Uncertainty Engagement Analysis Of Exo-Atmospheric Missile Defense System Based On Reachable Sets

In the missile defense progress,engagement analysis refers to a procedure that considering the incoming target,the command and control system computes the set of all possible intercept solutions and determines the optimal intercept plan.This procedure is of critical significance since it determines the consequent engagement geometry between the interceptor and target.Within the framework of exo-atmospheric missile defense,this dissertation develops an advanced approach for engagement analysis.The main achievements are summarized as follows.The development direction,ope ration process and primary missions of future command and control system are explored.The technique of ballistic missile defense has been evolved for decades.Equipments are developed and deployed,but their efficiencies are necessary to be enhanced.According to the evolution history of the US missile defense system,it is pointed out that future command and control system should adapt to the tendency of integration,network and collaboration.An exo-atmospheric missile defense system is modeled and the typical operation process and primary missions of command and control system are discussed,which serves as a reference for the practice in ballistic missile defense.A methodology of trajectory error propagation is established based on the relative motion theory.The relative motion theory is employed to solve the error propagation problem.The expectation trajectory is treated as the chief and the deviation trajectory is treated as the deputy,thus the propagation process of trajectory error can be characterized by the relative motion between the deputy and chief.Originating from the general relative dynamic equation,four different kinds of models are derived for different situations of error propagation.Under the assumptions of two-body or J2 gravitation,the state-transition-matrix-based methods are applicable to propagation problems with small initial error and short flight interval,while the state-transition-tensor-based methods are applicable not only to the above problems but also to those with large initial error or long flight interval.A methodology of trajectory error propagation is formed by the proposed four methods and simulation examples are fulfilled to prove its efficiency.A strategy of error chain analysis of exo-atmospheric target is proposed.One difficulty of engagement analysis is the characterization of uncertainty.An error-chain-based strategy is proposed to solve this problem.The target state is characterized by the error ellipsoid thus the target trajectory can be described by the error chain.Based on the detection of early warning satellites,the exponential weighted recursive least square algorithm is introduced to estimate the target burnout state.Based on the detection of early warning radar,the extended Kalman filter method is improved to estimate the target trajectory.Based on the state-transition-tensor method under J2 gravitation,a trajectory error prediction strategy is proposed for the exo-atmospheric target.Considering the three conditions of no-detection,single-radar-detection and multi-radar-detection,simulate examples are fulfilled to investigate the evolution philosophy of the error chain,which serves as an efficient approach for uncertainty characterization.A Reachable Set model of exo-atmosphe ric interceptor is established.The other difficulty of engagement analysis is the description of interceptor ability.A Reachable Set(RS)model is established for this purpose.Basic coordinate systems are introduced and an implicit trajectory equation is proposed according to the boost phase dynamics of interceptor.The precise definition and the distortion mechanism of RS are investigated and a mathematical model of the distorted RS is then formulated through a dimension-reduction analysis.By treating the outer boundary of the RS on a sphere surface as a spherical convex hull,two relevant theorems are proposed and the RS envelope is depicted by the computational geometry theory.Based on RS model,the algorithms of intercept window analysis and launch parameter determination are provided.Simulation examples show that the proposed method can avoid intensive on-line computation and provide an accurate and effective approach for interceptor engagement analysis.An approach of unce rtainty engagement analysis is proposed.By employing the trajectory error chain and Reachable Set model,an approach of intercept engagement analysis considering uncertainty is proposed.For the problem of intercept ability evaluation,a miss-distance-based strategy is provided.Uncertainty is projected from the target state to the intercept miss distance.The performance of the nominal trajectory of the interceptor can be measured by the statistic characteristics of miss distance.According to the correction capacity of the control system,the formula of kill probability of the interceptor can be obtained.For the problem of intercept mission planning,a multiple attribute decision making method is provided.The index system of intercept plan efficiency is constructed thus the selection of the optimal plan can be treated as a multi-alternatives sequencing problem.The algorithms of index normalization and weight determination are introduced and the formula of overall efficiency of different intercept plans is proposed.Simulation examples show that the proposed approach can accomplish the uncertainty engagement analysis effectively.The simulation software of command and control system is designed and developed.Based on the simulation platform of ballistic missile defense,the simulation software of command and control system is developed.This software is integrated with other simulation models and the management nodes to construct the distributed simulation system of exo-atmospheric missile defense.The structure,function and operation mechanism of the distributed system are introduced briefly.The development process,functional modules,simulation procedure and data interface of the command and control system software are explained in detail.At last,an application example of the simulation software is provided.The exo-atmospheric missile defense system is hard to characterize due to its complex structure,high nonlinearity and strong uncertainty.In this dissertation,effective efforts are made to explore the mechanism of the defense process.Mathematic tools,such as error chain analysis and Reachable Set model,are proposed and the uncertainty engagement analysis approach is developed consequently.The achievements obtained in the current dissertation serve as powerful support to the improvement of efficiency of exo-atmospheric missile defense.