Electronics    2022, 33 (4): 812-826.   DOI: 10.23919/JSEE.2022.000081
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With the advantage of fast calculation and map resources on cloud control system (CCS), cloud-based predictive cruise control (CPCC) for heavy trucks has great potential to improve energy efficiency, which is significant to achieve the goal of national carbon neutrality. However, most investigations focus on the on-board predictive cruise control (PCC) system, lack of research on CPCC architecture under CCS. Besides, the current PCC algorithms have the problems of a single control target and high computational complexity, which hinders the improvement of the control effect. In this paper, a layered architecture based on CCS is proposed to effectively address the real-time computing of CPCC system and the deployment of its algorithm on vehicle-cloud. In addition, based on the dynamic programming principle and the proposed road point segmentation method (RPSM), a PCC algorithm is designed to optimize the speed and gear of heavy trucks with slope information. Simulation results show that the CPCC system can adaptively control vehicle driving through the slope prediction, with fuel-saving rate of 6.17% in comparison with the constant cruise control. Also, compared with other similar algorithms, the PCC algorithm can make the engine operate more in the efficient zone by cooperatively optimizing the gear and speed. Moreover, the RPSM algorithm can reconfigure the road in advance, with a 91% roadpoint reduction rate, significantly reducing algorithm complexity. Therefore, this study has essential research significance for the economic driving of heavy trucks and the promotion of the CPCC system.

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DOA estimation based on multi-frequency joint sparse Bayesian learning for passive radar
Jinfang WEN, Jianxin YI, Xianrong WAN, Ziping GONG, Ji SHEN
Journal of Systems Engineering and Electronics    2022, 33 (5): 1052-1063.   DOI: 10.23919/JSEE.2022.000103
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This paper considers multi-frequency passive radar and develops a multi-frequency joint direction of arrival (DOA) estimation algorithm to improve estimation accuracy and resolution. The developed algorithm exploits the sparsity of targets in the spatial domain. Specifically, we first extract the required frequency channel data and acquire the snapshot data through a series of preprocessing such as clutter suppression, coherent integration, beamforming, and constant false alarm rate (CFAR) detection. Then, based on the framework of sparse Bayesian learning, the target’s DOA is estimated by jointly extracting the multi-frequency data via evidence maximization. Simulation results show that the developed algorithm has better estimation accuracy and resolution than other existing multi-frequency DOA estimation algorithms, especially under the scenarios of low signal-to-noise ratio (SNR) and small snapshots. Furthermore, the effectiveness is verified by the field experimental data of a multi-frequency FM-based passive radar.

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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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Accurate 3D geometry measurement for non-cooperative spacecraft with an unfocused light-field camera
Shengming XU, Shan LU, Yueyang HOU, Shengxian SHI
Journal of Systems Engineering and Electronics    2022, 33 (1): 11-21.   DOI: 10.23919/JSEE.2022.000002
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This work explores an alternative 3D geometry measurement method for non-cooperative spacecraft guiding navigation and proximity operations. From one snapshot of an unfocused light-field camera, the 3D point cloud of a non-cooperative spacecraft can be calculated from sub-aperture images with the epipolar plane image (EPI) based light-field rendering algorithm. A Chang’e?3 model (7.2 cm×5.6 cm×7.0 cm) is tested to validate the proposed technique. Three measurement distances (1.0 m, 1.2 m, 1.5 m) are considered to simulate different approaching stages. Measuring errors are quantified by comparing the light-field camera data with a high precision commercial laser scanner. The mean error distance for the three cases are 0.837 mm, 0.743 mm, and 0.973 mm respectively, indicating that the method can well reconstruct 3D geometry of a non-coope-rative spacecraft with a densely distributed 3D point cloud and is thus promising in space-related missions.

