薄煜明 , 郭治 , 钱龙军 , 等 . 现代火控理论与应用基础 [M ] . 北京 : 科学出版社 , 2012 .

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何山 , 吴盘龙 , 李星秀 , 等 . 基于刚体弹道模型的防空火控解算方法 [J ] . 兵工学报 , 2020 , 41 ( 8 ): 1494 - 1501 . DOI: 10.3969/j.issn.1000-1093.2020.08.003 http://doi.org/10.3969/j.issn.1000-1093.2020.08.003 为改善火控系统的通用性和实时性，提出了基于刚体弹道模型的防空火控解算方法。对目标量测信息进行无偏转换，并将无偏转换得到的噪声协方差矩阵做解耦，在对目标状态准确估计同时，降低滤波算法计算的复杂度；利用割弦迭代法计算出命中点坐标，并在每次迭代过程中，利用虚拟脱靶量对射击诸元进行修正，减少对弹道微分方程的计算次数，极大提高火控解算的求解速度。仿真实验结果表明，该方法有效和可行，可以更加精确地计算出射击诸元，且计算量相对于传统火控解算方法得到了显著改善。

HE S , WU P L , LI X X , et al. The antiaircraft fire control calculation method based on rigid body trajectory model [J ] . Acta Armamentarii , 2020 , 41 ( 8 ): 1494 - 1501 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.08.003 http://doi.org/10.3969/j.issn.1000-1093.2020.08.003 An antiaircraft fire control calculation method based on rigid body trajectory model is proposed for improving the versatility and real-time performance of fire control system. The target measurements are unbiasedly converted, and the noise covariance matrix is decoupled, which accurately estimates the target state and reduces the computational complexity of the filtering algorithm. The hit point is calculated by using the secant iteration method, and the firing data are corrected by the virtual miss distance in each iteration, which reduces the time of calculating the ballistic differential equation and greatly improves the speed of fire control calculation. The simulated results demonstrate the validness and feasibility of the proposed method. The firing data can be calculated more accurately, and the calculated amount is significantly improved compared with the traditional fire control calculation method.

宋丕极 . 枪炮与火箭外弹道学 [M ] . 北京 : 兵器工业出版社 , 1993 .

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CHEN M H , YU C H , GAO J L , et al. Quantum algorithm for Gaussian process regression [J ] . Physical Review A , 2022 , 106 ( 1 ): 012406 . DOI: 10.1103/PhysRevA.106.012406 http://doi.org/10.1103/PhysRevA.106.012406 https://link.aps.org/doi/10.1103/PhysRevA.106.012406 https://link.aps.org/doi/10.1103/PhysRevA.106.012406

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AMIT S , PUSHPENDRA S , BREJESH L , et al. Modeling and prediction of COVID-19 pandemic using Gaussian mixture model [J ] . Chaos,Solitons & Fractals , 2020 , 138 : 110023 . DOI: 10.1016/j.chaos.2020.110023 http://doi.org/10.1016/j.chaos.2020.110023 https://linkinghub.elsevier.com/retrieve/pii/S0960077920304215 https://linkinghub.elsevier.com/retrieve/pii/S0960077920304215

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张宏鹏 , 黄长强 , 唐上钦 . 基于卷积神经网络的无人作战飞机飞行轨迹实时预测 [J ] . 兵工学报 , 2020 , 41 ( 8 ): 1894 - 1903 .

ZHANG H P , HUANG C Q , TANG S Q . CNN-based real-time prediction method of flight trajectory of unmanned combat aerial vehicle [J ] . Acta Armamentarii , 2020 , 41 ( 9 ): 1894 - 1903 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2020.09.022 http://doi.org/10.3969/j.issn.1000-1093.2020.09.022 Trajectory prediction is part of air combat technology，and the predictors can select a more predictable maneuvering considerion of trajectory prediction results. A convolution neural network predicting method is proposed to obtain the position of unmanned combat aerial vehicle in a future time quickly and accurately. An improved model for limiting the angular velocity is presented since the original dynamic model can not correctly simulate the somersault maneuvering with roll angle deviation. The improved model is used for flight simulation under different conditions，and a large number of trajectory samples are obtained. The convolution neural networks with different layer number and convolution kernel number is trained and tested，and the network with the smallest prediction error is selected. Operational speed and error of the proposed method are compared with those of long short term memory neural network，recurrent neural network and fully connected neural network. The results show that the average prediction error of the proposed method is about 4.2 m on x axis，8.0 m on y axis and 19.5 m on z axis after 0.25 s without increasing operational time，and the errors are all smaller than those of the other methods.

