基于关机点状态的航天器落点计算及精度分析
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摘要
当全程测量数据不完备时,如何根据关机点状态进行事后精确落点计算对于航天器精度评估非常重要。首先建立了航天器自由段和再入段的动力学方程,再入段充分考虑了空气阻力。接着采用复合数值积分法对动力学方程进行求解,使用四阶Runge-Kutta法对积分进行起步,采用Admas-Cowell积分减少误差。通过建立误差系数矩阵,研究了关机点状态估计信息和再入段空气密度偏差对落点计算的影响。实际数据计算和仿真结果表明,采用的复合数值积分法能提高落点计算的精度和速度,建立的误差系数矩阵能分析关机点状态和空气密度偏差对落点位置的影响,具有良好的实际应用价值。
The post-flight fall point accurate estimation based on burnout point state is very important to spacecraft accuracy analysis and evaluation when the overall trajectory tacking data is missing. Firstly,the free and reentry flight dynamics equations of the spacecraft are established,which are fully considered by the air resistance. Then,the dynamics equations are solved by using the compound numerical method of integration and the integration is started by using four-steps Runge-Kutta method while Admas-Cowell method is used for integration to decrease the error. The influence of estimation information of burnout point state on fall point estimation is studied by applying error coefficient matrix. The results of real data computation and simulation show that the accuracy and speed of fall point estimation can be enhanced by using compound numerical method of integration. The influence of estimation information of burnout point state on fall point estimation can be studied though error coefficient matrix. This method is proven that it has good application value.
The post-flight fall point accurate estimation based on burnout point state is very important to spacecraft accuracy analysis and evaluation when the overall trajectory tacking data is missing. Firstly,the free and reentry flight dynamics equations of the spacecraft are established,which are fully considered by the air resistance. Then,the dynamics equations are solved by using the compound numerical method of integration and the integration is started by using four-steps Runge-Kutta method while Admas-Cowell method is used for integration to decrease the error. The influence of estimation information of burnout point state on fall point estimation is studied by applying error coefficient matrix. The results of real data computation and simulation show that the accuracy and speed of fall point estimation can be enhanced by using compound numerical method of integration. The influence of estimation information of burnout point state on fall point estimation can be studied though error coefficient matrix. This method is proven that it has good application value.
引文
[1]陈克俊,刘鲁华,孟云鹤.远程火箭飞行动力学与制导[M].北京:国防工业出版社,2014.(Chen Kejun,Liu Luhua,Meng Yunhe.Launch Vehicle Flight Dynamics and Guidance[M].Beijing:National Defense Industry Press,2014.)
[2]董燕琴,戴金海,安维廉.弹道导弹落点预报技术综述[J].航天控制,2008,26(1):91-95.(Dong Yanqin,Dai Jinhai,An Weilian.A Survey of Impact Point Prediction Technology for Ballistic Missile[J].Aerospace Control,2008,26(1):91-95.)
[3]刘仁,王爱华,郭桂治.基于关机点状态的战术弹道导弹落点估计[J].空军工程大学学报(自然科学版),2010,11(1):27-30.(Liu Ren,Wang Aihua,Guo Guizhi.Impact Point Estimation of Tactical Ballistic Missile Based on the State of Burnout Point[J].Journal of Air Force Engineering University(Natural Science Edition),2010,11(1):27-30.)
[4]常晓华,杨宇和,张鸣,等.任意大地高约束下的弹道飞行器自由段解析解[J].导弹与航天运载技术,2016,(5):62-66.(Chang Xiaohua,Yang Yuhe,Zhang Ming,et al.Analytical Solution of Arbitrary Geodetic Height Restricted for Free Flight Trajectory of Ballistic Vehicle[J].Missiles and Space Vehicles,2016,(5):62-66.)
[5]刘彦君,乔士东,黄金才,等.一种高精度弹道导弹落点预测方法[J].弹道学报,2012,24(1):22-26.(Liu Yanjun,Qiao Shidong,Huang Jincai,et al.A Method of Impact Point Prediction of Ballistic Missile[J].Journal of Ballistics,2012,24(1):22-26.)
