地球物理摄动因素对远程弹道导弹命中精度的影响分析及补偿方法研究
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摘要
论文以提高我国机动发射远程弹道导弹命中精度为背景,针对弹道导弹要求命中精度高、作战准备时间短的特点,深入分析了地球物理摄动因素的影响,开展了考虑地球物理摄动因素下的射击诸元快速计算和制导补偿的研究,得到许多有意义的结果。论文的工作和创新点体现在以下几个方面。
首先,论文提出了一套考虑地球物理摄动因素的弹道快速计算方法:
对于主动段标准弹道,论文分析了不同射向和纬度下的弹道特性,提出了大气层内固定飞行程序的弹道拟合方法和大气层外弹道解析方法。对于12,000km射程的典型弹道,该方法对主动段关机点的逼近误差,速度小于0.3m/s,位置小于20m;
对于自由段标准弹道,论文系统分析了考虑地球扁率的四种自由段解析方法,并针对自由段弹道的特点,推导出基于状态空间摄动的等大地高度约束解析解,提出只在地球外部轨迹上求平均值的平根数方法。如果以地心距或大地高度为终端条件,状态空间摄动法无须迭代,可以将落点计算误差控制在50m以内,相比其它方法,在计算精度和计算速度方面具有优势;
对于考虑扰动引力的偏差弹道,论文将广义延拓逼近法和球谐函数换极法应用到扰动引力的赋值中,大大提高了计算速度。相对于有限元法,广义延拓逼近法在相同的存储量下逼近精度可提高1倍以上。通过对球谐函数换极法的改进,使其平均方法误差降低到15m以下。将换极法与状态空间摄动法结合,推导出四阶带谐项作用下自由段弹道射程角的等高偏差解析解。
其次,论文系统分析了扰动引力、定位定向误差、高空大气、上升段引力常数变化、电磁力等地球物理摄动因素对远程弹道导弹命中精度的影响:利用状态空间摄动法,给出了各个因素的误差传播方程。计算结果表明扰动引力和定位定向误差是其中影响最大的因素,而简化计算方法具有很高的精度;
分析了扰动引力对主动段弹道、被动段弹道、显式制导和惯导系统误差标定的影响;
同时考虑几何项、初值项和引力项,推导出定位定向误差影响分析的完整解析解,并针对是否存在独立的天文观测和显式制导给出不同的计算公式。计算表明该解析解计算速度快,计算精度高,其中速度偏差逼近的方法误差小于10%,位置偏差逼近的方法误差小于1%。
最后,论文设计了诸元和制导计算中进行补偿的方案,开发了通用的动力学仿真系统:
考虑主动段弹道变形,推导出发射方位角初值的精确确定模型,可以将逼近精度由传统方法的5提高到0.5 ;
提出了诸元和制导计算中地球物理摄动因素快速补偿的算法。其方法误差小于15m,同时可避免复杂弹道的迭代;
提出考虑地球自转的零射程线方法,并应用于弹道导弹的末修级标准飞行程序设计、多头分导方案设计与固体弹道导弹的耗尽关机制导中;
基于面向对象思想和统一建模语言,设计了考虑地球物理摄动因素的弹道导弹飞行动力学仿真框架,开发了导弹飞行动力学通用仿真软件。将设计样式引入导弹动力学的面向对象建模,并针对其特点提出了通用积分和层次聚合两种新的设计样式。
论文的工作对于缩短导弹发射准备时间、减小制导方法误差、提高导弹作战效能具有重要意义。
The primary goal of the thesis is to improve hit accuracy of mobile long-range ballistic missile. Aiming at the requirements of high accuracy and short launching preparation time, geophysical disturbance factors impact was lucubrated and the compensatory approaches in ballistic data calculation and guidance equation were studied. Some meaningful results are achieved and shown as follows.
At first ,the thesis put forward one group of fast trajectory calculation techniques considering geophysical disturbance factors:
For power-flight reference trajectory, the thesis analyzed trajectory characteristics in different launching azimuths and launch latitudes. Then the atmospheric ballistic fitting method under constant flight program and the extra-atmospheric ballistic analytic method were advanced. The cutoff state evaluated error is less than 0.3m/s for velocity and 20m for position when the missile range is 12,000km, typically.
For free-flight reference trajectory, the thesis first analyzed four analytic methods considering earth oblateness roundly, then deduced contour restricted analytic solution based on state space perturbance method, and advanced an modified mean element models in view of missile free-flight characteristics. If the terminal condition is geocentric range or geodetic height, state space perturbance method has no need for iterative computation process and can limit position error below 50m. So this method wins an advantage of other methods in calculating speed and precision.