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Deinterleaving of radar pulse based on implicit feature
Qiang GUO, Long TENG, Xinliang WU, Liangang QI, Wenming SONG
Journal of Systems Engineering and Electronics    2023, 34 (6): 1537-1549.   DOI: 10.23919/JSEE.2023.000032
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In the complex countermeasure environment, the pulse description words (PDWs) of the same type of multi-function radar emitters are similar in multiple dimensions. Therefore, it is difficult for conventional methods to deinterleave such emitters. In order to solve this problem, a pulse deinterleaving method based on implicit features is proposed in this paper. The proposed method introduces long short-term memory (LSTM) neural networks and statistical analysis to mine new features from similar PDW features, that is, the variation law (implicit features) of pulse sequences of different radiation sources over time. The multi-function radar emitter is deinterleaved based on the pulse sequence variation law. Statistical results show that the proposed method not only achieves satisfactory performance, but also has good robustness.

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Combat situation suppression of multiple UAVs based on spatiotemporal cooperative path planning
Lei HU, Guoxing YI, Yi NAN, Hao WANG
Journal of Systems Engineering and Electronics    2023, 34 (5): 1191-1210.   DOI: 10.23919/JSEE.2023.000119
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Aiming at the suppression of enemy air defense (SEAD) task under the complex and complicated combat scenario, the spatiotemporal cooperative path planning methods are studied in this paper. The major research contents include optimal path points generation, path smoothing and cooperative rendezvous. In the path points generation part, the path points availability testing algorithm and the path segments availability testing algorithm are designed, on this foundation, the swarm intelligence-based path point generation algorithm is utilized to generate the optimal path. In the path smoothing part, taking terminal attack angle constraint and maneuverability constraint into consideration, the Dubins curve is introduced to smooth the path segments. In cooperative rendezvous part, we take estimated time of arrival requirement constraint and flight speed range constraint into consideration, the speed control strategy and flight path control strategy are introduced, further, the decoupling scheme of the circling maneuver and detouring maneuver is designed, in this case, the maneuver ways, maneuver point, maneuver times, maneuver path and flight speed are determined. Finally, the simulation experiments are conducted and the acquired results reveal that the time-space cooperation of multiple unmanned aeriel vehicles (UAVs) is effectively realized, in this way, the combat situation suppression against the enemy can be realized in SEAD scenarios.

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Anti-off-target control method for video satellite based on potential function
Caizhi FAN, Mengmeng WANG, Chao SONG, Zikai ZHONG, Yueneng YANG
Journal of Systems Engineering and Electronics    2024, 35 (6): 1583-1593.   DOI: 10.23919/JSEE.2024.000098
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Small video satellites have unique advantages of short development cycle, agile attitude maneuver, real-time video imaging. They have broad application prospects in space debris, faulty spacecraft, and other space target detection and tracking. However, when a space target first enters the camera’s visual field, it has a relatively large angular velocity relative to the satellite, which makes it easy to deviate from the visual field and cause off-target problems. This paper proposes a novel visual tracking control method based on potential function preventing missed targets in space. Firstly, a circular area in the image plane is designed as a mandatory restricted projection area of the target and a visual tracking controller based on image error. Then, a potential function is designed to ensure continuous and stable tracking of the target after entering the visual field. Finally, the stability of the control is proved using Barbarat’s lemma. By setting the same conditions and comparing with the simulation results of the proportion-derivative (PD) control method, the results show that when there is a large relative attitude motion angular velocity between the target and the satellite, the tracking method based on potential function can ensure that the target does not deviate from the field-of-view during the tracking control process, and the projection of target is controlled to the desired position. The proposed control method is effective in eliminating tracking error and preventing off-target simultaneously.

