Boost-Phase ballistic missile trajectory estimation with ground based radar

A conditional boost-phase trajectory estimation method based on ballistic missile （BM） information database and classification is developed to estimate and predict boos-phase BM trajectory. The main uncertain factors to describe BM dynamics equation are reduced to the control law of trajectory pitch angle in boost-phase. After the BM mass at the beginning of estimation, the BM attack angle and the modification of engine thrust denoting BM acceleration are modeled reasonably, the boost-phase BM trajectory estimation with ground based radar is well realized. The validity of this estimation method is testified by computer simulation with a typical example.

Multi-target tracking algorithm of boost-phase ballistic missile defense

Considering the problem of multiple ballistic missiles tracking of boost-phase ballistic missile defense, a boost-phase tracking algorithm based on multiple hypotheses tracking （MHT） concept is proposed. This paper focuses on the tracking algo- rithm for hypothesis generation, hypothesis probability calculation, hypotheses reduction and pruning and other sectors. From an engineering point of view, a technique called the linear assignment problem （LAP） used in the implementation of M-best feasible hypotheses generation, the number of the hypotheses is relatively small compared with the total number that may exist in each scan, also the N-scan back pruning is used, the algorithm＇s efficiency and practicality have been improved. Monte Carlo simulation results show that the proposed algorithm can track the boost phase of multiple ballistic missiles and it has a good tracking performance compared with joint probability data association （JPDA）.

Consecutive tracking for ballistic missile based on bearings-only during boost phase

This paper proposes a modified centralized shifted Rayleigh filter（MCSRF） algorithm for tracking boost phase of ballistic missile（BM） trajectory with a highly nonlinear dynamical model based on bearings-only.This paper contributes three folds.Firstly,the mathematical model of an MCSRF for multiple passive sensors is derived.Then,minimum entropy based onedimensional optimization search to adaptively adjust the probability of the different filters for real time state estimation is deployed.Finally,the unscented transform（UT） is introduced to resolve the asymmetric state estimation problem.Simulation results show that the proposed algorithm can consecutively track the BM precisely during the boost phase.In comparison with the unscented Kalman filter（UKF） algorithm,the proposed algorithm effectively reduces the tracking position and velocity root mean square（RMS） errors,which will make more sense for early precision interception.

Research on ballistic missile laser SIMU error propagation mechanism

It is necessary that the laser inertial system is used to further improve the fire accuracy and quick reaction capability in the ballistic missile strapdown inertial navigation system. According to the guidance controlling method and the output and error model of ballistic missile laser SIMU, the mathematical model of error propagation mechanism is set up and any transfer environmental function of error coefficient that affects the fire accuracy is deduced. Also, the missile longitudinal/lateral impact point is calculated using MATLAB. These establish the technical foundation for further researching the dispersion characteristics of impact point and reducing the laser guidance error.

Multidisciplinary integrated design of long-range ballistic missile using PSO algorithm

In the case of the given design variables and constraint functions, this paper is concerned with the rapid overall parameters design of trajectory, propulsion and aerodynamics for long-range ballistic missiles based on the index of the minimum take-off mass.In contrast to the traditional subsystem independent design, this paper adopts the research idea of the combination of the subsystem independent design and the multisystem integration design.Firstly, the trajectory, propulsion and aerodynamics of the subsystem are separately designed by the engineering design, including the design of the minimum energy trajectory, the computation of propulsion system parameters, and the calculation of aerodynamic coefficient and dynamic derivative of the missile by employing the software of missile DATCOM. Then, the uniform design method is used to simplify the constraint conditions and the design variables through the integration design, and the accurate design of the optimized variables would be accomplished by adopting the uniform particle swarm optimization(PSO) algorithm. Finally, the automation design software is written for the three-stage solid ballistic missile. The take-off mass of 29 850 kg is derived by the subsystem independent design, and 20 constraints are reduced by employing the uniform design on the basis of 29 design variables and 32 constraints, and the take-off mass is dropped by 1 850 kg by applying the combination of the uniform design and PSO. The simulation results demonstrate the effectiveness and feasibility of the proposed hybrid optimization technique.

