Research Of Ballistic Missile Trajectory Tracking With High-degree Cubature Kalman Filter

The issue of tracking ballistic missile is always a hotspot.With rapid development of ballistic missile technology and the worldwide spread,the importance of missile defense(MD)is becoming increasingly prominent.As the core of MD system,the research of precisely tracking ballistic missile has attracted much attention.In this paper,the application of nonlinear filtering method in ballistic missile tracking is studied under the background of ballistic missile tracking,By contrast with several nonlinear filtering methods,Higher-degree Cubature Kalman Filter(HCKF)is adopted to improve the estimation accuracy,and a variety of tracking filters based on HCKF are designed for different problems.The major contents are as follows:The radar measurement model and ballistic missile maneuver model are introduced.According to the traditional Gravity Turn(GT)model constraining from zero angle-attack,a new maneuvering model with the lateral force but without angle-attack constraints is derived.The Gauss integral is transformed into the sphere phase integral domain,and the integral is approximated by arbitrary order spherical rule and the phase rule.Therefore,fifth-degree spherical phase cubature rules are derived.HCKF is proposed based on this rule and applied to simulation of ballistic missile tracking.The results show that,under the same Gauss noise condition,the estimation accuracy of the HCKF is better than that of the conventional CKF,but with higher computational complexity.Continuously tracking ballistic missile in boost and coast phase with high precision is difficult for a single model.Combining HCKF and Interacting Multiple Model(IMM)method,IMM-HCKF is proposed.Based on the maneuvering model in boost and coast phase,the IMM-HCKF filter is designed.To improve the calculation efficiency and estimated accuracy,the calculation of model transition probability is improved.The method of determining the initial model transition probability is introduced.But the method to calculate model transfer probability online by the measurement is designed.The estimation method of target launch point and shutdown point parameter is derived.Simulation shows that IMM-HCKF can effectively reduce the estimation error of separation phase and shutdown point,and improve the estimation accuracy of key parameters.Generally,the dimension of ballistic missile tracking system is high,and the computational complexity is increased when HCKF is used to process the data.To solve this problem,the basic theory and characteristics of the reduced dimension filter is introduced.Some key formulas and propositions of the filter are deduced.According to the characteristics of nonlinear state equation and measurement equation,combining the fifth-degree spherical-radial cubature rule,a reduced-dimension HCKF is proposed.Based on the special form of measurement model,the detailed algorithm of reduced dimension and HCKF in trajectory tracking is presented.Trajectory tracking filter is designed for trajectory tracking simulation.The results show that the reduceddimension HCKF can reduce the computational complexity while maintaining the estimation accuracy of the HCKF.The deviation produced in the linear transformation process can not be ignored when the measurement noise is large,which reduce estimation accuracy of Exact Method(EX).Therefore,the measurement system model and the linear radar measurement equation of EX are introduced.The measurement error switching from polar coordinate system to Cartesian coordinate system is analyzed,and the unbiased linear measurement equation is established,A nonlinear EX pseudo measurement equation is constructed,change EX linear estimation of system errors into nonlinear estimation problems.Combining EX with HCKF,the UEX-HCKF(Unbiased EX-HCKF)method and its improved form IUEX-HCKF(Improved UEX-HCKF)are proposed to avoid the inverse calculation of local filter gain.Simulation results show that when the radar measurement noise is large,the estimation accuracy of UEX-HCKF and IUEX-HCKF is significantly improved compared with the traditional EX.To improve the convergence performance and the filter robustness of tracking ballistic missile in midcourse maneuver,the strong tracking HCKF is derived,combing the HCKF with strong tracking filtering(STF)theory.Since additional cubature points need to be calculated,the amount of calculation increases.The method is improved on the basis of strong tracking HCKF,and the two methods are proved to be equivalent.A method of on-line generation of multiple fading factors is designed,and a strong tracking HCKF with multiple fading factors is proposed.Simulation results show that the strong tracking HCKF algorithm has the advantages of robust STF and high precision of HCKF,convergence performance is improved.