For warp trajectory considering gravity anomaly, the thesis applied extension approximate method and pole changing spherical harmonics method to gravity anomaly calculation, and gain faster calculating rate. Using the same memory space, extensive approximate method gets twice the precision as the finite element method can. Pole changing spherical harmonics method was modified to keep the fall point warp below 15m. Combining Pole changing spherical harmonics method and state space perturbance method, contour restricted range angle analytic solution considering J3,J4 perturbance was deduced.
Then, the thesis analyzed geophysical disturbance factors impacting on hit accuracy such as gravity anomaly, positioning and orientation deviation, upper atmosphere, gravitation constant variety in power-flight phase, electromagnetic force systemically:
Error propagation equations were given for every factor based on state space perturbance method. Experiment results indicate that gravity anomaly, positioning and orientation deviation are the most significant factors, and simplified methods have high calculating precision.
Gravity anomaly influences power-flight trajectory, free-flight trajectory, explicit guidance and inertial system error calibration. All above were investigated in the thesis.
Integrated analytic solution about positioning and orientation deviation impact was proposed in view of geometry item, initial state item and gravitation item, and different calculation equations were deduced depending on whether independent celestial observation is existed or guidance mode is considered. Experiment results show that the method has high calculating rate, and velocity deviation evaluation is less than 10%, and position deviation evaluation is less than 1%.
At last, the thesis designed a data and guidance compensatory scheme, and developed a common dynamics simulation system:
Initial azimuth determination method in view of ballistic deformation was deduced, that reduces estimated error from 5 to 0.5 .
Geophysical disturbance factors compensatory arithmetic in data and guidance was built up, that can avoid complicated ballistic iterativeness and keep the fall point warp within 15m.
Zero range orientation in the spinning earth was presented, and was applied to reference flight program design in terminal correction phase, multiple independently-targeted sequence plan and burnout guidance in solid rocket.
A general simulation frame about ballistic missile dynamics was put forward based on object-oriented methodology and united modeling language, and common simulation software was developed to sustain study work. Design patterns can improve modeling level and efficiency, so four patterns were discussed, and two new patterns, namely common integral pattern and hiberarchy aggregation pattern, were put forward to satisfy vehicle dynamics specialty.
In summing up, it may be stated that the research work has contributed to shorten launching preparation time, decrease guidance equation error and improve fighting efficiency for ballistic missile.
首先,论文提出了一套考虑地球物理摄动因素的弹道快速计算方法:
对于主动段标准弹道,论文分析了不同射向和纬度下的弹道特性,提出了大气层内固定飞行程序的弹道拟合方法和大气层外弹道解析方法。对于12,000km射程的典型弹道,该方法对主动段关机点的逼近误差,速度小于0.3m/s,位置小于20m;
对于自由段标准弹道,论文系统分析了考虑地球扁率的四种自由段解析方法,并针对自由段弹道的特点,推导出基于状态空间摄动的等大地高度约束解析解,提出只在地球外部轨迹上求平均值的平根数方法。如果以地心距或大地高度为终端条件,状态空间摄动法无须迭代,可以将落点计算误差控制在50m以内,相比其它方法,在计算精度和计算速度方面具有优势;
对于考虑扰动引力的偏差弹道,论文将广义延拓逼近法和球谐函数换极法应用到扰动引力的赋值中,大大提高了计算速度。相对于有限元法,广义延拓逼近法在相同的存储量下逼近精度可提高1倍以上。通过对球谐函数换极法的改进,使其平均方法误差降低到15m以下。将换极法与状态空间摄动法结合,推导出四阶带谐项作用下自由段弹道射程角的等高偏差解析解。
其次,论文系统分析了扰动引力、定位定向误差、高空大气、上升段引力常数变化、电磁力等地球物理摄动因素对远程弹道导弹命中精度的影响:利用状态空间摄动法,给出了各个因素的误差传播方程。计算结果表明扰动引力和定位定向误差是其中影响最大的因素,而简化计算方法具有很高的精度;
分析了扰动引力对主动段弹道、被动段弹道、显式制导和惯导系统误差标定的影响;
同时考虑几何项、初值项和引力项,推导出定位定向误差影响分析的完整解析解,并针对是否存在独立的天文观测和显式制导给出不同的计算公式。计算表明该解析解计算速度快,计算精度高,其中速度偏差逼近的方法误差小于10%,位置偏差逼近的方法误差小于1%。
最后,论文设计了诸元和制导计算中进行补偿的方案,开发了通用的动力学仿真系统:
考虑主动段弹道变形,推导出发射方位角初值的精确确定模型,可以将逼近精度由传统方法的5提高到0.5 ;
提出了诸元和制导计算中地球物理摄动因素快速补偿的算法。其方法误差小于15m,同时可避免复杂弹道的迭代;
提出考虑地球自转的零射程线方法,并应用于弹道导弹的末修级标准飞行程序设计、多头分导方案设计与固体弹道导弹的耗尽关机制导中;
基于面向对象思想和统一建模语言,设计了考虑地球物理摄动因素的弹道导弹飞行动力学仿真框架,开发了导弹飞行动力学通用仿真软件。将设计样式引入导弹动力学的面向对象建模,并针对其特点提出了通用积分和层次聚合两种新的设计样式。
论文的工作对于缩短导弹发射准备时间、减小制导方法误差、提高导弹作战效能具有重要意义。
The primary goal of the thesis is to improve hit accuracy of mobile long-range ballistic missile. Aiming at the requirements of high accuracy and short launching preparation time, geophysical disturbance factors impact was lucubrated and the compensatory approaches in ballistic data calculation and guidance equation were studied. Some meaningful results are achieved and shown as follows.