A split target detection and tracking algorithm for ballistic missile tracking during the re-entry phase

In the re-entry phase of a ballistic missile,decoys can be deployed as a mean to overburden enemy defenses.This results in a single track being split into multiple track-lets.Tracking of these track-lets is a critical task as any miss in the tracking procedure can become a cause of a major threat.The tracking process becomes more complicated in the presence of clutter.The low detection rate is one of the factors that may contribute to increasing the difficulty level in terms of tracking in the cluttered environment.This work introduces a new algorithm for the split event detection and target tracking under the framework of the joint integrated probabilistic data association(JIPDA)algorithm.The proposed algorithm is termed as split event-JIPDA(SE-JIPDA).This work establishes the mathematical foundation for the split target detection and tracking mechanism.The performance analysis is made under different simulation conditions to provide a clear insight into the merits of the proposed algorithm.The performance parameters in these simulations are the root mean square error(RMSE),confirmed true track rate(CTTR)and confirmed split true track rate(CSTTR).

Impact point prediction guidance of ballistic missile in high maneuver penetration condition

An impact point prediction(IPP) guidance based on supervised learning is proposed to address the problem of precise guidance for the ballistic missile in high maneuver penetration condition.An accurate ballistic trajectory model is applied to generate training samples,and ablation experiments are conducted to determine the mapping relationship between the flight state and the impact point.At the same time,the impact point coordinates are decoupled to improve the prediction accuracy,and the sigmoid activation function is improved to ameliorate the prediction efficiency.Therefore,an IPP neural network model,which solves the contradiction between the accuracy and the speed of the IPP,is established.In view of the performance deviation of the divert control system,the mapping relationship between the guidance parameters and the impact deviation is analysed based on the variational principle.In addition,a fast iterative model of guidance parameters is designed for reference to the Newton iteration method,which solves the nonlinear strong coupling problem of the guidance parameter solution.Monte Carlo simulation results show that the prediction accuracy of the impact point is high,with a 3 σ prediction error of 4.5 m,and the guidance method is robust,with a 3 σ error of 7.5 m.On the STM32F407 singlechip microcomputer,a single IPP takes about 2.374 ms,and a single guidance solution takes about9.936 ms,which has a good real-time performance and a certain engineering application value.

Conceptual Design Architecture Modeling and Simulation for Boost Phase Ballistic Missile Defense

The design review, simulation and validation of a Conceptual Design Architecture (CDA) for Ballistic Missile Defense (BMD) are presented. An intercept system that contains a Ground Based Interceptor (GBI) and its guidance sensors (both radar and infrared) are simulated. 3D model using MATLAB is developed for a multistage target with ascent phase acceleration profile that depends on total mass, propellant mass and the specific impulse in the gravity field. The radar cross section (RCS) and infrared radiation (IR) of the target structure is estimated as a function of the flight profile. The Kill Vehicle (KV) design is examined as a function of the KV mass, acceleration capability, aimpoint offset and impact energy to destroy the target. The aim of the CDA is to: detect the launch of a threat ballistic missile, determine whether the detected object is a threat,define the characteristics of the threat ballistic missile, develop a firing solution to negate the threat ballistic missile, engage the threat ballistic missile, and assess the effectiveness for ballistic missile intercept. The architecture is modeled in Matlab.

Robust Graded Sliding Mode Tracking Control for Low Speed Spinning Ballistic Missiles

The nonlinear dynamic model of spinning ballistic missiles is established during the first boosting phase of the missile. Based on the conventional backstepping sliding mode control and the assumption of a two time-scale separation of missile dynamics, a graded sliding mode controller is designed with two sub-sliding surfaces which have invariability to external disturbances and parameter perturbations, and a matrix which comprises three first order low pass filters is introduced to prevent “explosion of terms”. Owing to the upper bounds of the uncertainties are difficult to obtain in advance, adaptive laws are introduced to estimate the values of the uncertainties in real-time. Eventually, the numerical simulation results given to show the proposed controller can ensure the steady flight of missiles.

