Analysis And Compensation Methods Effects For The Earth's Gravity Anomaly Field On Ballistic Missile Guidance Accuracy

The disturbing gravity field of the Earth is an important error source of the hit accuracy of long-range ballistic missiles.It is necessary to analyze the properties of disturbing gravity field and find effective compensation methods.Taking this as the background,this thesis makes efforts on the relevant theories and key technologies which are focused on improving the hit accuracy of maneuverable launched ballistic missiles considering the influence of disturbing gravity field.The main work and conclusions are as follows:First,the influence of the disturbing gravity field on navigation is analyzed.The initial state error of the missile and the disturbing gravity of active phase are two main error sources of disturbing gravity field imposed on the navigation.Based on propagation mechanism of initial positioning and orientating errors,the influence analysis model which includes apparent projection error,initial value error and force error influence model are derived.The influence mechanism of disturbing gravity of powered phase on navigation is analyzed based on the perturbation analysis.The simulation results show that the cut-off point error resulting from different initial state errors of the launch point is positively correlated with the plumb line deviation given the same launch direction.The influence of active disturbing gravity on navigation solutions mainly depends on the region that the missile flies across during the active phase.Second,the influence of the disturbing gravity field on the guidance accuracy of the ballistic missile is analyzed.(1)By substituting the error quantity of disturbing gravity imposed on flight characteristic quantity(navigation parameters,state parameters of standard cut-off point and error coefficients)into the cut-off point equations,an analytical model for the influence of flight characteristic error terms on perturbation guidance impact accuracy is established.(2)The effects of disturbing gravity on the required velocity are analyzed.Based on the analysis of the influence of disturbing gravity on the navigation parameters and the required velocity,the analytical model of the influence of disturbing gravity on the hit precision through gain velocity error is established.(3)By analyzing the influence of flight characteristic quantity which includes star sensor observations and the optimum coefficients of correction,the influence of the disturbing gravity field on stellar/inertial integrated guidance is analyzed.Monte Carlo simulation results show that starlight is effective information to correct the initial orienting error.Because starlight cannot reflect the information of the disturbing gravity,starlight cannot correct the effects of disturbing gravity.Third,the equivalent compensation theory and mode of the influence of disturbing gravity on the hit accuracy of the ballistic missile are established.Based on the control system theory,the difference of the perturbed system which considering the influence of disturbing gravity and the normal system which does not consider the influence of disturbing gravity is distinguished.And the relationships of equivalent compensation system with the perturbed system and the normal system are also analyzed.An equivalent compensation theory which uses ballistic data or guidance data for compensation and thus could achieve the same hit accuracy as that of directly compensating the disturbing gravity.This provides a general framework and theoretical basis for compensating the influence of disturbing gravity on the movement of the ballistic missile.According to the different design methods of observer and controller during the compensation process,the compensation modes of embedded mode,fractional step mode,sectional mode and map mode,etc.are proposed,which clarifies the relationships of the input and output of different compensation modes and the general principles of different compensation modes.Fourth,a fast compensation method is proposed ground launching data computation for the influence of the disturbing gravity field.Based on the approximate analytical solution to the motion equation for a long-range ballistic missile in free flight phase,the analytical solutions to two partial derivatives,i.e.,state error in cut-off point to launch azimuth and to program pitch rate,are derived with initial position and orientation error propagation under disturbing gravity field.Then,the corrected launching data can be obtained with the fast calculation formula based on the basic data.The simulation results show that the proposed method can reduce 99.9% computation time,compared with the widely used differentiation method.Moreover,the corrected impact point errors are less than 20 m in longitudinal direction and 10 m in lateral direction.This can meet the requirements of high-accuracy and rapidity for a long-range ballistic vehicle.Finally,the compensation method for ground data is proposed to tackle the influence of disturbing gravity field upon the guidance accuracy.For perturbation guidance compensation: a step-by-step compensation method is proposed for characteristic quantity affected by disturbing gravity,and a mapping compensation method adopting the cut-off equation correction is proposed for the influence of disturbing gravity upon perturbation guidance accuracy.The simulation results show that the longitudinal deviation is less than 5m,and the lateral deviation is less than 1m using the mapping compensation.The compensated results meet the demands of long-range ballistic missiles with simplified compensation procedure,which is of significant potential in applications.For closed guidance compensation: an error-coefficient-based mapping compensation method is established based on equivalent compensation theory by analyzing the variation of impact accuracy affected by irregular sphere gravity caused by trajectory deformation along with cut-off point position errors in the existence of large deviations.The simulation results show that both the compensated longitudinal and lateral deviations are all less than 5m when the final-stage engine thrust error increases by 10%.The proposed method can rapidly and effectively compensate for impact error affected by the irregular sphere gravity.This dissertation reveals the influence mechanism of disturbing gravity field on the accuracy of different guidance methods.The equivalent compensation theory is established for theoretical guide,and compensation methods are put forward accordingly for engineering applications.It is of great significance to further improve the missile hit accuracy and shorten the preparation time.