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Research on three-dimensional attack area based on improved backtracking and ALPS-GP algorithms of air-to-air missile
Haodi ZHANG, Yuhui WANG, Jiale HE
Journal of Systems Engineering and Electronics    2025, 36 (1): 292-310.   DOI: 10.23919/JSEE.2024.000129
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In the field of calculating the attack area of air-to-air missiles in modern air combat scenarios, the limitations of existing research, including real-time calculation, accuracy efficiency trade-off, and the absence of the three-dimensional attack area model, restrict their practical applications. To address these issues, an improved backtracking algorithm is proposed to improve calculation efficiency. A significant reduction in solution time and maintenance of accuracy in the three-dimensional attack area are achieved by using the proposed algorithm. Furthermore, the age-layered population structure genetic programming (ALPS-GP ) algorithm is introduced to determine an analytical polynomial model of the three-dimensional attack area, considering real-time requirements. The accuracy of the polynomial model is enhanced through the coefficient correction using an improved gradient descent algorithm. The study reveals a remarkable combination of high accuracy and efficient real-time computation, with a mean error of 91.89 m using the analytical polynomial model of the three-dimensional attack area solved in just 10?4 s, thus meeting the requirements of real-time combat scenarios.

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RflySim ToolChain: a rapid development and validation toolchain for intelligent unmanned swarm systems
Xunhua DAI, Jinhu TU, Quan QUAN
Journal of Systems Engineering and Electronics    2025, 36 (4): 1077-1093.   DOI: 10.23919/JSEE.2025.000079
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Developing intelligent unmanned swarm systems (IUSSs) is a highly intricate process. Although current simulators and toolchains have made a notable contribution to the development of algorithms for IUSSs, they tend to concentrate on isolated technical elements and are deficient in addressing the full spectrum of critical technologies and development needs in a systematic and integrative manner. Furthermore, the current suite of tools has not adequately addressed the challenge of bridging the gap between simulation and real-world deployment of algorithms. Therefore, a comprehensive solution must be developed that encompasses the entire IUSS development lifecycle. In this study, we present the RflySim ToolChain, which has been developed with the specific aim of facilitating the rapid development and validation of IUSSs. The RflySim ToolChain employs a model-based design (MBD) approach, integrating a modeling and simulation module, a lower reliable control module, and an upper swarm decision-making module. This comprehensive integration encompasses the entire process, from modeling and simulation to testing and deployment, thereby enabling users to rapidly construct and validate IUSSs. The principal advantages of the RflySim ToolChain are as follows: it provides a comprehensive solution that meets the full-stack development needs of IUSSs; the highly modular architecture and comprehensive software development kit (SDK) facilitate the automation of the entire IUSS development process. Furthermore, the high-fidelity model design and reliable architecture solution ensure a seamless transition from simulation to real-world deployment, which is known as the simulation to reality (Sim2Real) process. This paper presents a series of case studies that illustrate the effectiveness of the RflySim ToolChain in supporting the research and application of IUSSs.

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Distributed continuous-time aggregative optimization and its applications to power generation systems
Chengxin XIAN, Yu ZHAO, Yongfang LIU
Journal of Systems Engineering and Electronics    2026, 37 (1): 1-8.   DOI: 10.23919/JSEE.2026.000015
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This paper investigates the distributed continuous-time aggregative optimization problem for second-order multi-agent systems, where the local cost function is not only related to its own decision variables, but also to the aggregation of the decision variables of all the agents. By using the gradient descent method, the distributed average tracking (DAT) technique and the time-base generator (TBG) technique, a distributed continuous-time aggregative optimization algorithm is proposed. Subsequently, the optimality of the system’s equilibrium point is analyzed, and the convergence of the closed-loop system is proved using the Lyapunov stability theory. Finally, the effectiveness of the proposed algorithm is validated through case studies on multirobot systems and power generation systems.