Optimal guidance against active defense ballistic missiles via differential game strategies

The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper.A class of optimal guidance schemes are proposed based on linear quadratic differential game method and numerical solution of Riccati differential equation.By choosing proper parameters, the proposed guidance schemes are able to drive the interceptor to the target and away from the defender simultaneously.Additionally, fuel cost, control saturation,chattering phenomenon and parameters selection were taken into account.Satisfaction of the proposed guidance schemes of the saddle point condition is proven theoretically.Finally, nonlinear numerical examples are included to demonstrate the effectiveness and performance of the developed guidance approaches.Comparison of control performance between different guidance schemes are presented and analysis.

Trajectory prediction of ballistic missiles using Gaussian process error model

Ballistic Missile Trajectory Prediction(BMTP)is critical to air defense systems.Most Trajectory Prediction(TP)methods focus on the coast and reentry phases,in which the Ballistic Missile(BM)trajectories are modeled as ellipses or the state components are propagated by the dynamic integral equations on time scales.In contrast,the boost-phase TP is more challenging because there are many unknown forces acting on the BM in this phase.To tackle this difficult problem,a novel BMTP method by using Gaussian Processes(GPs)is proposed in this paper.In particular,the GP is employed to train the prediction error model of the boost-phase trajectory database,in which the error refers to the difference between the true BM state at the prediction moment and the integral extrapolation of the BM state.And the final BMTP is a combination of the dynamic equation based numerical integration and the GP-based prediction error.Since the trained GP aims to capture the relationship between the numerical integration and the unknown error,the modified BM state prediction is closer to the true one compared with the original TP.Furthermore,the GP is able to output the uncertainty information of the TP,which is of great significance for determining the warning range centered on the predicted BM state.Simulation results show that the proposed method effectively improves the BMTP accuracy during the boost phase and provides reliable uncertainty estimation boundaries.

Robust Hybrid Control for Ballistic Missile Longitudinal Autopilot

This paper investigates the boost phase＇s longitudinal autopilot of a ballistic missile equipped with thrust vector control. The existing longitudinal autopilot employs time-invariant passive resistor-inductor-capacitor （RLC） network compensator as a control strategy, which does not take into account the time-varying missile dynamics. This may cause the closed-loop system instability in the presence of large disturbance and dynamics uncertainty. Therefore, the existing controller should be redesigned to achieve more stable vehicle response. In this paper, based on gain-scheduling adaptive control strategy, two different types of optimal controllers are proposed. The first controller is gain-scheduled optimal tuning-proportional-integral-derivative （PID） with actuator constraints, which supplies better response but requires a priori knowledge of the system dynamics. Moreover, the controller has oscillatory response in the presence of dynamic uncertainty. Taking this into account, gain-scheduled optimal linear quadratic （LQ） in conjunction with optimal tuning-compensator offers the greatest scope for controller improvement in the presence of dynamic uncertainty and large disturbance. The latter controller is tested through various scenarios for the validated nonlinear dynamic flight model of the real ballistic missile system with autopilot exposed to external disturbances.

2023年国外航天领域发展综述

为及时、准确地了解2023年度国外航天领域的发展动向,对国外航天运输领域、弹道导弹领域以及高超声速技术领域的最新发展情况进行了全面梳理,涉及美、俄等各国航天领域的重点型号研发、飞行试验情况以及重大热点事件等,并通过综述分析对2024年国外航天领域的发展进行了展望。

雷达干扰信号弹道参数变化量分析方法

本文中从模拟弹道导弹突防中末段对抗场景出发,依据弹道导弹的弹道特性以及突防中所产生的干扰信号延时特征,提出了一种雷达干扰信号弹道参数变化量的分析方法。通过提取有效的轨道数据,确定干扰信号的位置,计算干扰信号的轨道,定量地分析干扰信号的弹道参数的变化结果。结果表明,雷达干扰信号的轨迹能形成稳定逼真的弹道,所提出的方法对选择更优的弹道导弹突防策略有指导意义。

