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.

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.

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.

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).

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）.

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.

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.

Damage behavior of the KKV direct hit against fluid-filled submunition payload

The damage effects of fluid-filled submunition payload impacted by the kinetic kill vehicle(KKV)are investigated by simulations and ground-based experiments.Numerical simulations showed that the damage level and number of submunitions were significantly influenced by the diameter of the KKV compared with its length.Based on that,a high velocity penetrator formed by shaped charge explosion was used to simulate the direct hit experiment of a KKV impacting submunition payload.Experimental results demonstrated that the damage modes of submunitions mainly included the slight damage,perforation and total smash,showing a good agreement with the simulations.To understand the multiple damage modes of submunitions,the damage behavior of the submunitions in direct hit process were analyzed based on the AUTODYN-3D code.Numerical results presented that increased KKV diameter can increase the crater diameter and expand the damage volume,which will achieve a higher direct hit lethality.Further analysis indicated that there were other mechanical behaviors can enhance the damage to submunitions not lying in the KKV flight path,such as secondary debris kill,neighboring submunitions collision with each other,and high-speed fluid injection effect.

Directional Dispensing of KE-Rod

With the numerical simulation and high-speed camera, a series of images of dispensing of rod from different devices were obtained. The process of dispensing of rods driven by aiming explosive charge and the influence of different structures on dispensing velocity and angle of KE-rod were studied through analyzing the images. All these can be helpful for the design of new concept anti tactical ballistic missile(ATBM) KE-rod warheads.