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韩春耀 , 熊家军 , 张凯 , 等 . 高超声速飞行器分解集成轨迹预测算法 [J ] . 系统工程与电子技术 , 2018 , 40 ( 1 ): 151 - 158 .

HAN C Y , XIONG J J , ZHANG K , et al . Decomposition ensemble trajectory prediction algorithm for hypersonic vehicle [J ] . Systems Engineering and Electronics , 2018 , 40 ( 1 ): 151 - 158 . (in Chinese) DOI: 10.3969/j.issn.1001-506X.2018.01.22 http://doi.org/10.3969/j.issn.1001-506X.2018.01.22 <div style="text-align:justify;"> <span style="line-height:1.5;">Aiming at the trajectory prediction of unpowered gliding hypersonic vehicle and its application requirements, a decomposition ensemble trajectory prediction model is proposed.&nbsp;</span><span style="line-height:1.5;">Firstly, according to the periodicity leap characteristic of the hypersonic vehicle, the trajectory sequence is decomposed into sub-sequences with trend, periodicity and random&nbsp;</span><span style="line-height:1.5;">characteristics by using the thought of decomposition and integration. Then, using the corresponding trajectory prediction model to predict each trajectory sub-sequence on the&nbsp;</span><span style="line-height:1.5;">basis of sub-sequence characteristics. Finally, the ensemble of the prediction </span><span style="line-height:1.5;">result of each trajectory prediction sub-model is taken as the final prediction value.&nbsp;</span><span style="line-height:1.5;">Due to the high degree of fit between the sub-sequence and the trajectory prediction sub-model, the decomposition ensemble trajectory prediction algorithm has more&nbsp;</span><span style="line-height:1.5;">advantages than the trajectory prediction algorithm using a single model. The simulation results show that the decomposition ensemble trajectory prediction algorithm can&nbsp;</span><span style="line-height:1.5;">improve the accuracy of trajectory prediction effectively.</span></div>

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魏喜庆 , 顾龙飞 , 李瑞康 . 基于Singer模型的高超声速飞行器轨迹跟踪与预测 [J ] . 航天控制 , 2017 , 35 ( 4 ): 62 - 72 .

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翟岱亮 , 雷虎民 , 李炯 , 等 . 基于自适应IMM的高超声速飞行器轨迹预测 [J ] . 航空学报 , 2016 , 37 ( 11 ): 3466 - 3475 . DOI: 10.7527/S1000-6893.2016.0044 http://doi.org/10.7527/S1000-6893.2016.0044 为了给基于预测命中点法的高超声速飞行器中制导拦截提供先验知识，提出高超声速飞行器的轨迹预测方法。首先，给出高超声速环境下与目标姿态近似线性的气动参数；其次，针对气动参数作控制量的运动模型，设计自适应交互多模型（IMM）跟踪算法，并进行性能有效性验证；然后，根据气动参数特性和目标假设机动方式，设计基于最小二乘拟合的轨迹预测方法。通过对目标轨迹进行跟踪和预测仿真，预测100 s的位置误差均小于5 km，速度误差均小于100 m/s，结果表明基于自适应IMM的轨迹预测方法对有规律机动的目标进行轨迹预测，效果良好。

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吉瑞萍 , 张程祎 , 梁彦 , 等 . 基于LSTM的弹道导弹主动段轨迹预报 [J ] . 系统工程与电子技术 , 2022 , 44 ( 6 ): 1968 - 1976 . DOI: 10.12305/j.issn.1001-506X.2022.06.24 http://doi.org/10.12305/j.issn.1001-506X.2022.06.24 弹道导弹主动段长周期轨迹预报能够为导弹防御系统提供早期预警信息。传统的轨迹预报方法大多集中在导弹的自由段与再入段, 通过解析法、数值积分法或函数逼近法推断未来时刻目标的状态。由于弹道导弹在主动段会受到多个未知作用力的影响, 其轨迹预报相比自由段与再入段更具挑战性。为此, 本文提出了一种基于长短时记忆(long short-term memeory, LSTM)网络的弹道导弹主动段轨迹预报方法。首先, 根据导弹主动段动力学模型与弹道参数典型取值生成用于网络训练的大规模轨迹样本; 其次, 设计了基于深度LSTM网络的弹道导弹主动段轨迹递归预报方法; 最后, 与基于数值积分法、多项式拟合及反向传播神经网络的轨迹预报方法的实验对比, 表明了所提方法在主动段轨迹预报上的优越性。

JI R P , ZHANG C Y , LIANG Y , et al . Trajectory prediction of boost-phase ballistic missile based on LSTM [J ] . Systems Engineering and Electronics , 2022 , 44 ( 6 ): 1968 - 1976 . (in Chinese) DOI: 10.12305/j.issn.1001-506X.2022.06.24 http://doi.org/10.12305/j.issn.1001-506X.2022.06.24 Long term trajectory prediction for boost-phase ballistic missile (BM) can provide early warning information for the missile defense system. Traditional trajectory prediction methods mostly focus on the BM's coast and reentry phases, inferring the target state at future time through analytical, numerical integration or function approximation methods. In contrast, the boost-phase trajectory prediction is more challenging because there are many unknown forces acting on the BM during this stage. To this end, a long short-term memory (LSTM) network based boost-phase BM trajectory prediction method is proposed in this paper. Specifically, large-scale trajectory samples for the network training are generated first according to the dynamic model of the boost-phase BM and the typical ballistic parameters. Next, a recursive trajectory prediction method for the boost-phase BM based on deep LSTM network is designed. Finally, simulation results compared with the numerical integration, polynomial fitting and back propagation neural network based trajectory prediction methods show the superiority of the proposed method in long term boost-phase BM trajectory prediction.