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A method of line spectrum extraction based on target radiated spectrum feature and its post-processing
Wenshu DAI, Enming ZHENG, Kaikai BAO
Journal of Systems Engineering and Electronics    2021, 32 (6): 1381-1393.   DOI: 10.23919/JSEE.2021.000118
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To improve the ability of detecting underwater targets under strong wideband interference environment, an efficient method of line spectrum extraction is proposed, which fully utilizes the feature of the target spectrum that the high intense and stable line spectrum is superimposed on the wide continuous spectrum. This method modifies the traditional beam forming algorithm by calculating and fusing the beam forming results at multi-frequency band and multi-azimuth interval, showing an excellent way to extract the line spectrum when the interference and the target are not in the same azimuth interval simultaneously. Statistical efficiency of the estimated azimuth variance and corresponding power of the line spectrum band depends on the line spectra ratio (LSR) of the line spectrum. The change laws of the output signal to noise ratio (SNR) with the LSR, the input SNR, the integration time and the filtering bandwidth of different algorithms bring the selection principle of the critical LSR. As the basis, the detection gain of wideband energy integration and the narrowband line spectrum algorithm are theoretically analyzed. The simulation detection gain demonstrates a good match with the theoretical model. The application conditions of all methods are verified by the receiver operating characteristic (ROC) curve and experimental data from Qiandao Lake. In fact, combining the two methods for target detection reduces the missed detection rate. The proposed post-processing method in 2-dimension with the Kalman filter in the time dimension and the background equalization algorithm in the azimuth dimension makes use of the strong correlation between adjacent frames, could further remove background fluctuation and improve the display effect.

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Multi-objective frequency planning: concept, modeling, and solution
Hang GAO, Song ZHA, Jijun HUANG, Haiyang XIA, Jibin LIU
Journal of Systems Engineering and Electronics    2026, 37 (2): 337-356.   DOI: 10.23919/JSEE.2026.000058
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Frequency planning is of great significance which can effectively dispatch the battlefield resources of radio equipment. To enhance the efficiency of scheduling, this paper investigates the frequency planning problem (FPP) and puts forward a multi-objective approach. The proposed multi-objective model considers the coordination constraints of radio equipment alongside diverse resources, defining key points to delineate the cooperative interactions among radio equipment. The model integrates considerations of time, space, and energy, focusing on electromagnetic interference, frequency demand satisfaction and frequency occupancy as its primary optimization objectives. To improve the accuracy of the solution, this study proposes a multi-population multi-objective memetic algorithm (MPMA). This algorithm employs a segment-based coding strategy and a specialized genetic operator to facilitate the integration of global and local search techniques. Additionally, chaos initialization and a multi-population-based scheduling approach are incorporated to enhance global search performance. The experimental results demonstrate the superiority of the proposed model and MPMA in meeting the diverse scheduling needs of radio equipment across various scenarios.

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Threshold-type memristor-based crossbar array design and its application in handwritten digit recognition
Qingjian LI, Yan LIANG, Zhenzhou LU, Guangyi WANG
Journal of Systems Engineering and Electronics    2023, 34 (2): 324-334.   DOI: 10.23919/JSEE.2023.000018
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Neuromorphic computing simulates the operation of biological brain function for information processing and can potentially solve the bottleneck of the Von Neumann architecture. Inspired by the real characteristics of physical memristive devices, we propose a threshold-type nonlinear voltage-controlled memristor mathematical model which is used to design a novel memristor-based crossbar array. The presented crossbar array can simulate the synaptic weight in real number field rather than only positive number field. Theoretical analysis and simulation results of a 2×2 image inversion operation validate the feasibility of the proposed crossbar array and the necessary training and inference functions. Finally, the presented crossbar array is used to construct the neural network and then applied in the handwritten digit recognition. The Mixed National Institute of Standards and Technology (MNIST) database is adopted to train this neural network and it achieves a satisfactory accuracy.