At first ,the thesis put forward one group of fast trajectory calculation techniques considering geophysical disturbance factors:
For power-flight reference trajectory, the thesis analyzed trajectory characteristics in different launching azimuths and launch latitudes. Then the atmospheric ballistic fitting method under constant flight program and the extra-atmospheric ballistic analytic method were advanced. The cutoff state evaluated error is less than 0.3m/s for velocity and 20m for position when the missile range is 12,000km, typically.
For free-flight reference trajectory, the thesis first analyzed four analytic methods considering earth oblateness roundly, then deduced contour restricted analytic solution based on state space perturbance method, and advanced an modified mean element models in view of missile free-flight characteristics. If the terminal condition is geocentric range or geodetic height, state space perturbance method has no need for iterative computation process and can limit position error below 50m. So this method wins an advantage of other methods in calculating speed and precision.
For warp trajectory considering gravity anomaly, the thesis applied extension approximate method and pole changing spherical harmonics method to gravity anomaly calculation, and gain faster calculating rate. Using the same memory space, extensive approximate method gets twice the precision as the finite element method can. Pole changing spherical harmonics method was modified to keep the fall point warp below 15m. Combining Pole changing spherical harmonics method and state space perturbance method, contour restricted range angle analytic solution considering J3,J4 perturbance was deduced.
Then, the thesis analyzed geophysical disturbance factors impacting on hit accuracy such as gravity anomaly, positioning and orientation deviation, upper atmosphere, gravitation constant variety in power-flight phase, electromagnetic force systemically:
Error propagation equations were given for every factor based on state space perturbance method. Experiment results indicate that gravity anomaly, positioning and orientation deviation are the most significant factors, and simplified methods have high calculating precision.
Gravity anomaly influences power-flight trajectory, free-flight trajectory, explicit guidance and inertial system error calibration. All above were investigated in the thesis.
Integrated analytic solution about positioning and orientation deviation impact was proposed in view of geometry item, initial state item and gravitation item, and different calculation equations were deduced depending on whether independent celestial observation is existed or guidance mode is considered. Experiment results show that the method has high calculating rate, and velocity deviation evaluation is less than 10%, and position deviation evaluation is less than 1%.
At last, the thesis designed a data and guidance compensatory scheme, and developed a common dynamics simulation system:
Initial azimuth determination method in view of ballistic deformation was deduced, that reduces estimated error from 5 to 0.5 .
Geophysical disturbance factors compensatory arithmetic in data and guidance was built up, that can avoid complicated ballistic iterativeness and keep the fall point warp within 15m.
Zero range orientation in the spinning earth was presented, and was applied to reference flight program design in terminal correction phase, multiple independently-targeted sequence plan and burnout guidance in solid rocket.
A general simulation frame about ballistic missile dynamics was put forward based on object-oriented methodology and united modeling language, and common simulation software was developed to sustain study work. Design patterns can improve modeling level and efficiency, so four patterns were discussed, and two new patterns, namely common integral pattern and hiberarchy aggregation pattern, were put forward to satisfy vehicle dynamics specialty.
In summing up, it may be stated that the research work has contributed to shorten launching preparation time, decrease guidance equation error and improve fighting efficiency for ballistic missile.
引文
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