杨春伟 , 刘炳琪 , 王继平 , 等 . 基于注意力机制的高超声速飞行器LSTM智能轨迹预测 [J ] . 兵工学报 , 2022 , 43 ( 增刊2 ): 78 - 86 .

YANG C W , LIU B Q , WANG J P , et al . LSTM intelligent trajectory prediction for hypersonic vehicles based on attention mechanism [J ] . Acta Armamentarii , 2022 , 43 ( S2 ): 78 - 86 . (in Chinese) DOI: 10.12382/bgxb.2022.B002 http://doi.org/10.12382/bgxb.2022.B002 The near-space hypersonic vehicle has a non-inertial trajectory form and large-scale and strong maneuvering penetration capabilities.The accurate prediction of the target's flight trajectory can provide strong technical support for the effective interception of the missile interception system.To address the problem of glide and skiptrajectory prediction of hypersonic aircrafts, this paper proposes a Seq2Seq trajectory prediction model based on attention mechanism, which employsthe LSTM network to design the encoder and decoder, and uses the information extracted by attention mechanism to performdecodingand prediction. The network takes the six-dimensional feature sequence of the target trajectory's position, velocity, trajectory inclination angle and attack angle as the input network, and the continuous trajectory sequence during a certain period in the futureis the network output. The trajectory data of the target aircraft obtained by the trajectory simulation model is used as the training setto train and optimize the network. The experimental results show that the proposed network can effectively predict the various flight trajectories of hypersonic aircrafts with small prediction errors, which can provide some insights into the missile interception system.

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张堃 , 杜睿怡 , 时昊天 , 等 . 基于Mogrifier-BiGRU的飞行器轨迹预测 [J ] . 兵工学报 , 2024 , 45 ( 2 ): 373 - 384 . DOI: 10.12382/bgxb.2022.0750 http://doi.org/10.12382/bgxb.2022.0750 针对当前飞行器轨迹预测准确性低的问题,引入双向传播机制和Mogrifier数据耦合模块,改进传统门控循环单元网络,提出基于Mogrifier-BiGRU的飞行器轨迹预测算法,加强网络对历史数据的学习与记忆,使得输入信息与隐藏层数据的充分耦合,提高预测准确度。仿真结果表明,所提方法对飞行器轨迹预测的准确度可达到96.26%,满足我方作战指挥人员对战场态势趋势准确预测的实际需求。

ZHANG K , DU R Y , SHI H T , et al . Prediction of aircraft trajectory based on Mogrifier-BiGRU [J ] . Acta Armamentarii , 2024 , 45 ( 2 ): 373 - 384 . (in Chinese) DOI: 10.12382/bgxb.2022.0750 http://doi.org/10.12382/bgxb.2022.0750 For the low accuracy of trajectory prediction of current aircraft, the bidirectional propagation mechanism and Mogrifier data coupling module are introduced to improve the gated recurrent unit (GRU) network. A prediction algorithm of aircraft trajectory based on Mogrifier-BiGRU is proposed, which strengthens the learning and memory of historical data, makes the input information fully coupled with the hidden layer data, and improves the prediction accuracy. The simulated results show that the accuracy of the proposed method for predicting the aircraft maneuver trajectory can reach 96.26%, which meets the actual demand of combat commanders for accurate prediction of battlefield situation.

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李世杰 , 雷虎民 , 周池军 , 等 . 基于控制变量估计的高超声速再入滑翔目标轨迹预测算法 [J ] . 系统工程与电子技术 , 2020 , 42 ( 10 ): 2320 - 2327 . DOI: 10.3969/j.issn.1001-506X.2020.10.21 http://doi.org/10.3969/j.issn.1001-506X.2020.10.21 以高超声速再入滑翔目标为研究对象,在对目标机动控制变量进行建模分析的基础上提出了一种轨迹预测算法。首先,基于动力学建模构建了目标跟踪模型,利用气动参数对目标状态向量进行扩维并推导了对应的运动模型。其次,构造了适用于轨迹预测的目标机动控制变量,在不同机动模式下分析了控制变量的变化规律,基于控制变量设计了对应运动方程以及轨迹预测模型。最后,仿真生成了两条轨迹并对所提算法进行了仿真验证,分析了算法性能。仿真结果表明所提轨迹预测算法能够取得较好的预测效果。

LI S J , LEI H M , ZHOU C J , et al . Trajectory prediction algorithm for hypersonic reentry gliding target based on control variables estimation [J ] . Systems Engineering and Electronics , 2020 , 42 ( 10 ): 2320 - 2327 . (in Chinese) DOI: 10.3969/j.issn.1001-506X.2020.10.21 http://doi.org/10.3969/j.issn.1001-506X.2020.10.21 A trajectory prediction algorithm for hypersonic reentry gliding target based on the modeling and analysis of target maneuver control variables is proposed. Firstly, the target tracking model based on the dynamic model is established, the target state vector is augmented with the aerodynamic parameters and the corresponding motion model is deduced. Secondly, the target maneuver control variables suitable for trajectory prediction are constructed, and the change rules of the control variables in variable maneuvering modes are analyzed. Based on the control variables, the corresponding equations of motion and the prediction model are designed. Finally, the simulations are carried out for two trajectories, and the proposed algorithm is verified by simulation to analyze the performance of algorithm. Simulation results indicate that the proposed trajetory prediction algorithm is able to get satisfying prediction effects.

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