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DEF-based energy consumption balancing optimization for LEO satellite networks
Hang DI, Tao DONG, Zhihui LIU, Shichao JIN
Journal of Systems Engineering and Electronics    2025, 36 (4): 922-931.   DOI: 10.23919/JSEE.2025.000054
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In low Earth orbit (LEO) satellite networks, on-board energy resources of each satellite are extremely limited. And with the increase of the node number and the traffic transmission pressure, the energy consumption in the networks presents uneven distribution. To achieve energy balance in networks, an energy consumption balancing optimization algorithm of LEO networks based on distance energy factor (DEF) is proposed. The DEF is defined as the function of the inter-satellite link distance and the cumulative network energy consumption ratio. According to the minimum sum of DEF on inter-satellite links, an energy consumption balancing algorithm based on DEF is proposed, which can realize dynamic traffic transmission optimization of multiple traffic services. It can effectively reduce the energy consumption pressure of core nodes with high energy consumption in the network, make full use of idle nodes with low energy consumption, and optimize the energy consumption distribution of the whole network according to the continuous iterations of each traffic service flow. Simulation results show that, compared with the traditional shortest path algorithm, the proposed method can improve the balancing performance of nodes by 75% under certain traffic pressure, and realize the optimization of energy consumption balancing of the whole network.

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Detecting spatio-temporal urban surface changes using identified temporary coherent scatterers
Fengming HU, Jicang WU
Journal of Systems Engineering and Electronics    2021, 32 (6): 1304-1317.   DOI: 10.23919/JSEE.2021.000110
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Synthetic aperture radar (SAR) is able to detect surface changes in urban areas with a short revisit time, showing its capability in disaster assessment and urbanization monitoring. Most presented change detection methods are conducted using couples of SAR amplitude images. However, a prior date of surface change is required to select a feasible image pair. We propose an automatic spatio-temporal change detection method by identifying the temporary coherent scatterers. Based on amplitude time series, ${\chi ^2} $ -test and iterative single pixel change detection are proposed to identify all step-times: the moments of the surface change. Then the parameters, e.g., deformation velocity and relative height, are estimated and corresponding coherent periods are identified by using interferometric phase time series. With identified temporary coherent scatterers, different types of temporal surface changes can be classified using the location of the coherent periods and spatial significant changes are identified combining point density and F values. The main advantage of our method is automatically detecting spatio-temporal surface changes without prior information. Experimental results by the proposed method show that both appearing and disappearing buildings with their step-times are successfully identified and results by ascending and descending SAR images show a good agreement.

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Ambiguity function analysis and side peaks suppression of Link16 signal based passive radar
Luyang BAI, Jun WANG, Xiaoling CHEN
Journal of Systems Engineering and Electronics    2023, 34 (6): 1526-1536.   DOI: 10.23919/JSEE.2023.000152
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Link16 data link is the communication standard of the joint tactical information distribution system (JTIDS) used by the U.S. military and North Atlantic Treaty Organization, which is applied as the opportunistic illuminator for passive radar in this paper. The time-domain expression of the Link16 signal is established, and its ambiguity function expression is derived. The time-delay dimension and Doppler dimension side peaks of which lead to the appearance of the false target during target detection. To solve the problem, the time-delay dimension and Doppler dimension side peaks suppression methods are proposed. For the problem that the conventional mismatched filter (MMF) cannot suppress the time-delay dimension side peaks, a neighborhood MMF (NMMF) is proposed. Experimental results demonstrate the effectiveness of the proposed methods.

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Failure analysis of unmanned autonomous swarm considering cascading effects
Bei XU, Guanghan BAI, Yun’an ZHANG, Yining FANG, Junyong TAO
Journal of Systems Engineering and Electronics    2022, 33 (3): 759-770.   DOI: 10.23919/JSEE.2022.000069
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In this paper, we focus on the failure analysis of unmanned autonomous swarm (UAS) considering cascading effects. A framework of failure analysis for UAS is proposed. Guided by the framework, the failure analysis of UAS with crash fault agents is performed. Resilience is used to analyze the processes of cascading failure and self-repair of UAS. Through simu-lation studies, we reveal the pivotal relationship between resilience, the swarm size, and the percentage of failed agents. The simulation results show that the swarm size does not affect the cascading failure process but has much influence on the process of self-repair and the final performance of the swarm. The results also reveal a tipping point exists in the swarm. Meanwhile, we get a counter-intuitive result that larger-scale UAS loses more resilience in the case of a small percentage of failed individuals, suggesting that the increasing swarm size does not necessarily lead to high resilience. It is also found that the temporal degree failure strategy performs much more harmfully to the resilience of swarm systems than the random failure. Our work can provide new insights into the mechanisms of swarm collapse, help build more robust UAS, and develop more efficient failure or protection strategies.