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[9]Leonard C,Hainz III,Mark C.Modified Projectile Linear Theory for Rapid Trajectory Prediction[J].Journal of Guidance,Control,and Dynamics,2005,28(5):1006-1014.
[10]赵捍东,李志鹏.基于径向基函数神经网络和无迹卡尔曼滤波的弹丸落点预报方法研究[J].兵工学报,2014,35(7):965-971.(Zhao Handong,Li Zhipeng.Projectile Impact-point Prediction Method Based on Radial Basis Function Neural Network and Unscented Kalman Filter[J].Acta Armamentarii,2014,35(7):965-971.)
[11]黄鑫,赵捍东,李志鹏.基于插值型径向基神经网络的弹丸落点预报方法[J].探测与控制学报,2015,37(4):101-105.(Huang Xin,Zhao Handong,Li Zhipeng.A Projectile Impact-point Prediction Method Based on Interpolation Radial Basis Function Neural Network[J].Journal of Detection and Control,2015,37(4):101-105.)
[12]Ma Y,Zhao H D,Xu J P,et al.Simulation and Comparison of Several Numerical Algorithms for Solving Ballistic Differential Equations[J].Journal of Measurement Science and Instrumentation,2016,7(1):35-39.
[13]陈国敏.基于UKF和抗差估计的外弹道估计方法[D].长沙:国防科技大学研究生院,2009.(Chen Guomin.Exterior Ballistic Trajectory Determination Method Based on UKF and Robust Estimation[D].Changsha:Graduate School of National University of Defense Technology,2009.)
[14]陈世年,李连仲,王京武,等.控制系统设计[M].北京:宇航出版社,1996.(Chen Shinian,Li Lianzhong,Wang Jingwu,et al.Control System Design[M].Beijing:Astronautics Press,1996.)
[15]张金槐,贾沛然,唐雪梅,等.远程火箭精度分析与评估[M].长沙:国防科技大学出版社,1994.(Zhang Jinhuai,Jia Peiran,Tang Xuemei,et al.Launch Vehicle Accuracy Analysis and Assessment[M].Changsha:National University of Defense Technology Press,1994.)
[16]黄世勇,闻悦.20km~85km高空大气密度与风场研究[J].导弹与航天运载技术,2017,(3):17-21.(Huang Shiyong,Wen Yue.Reasearch for Atmospheric Density and Wind Field from 20km to 85km[J].Missiles and Space Vehicles,2017,(3):17-21.)
[17]Torrieri D J.Statistical Theory of Passive Location System[J].IEEE Transaction on Aerospace and Electronic Systems,1984,20(2):183-198.
[18]李晓宇,田康生,郑玉军,等.基于关机点状态的弹道导弹落点估计及误差分析[J].舰船电子对抗,2014,37(5):71-74.(Li Xiaoyu,Tian Kangsheng,Zheng Yujun,et al.Estimation and Error Analysis of Ballistic Missile Fall Point[J].Shipboard Electronic Countermeasure,2014,37(5):71-74.)
[2]董燕琴,戴金海,安维廉.弹道导弹落点预报技术综述[J].航天控制,2008,26(1):91-95.(Dong Yanqin,Dai Jinhai,An Weilian.A Survey of Impact Point Prediction Technology for Ballistic Missile[J].Aerospace Control,2008,26(1):91-95.)
[3]刘仁,王爱华,郭桂治.基于关机点状态的战术弹道导弹落点估计[J].空军工程大学学报(自然科学版),2010,11(1):27-30.(Liu Ren,Wang Aihua,Guo Guizhi.Impact Point Estimation of Tactical Ballistic Missile Based on the State of Burnout Point[J].Journal of Air Force Engineering University(Natural Science Edition),2010,11(1):27-30.)