双层三阶多项式拟合的弹道导弹发射点估计方法

发射点估计是炮位侦察校射雷达的重要任务之一。在仅利用雷达测量数据的情况下,先通过三阶函数拟合弹道导弹主动段时间-高度曲线估计导弹的绝对发射时刻,从而求得各个弹道轨迹点相对于绝对发射时刻的相对发射时间,然后再次利用三阶函数拟合主动段相对时间-水平位移,进而得到弹道导弹发射点估计结果。通过弹道导弹运动模型仿真具有一二级助推的弹道数据,并增加雷达观测误差,分析验证了所提方法的有效性和精确性。经测试,所提方法求解过程简单,对主动段弹道拟合准确,发射点估计精度达到0.6%以内,定位误差较传统方法降低了50%以上。

美国KEI导弹发展研究及性能分析

动能拦截弹(kinetic energy interceptor,KEI)主要用于拦截在助推段、上升段以及中段飞行的中远程和洲际弹道导弹,具有高速、高加速的特点。通过文献资料的研究分析和建模仿真,对KEI导弹的总体参数、气动参数、动力参数进行了反设计和研究,并对KEI导弹的飞行性能和拦截性能进行了仿真,结果表明:KEI导弹能够在约60 s内加速至6 km/s,并对典型目标具备在助推段/上升段拦截弹道导弹的能力,对国内拦截武器的发展和研究具有参考意义。

导弹突防后弹道机动调整策略强化学习

针对弹道导弹中段突防后飞行弹道与标准弹道产生较大偏离的弹道机动调整问题,建立了机动调整时机策略最优化模型。设计了机动调整逆序Q学习算法,采用Tile coding逼近器编码状态特征空间,并对其进行线性逼近。构建了Q学习算法与蒙特卡罗方法相结合的逆序更新策略机制,以对导弹机动调整最优时机进行训练。仿真测试分析结果表明,在给定场景参数下,通过10000代强化学习算法训练得到的策略能够可靠地使用最少机动次数控制导弹突防后飞行弹道的调整决策,验证了方法的有效性。

首要教学原理下反导预警雷达探测技术课程教学改革

针对反导预警雷达探测技术课程教学中存在的基础衔接不流畅、高阶挑战有差距、理实一体落实差问题,以“为战育人”为核心导向,引入首要教学原理,提出了课程的“聚焦问题-激活旧知-示证新知-应用新知-融会贯通”五步教学方法.教学实践表明,该教学方法用于反导预警雷达探测技术课程教学改善效果明显.

基于三维空间的激光驾束炮射导弹设计及外弹道仿真

在激光驾束炮射导弹外弹道半实物仿真,以装备模拟器为核心的军事仿真训练系统的研究背景下,建立炮射导弹的外弹道运动学方程和动力学方程;以“芦笛”炮射导弹为参考模型,对导弹进行总体结构设计,并进行三维建模;并用Missile Datcom软件编程对炮射导弹的气动力系数和气动力矩系数进行计算;最后运用MATLAB软件建立炮射导弹的仿真模型,通过函数提取气动特性计算得到炮射导弹在打击目标时外弹道及飞行姿态随时间变化的曲线,并对其进行分析,实现在三维空间下运用三点法对任意运动目标进行精准打击。

地球同步轨道卫星对低轨卫星的目标引导方法

在实际作战中,地球同步轨道卫星通常是最先发现弹道导弹发射的预警装备,然而,其提供的缺维探测信息,使得传统的引导交接方法难以直接应用于其对低轨卫星的目标引导上。针对此问题,对地球同步轨道卫星对低轨卫星的目标引导方法进行研究。首先,根据弹道导弹在发射及主动段飞行过程中产生红外辐射特性时的飞行高度约束,计算在单颗地球同步轨道卫星引导下,低轨卫星红外传感器的方位和俯仰探测范围。其次,对低轨卫星红外传感器的探测距离进行建模和计算,实现低轨卫星对目标的成功探测。最后,通过模拟仿真实验,验证了该方法的有效性和准确性。