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Sliding mode control of three-phase AC/DC converters using exponential rate reaching law
Narin JEERANANTASIN, Suksun NUNGAM
Journal of Systems Engineering and Electronics    2022, 33 (1): 210-221.   DOI: 10.23919/JSEE.2022.000021
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Sliding mode control (SMC) becomes a common tool in designing robust nonlinear control systems, due to its inherent characteristics such as insensitivity to system uncertainties and fast dynamic response. Two modes are involved in the SMC operation, namely reaching mode and sliding mode. In the reaching mode, the system state is forced to reach the sliding surface in a finite time. The major drawback of the SMC approach is the occurrence of chattering in the sliding mode, which is undesirable in most applications. Generally, the trade-off between chattering reduction and fast reaching time must be considered in the conventional SMC design. This paper proposes SMC design with a novel reaching law called the exponential rate reaching law (ERRL) to reduce chattering, and the control structure of the converter is designed based on the multi-input SMC that is applied to a three-phase AC/DC power converter. The simulation and experimental results show the effectiveness of the proposed technique.

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A survey of fine-grained visual categorization based on deep learning
Yuxiang XIE, Quanzhi GONG, Xidao LUAN, Jie YAN, Jiahui ZHANG
Journal of Systems Engineering and Electronics    2024, 35 (6): 1337-1356.   DOI: 10.23919/JSEE.2022.000155
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Deep learning has achieved excellent results in various tasks in the field of computer vision, especially in fine-grained visual categorization. It aims to distinguish the subordinate categories of the label-level categories. Due to high intra-class variances and high inter-class similarity, the fine-grained visual categorization is extremely challenging. This paper first briefly introduces and analyzes the related public datasets. After that, some of the latest methods are reviewed. Based on the feature types, the feature processing methods, and the overall structure used in the model, we divide them into three types of methods: methods based on general convolutional neural network (CNN) and strong supervision of parts, methods based on single feature processing, and methods based on multiple feature processing. Most methods of the first type have a relatively simple structure, which is the result of the initial research. The methods of the other two types include models that have special structures and training processes, which are helpful to obtain discriminative features. We conduct a specific analysis on several methods with high accuracy on public datasets. In addition, we support that the focus of the future research is to solve the demand of existing methods for the large amount of the data and the computing power. In terms of technology, the extraction of the subtle feature information with the burgeoning vision transformer (ViT) network is also an important research direction.

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An improved genetic algorithm for causal discovery
Tengjiao MAO, Xianjin BU, Chunxiao CAI, Yue LU, Jing DU
Journal of Systems Engineering and Electronics    2025, 36 (3): 768-777.   DOI: 10.23919/JSEE.2025.000015
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The learning algorithms of causal discovery mainly include score-based methods and genetic algorithms (GA). The score-based algorithms are prone to searching space explosion. Classical GA is slow to converge, and prone to falling into local optima. To address these issues, an improved GA with domain knowledge (IGADK) is proposed. Firstly, domain knowledge is incorporated into the learning process of causality to construct a new fitness function. Secondly, a dynamical mutation operator is introduced in the algorithm to accelerate the convergence rate. Finally, an experiment is conducted on simulation data, which compares the classical GA with IGADK with domain knowledge of varying accuracy. The IGADK can greatly reduce the number of iterations, populations, and samples required for learning, which illustrates the efficiency and effectiveness of the proposed algorithm.