PARK M K , LEE J M , KANG W H , et al. Predictive model for PV power generation using RNN (LSTM) [J ] . Journal of Mechanical Science and Technology , 2021 , 35 ( 2 ): 795 - 803 . DOI: 10.1007/s12206-021-0140-0 http://doi.org/10.1007/s12206-021-0140-0

GREG V H , CARLOS M , GONZALO N . A review on the long short-term memory model [J ] . Artificial Intelligence Review , 2020 , 53 ( 8 ): 5929 - 5955 . DOI: 10.1007/s10462-020-09838-1 http://doi.org/10.1007/s10462-020-09838-1

XIE A Q , YANG H , CHEN J , et al. A Short-term wind speed forecasting model based on a multi-variable long short-term memory network [J ] . Atmosphere , 2021 , 12 ( 5 ): 651 . DOI: 10.3390/atmos12050651 http://doi.org/10.3390/atmos12050651 https://www.mdpi.com/2073-4433/12/5/651 https://www.mdpi.com/2073-4433/12/5/651 Accurately forecasting wind speed on a short-term scale has become essential in the field of wind power energy. In this paper, a multi-variable long short-term memory network model (MV-LSTM) based on Pearson correlation coefficient feature selection is proposed to predict the short-term wind speed. The proposed method utilizes multiple historical meteorological variables, such as wind speed, temperature, humidity, and air pressure, to predict the wind speed in the next hour. Hourly data collected from two ground observation stations in Yanqing and Zhaitang in Beijing were divided into training and test sets. The training sets were used to train the model, and the test sets were used to evaluate the model with the root-mean-square error (RMSE), mean absolute error (MAE), mean bias error (MBE), and mean absolute percentage error (MAPE) metrics. The proposed method is compared with two other forecasting methods (the autoregressive moving average model (ARMA) method and the single-variable long short-term memory network (LSTM) method, which inputs only historical wind speed data) based on the same dataset. The experimental results prove the feasibility of the MV-LSTM method for short-term wind speed forecasting and its superiority to the ARMA method and the single-variable LSTM method.

LANDI F , BARADI L , CORNIA M , et al. Working memory connections for LSTM [J ] . Neural Networks , 2021 , 144 : 334 - 341 . DOI: 10.1016/j.neunet.2021.08.030 http://doi.org/10.1016/j.neunet.2021.08.030 Recurrent Neural Networks with Long Short-Term Memory (LSTM) make use of gating mechanisms to mitigate exploding and vanishing gradients when learning long-term dependencies. For this reason, LSTMs and other gated RNNs are widely adopted, being the standard de facto for many sequence modeling tasks. Although the memory cell inside the LSTM contains essential information, it is not allowed to influence the gating mechanism directly. In this work, we improve the gate potential by including information coming from the internal cell state. The proposed modification, named Working Memory Connection, consists in adding a learnable nonlinear projection of the cell content into the network gates. This modification can fit into the classical LSTM gates without any assumption on the underlying task, being particularly effective when dealing with longer sequences. Previous research effort in this direction, which goes back to the early 2000s, could not bring a consistent improvement over vanilla LSTM. As part of this paper, we identify a key issue tied to previous connections that heavily limits their effectiveness, hence preventing a successful integration of the knowledge coming from the internal cell state. We show through extensive experimental evaluation that Working Memory Connections constantly improve the performance of LSTMs on a variety of tasks. Numerical results suggest that the cell state contains useful information that is worth including in the gate structure.Copyright © 2021 Elsevier Ltd. All rights reserved.

ZHU Y , LIU J L , GUO C , et al. Prediction of battlefield target trajectory based on LSTM [C ] // Proceedings of the 2020 IEEE 16th International Conference on Control & Automation . Singapore : IEEE , 2020 : 725 - 730 .

SEPP H , JÜRGEN S . Long short-term memory [J ] . Neural Computation , 1997 , 9 ( 8 ): 1735 - 1780 . DOI: 10.1162/neco.1997.9.8.1735 http://doi.org/10.1162/neco.1997.9.8.1735 Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient-based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O(1). Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.

韩子鹏 . 弹箭外弹道学 [M ] . 北京 : 北京理工大学出版社 , 2014 : 74 - 86 .

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MUKADDES Ö T , TURGUT Ö . Derivation of three-derivative Runge-Kutta methods [J ] . Numerical Algorithms , 2017 , 74 ( 1 ): 247 - 265 . DOI: 10.1007/s11075-016-0147-2 http://doi.org/10.1007/s11075-016-0147-2 http://link.springer.com/10.1007/s11075-016-0147-2 http://link.springer.com/10.1007/s11075-016-0147-2