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Group cooperative midcourse guidance law design considering time-to-go
Ruitao ZHANG, Yangwang FANG, Zhan CHEN, Hang GUO, Wenxing FU
Journal of Systems Engineering and Electronics    2025, 36 (3): 835-853.   DOI: 10.23919/JSEE.2025.000065
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To solve the problem of providing the best initial situation for terminal guidance when multiple missiles intercept multiple targets, a group cooperative midcourse guidance law (GCMGL) considering time-to-go is proposed. Firstly, a three-dimensional (3D) guidance model is established and a cooperative trajectory shaping guidance law is given. Secondly, for estimating the unknown target maneuvering acceleration, an adaptive disturbance observer (ADO) is designed, combining finite-time theory with a radial basis function (RBF) neural network, and the convergence of the estimation error is proven using Lyapunov stability theory. Then, to ensure time-to-go cooperation among missiles within the same group and across different groups, the group consensus protocols of virtual collision point mean and the inter-group cooperative consensus protocol are designed respectively. Based on the group consensus protocols, the virtual collision point cooperative guidance law is given, and the finite-time convergence is proved by Lyapunov stability theory. Simultaneously, combined with trajectory shaping guidance law, virtual collision point cooperative guidance law and the inter-group cooperative consensus protocol, the design of GCMGL considering time-to-go is given. Finally, numerical simulation results show the effectiveness and the superiority of the proposed GCMGL.

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Lanchester equation for cognitive domain using hesitant fuzzy linguistic terms sets
Qi HAN, Weimin LI, Qiling XU, Minrui ZHAO, Runze HUO, Tao ZHANG
Journal of Systems Engineering and Electronics    2022, 33 (3): 674-682.   DOI: 10.23919/JSEE.2022.000062
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Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain. The cognitive domain will become the key domain to win in the future intelligent war. A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper. One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function. The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators. Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators, hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here. A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.

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Range estimation of few-shot underwater sound source in shallow water based on transfer learning and residual CNN
Qihai YAO, Yong WANG, Yixin YANG
Journal of Systems Engineering and Electronics    2023, 34 (4): 839-850.   DOI: 10.23919/JSEE.2023.000095
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Taking the real part and the imaginary part of complex sound pressure of the sound field as features, a transfer learning model is constructed. Based on the pre-training of a large amount of underwater acoustic data in the preselected sea area using the convolutional neural network (CNN), the few-shot underwater acoustic data in the test sea area are retrained to study the underwater sound source ranging problem. The S5 voyage data of SWellEX-96 experiment is used to verify the proposed method, realize the range estimation for the shallow source in the experiment, and compare the range estimation performance of the underwater target sound source of four methods: matched field processing (MFP), generalized regression neural network (GRNN), traditional CNN, and transfer learning. Experimental data processing results show that the transfer learning model based on residual CNN can effectively realize range estimation in few-shot scenes, and the estimation performance is remarkably better than that of other methods.

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Recognition of dynamically varying PRI modulation via deep learning and recurrence plot
Pengcheng WANG, Weisong LIU, Zheng LIU
Journal of Systems Engineering and Electronics    2023, 34 (4): 815-826.   DOI: 10.23919/JSEE.2022.000071
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Recognition of pulse repetition interval (PRI) modulation is a fundamental task in the interpretation of radar intentions. However, the existing PRI modulation recognition methods mainly focus on single-label classification of PRI sequences. The prerequisite for the effectiveness of these methods is that the PRI sequences are perfectly divided according to different modulation types before identification, while the actual situation is that radar pulses reach the receiver continuously, and there is no completely reliable method to achieve this division in the case of non-cooperative reception. Based on the above actual needs, this paper implements an algorithm based on the recurrence plot technique and the multi-target detection model, which does not need to divide the PRI sequence in advance. Compared with the sliding window method, it can more effectively realize the recognition of the dynamically varying PRI modulation.

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