[4]常晓华,杨宇和,张鸣,等.任意大地高约束下的弹道飞行器自由段解析解[J].导弹与航天运载技术,2016,(5):62-66.(Chang Xiaohua,Yang Yuhe,Zhang Ming,et al.Analytical Solution of Arbitrary Geodetic Height Restricted for Free Flight Trajectory of Ballistic Vehicle[J].Missiles and Space Vehicles,2016,(5):62-66.)
[5]刘彦君,乔士东,黄金才,等.一种高精度弹道导弹落点预测方法[J].弹道学报,2012,24(1):22-26.(Liu Yanjun,Qiao Shidong,Huang Jincai,et al.A Method of Impact Point Prediction of Ballistic Missile[J].Journal of Ballistics,2012,24(1):22-26.)
[6]方建勋,于古胜,张斌.“龙格/库塔”算法在航天器实时落点计算中的应用[J].舰船电子工程,2009,29(6):59-62.(Fang Jianxun,Yu Gusheng,Zhang Bin.Application of the Runge-Kutta Algorithm in Real Time Estimating Aerocraft Fall Point[J].Ship Electronic Engineering,2009,29(6):59-62.)
[7]贺明科,朱炬波,周海银,等.弹道导弹落点的外推方法[J].战术导弹技术,2002,(5):1-5.(He Mingke,Zhu Jubo,Zhou Haiyin,et al.An Extrapolation Method for Ballistic Missile Impact Point[J].Tactical Missile Technology,2002,(5):1-5.)
[8]陈映,文树梁,程臻.一种基于多模型算法的纯弹道式弹道落点预报方法[J].宇航学报,2010,31(7):1825-1831.(Chen Ying,Wen Shuliang,Cheng Zhen.An IMM-based Impact Point Prediction Method of Ballistic Target[J].Journal of Astronautics,2010,31(7):1825-1831.)
[9]Leonard C,Hainz III,Mark C.Modified Projectile Linear Theory for Rapid Trajectory Prediction[J].Journal of Guidance,Control,and Dynamics,2005,28(5):1006-1014.
[10]赵捍东,李志鹏.基于径向基函数神经网络和无迹卡尔曼滤波的弹丸落点预报方法研究[J].兵工学报,2014,35(7):965-971.(Zhao Handong,Li Zhipeng.Projectile Impact-point Prediction Method Based on Radial Basis Function Neural Network and Unscented Kalman Filter[J].Acta Armamentarii,2014,35(7):965-971.)
[11]黄鑫,赵捍东,李志鹏.基于插值型径向基神经网络的弹丸落点预报方法[J].探测与控制学报,2015,37(4):101-105.(Huang Xin,Zhao Handong,Li Zhipeng.A Projectile Impact-point Prediction Method Based on Interpolation Radial Basis Function Neural Network[J].Journal of Detection and Control,2015,37(4):101-105.)
[12]Ma Y,Zhao H D,Xu J P,et al.Simulation and Comparison of Several Numerical Algorithms for Solving Ballistic Differential Equations[J].Journal of Measurement Science and Instrumentation,2016,7(1):35-39.
[13]陈国敏.基于UKF和抗差估计的外弹道估计方法[D].长沙:国防科技大学研究生院,2009.(Chen Guomin.Exterior Ballistic Trajectory Determination Method Based on UKF and Robust Estimation[D].Changsha:Graduate School of National University of Defense Technology,2009.)
[14]陈世年,李连仲,王京武,等.控制系统设计[M].北京:宇航出版社,1996.(Chen Shinian,Li Lianzhong,Wang Jingwu,et al.Control System Design[M].Beijing:Astronautics Press,1996.)
[15]张金槐,贾沛然,唐雪梅,等.远程火箭精度分析与评估[M].长沙:国防科技大学出版社,1994.(Zhang Jinhuai,Jia Peiran,Tang Xuemei,et al.Launch Vehicle Accuracy Analysis and Assessment[M].Changsha:National University of Defense Technology Press,1994.)
[16]黄世勇,闻悦.20km~85km高空大气密度与风场研究[J].导弹与航天运载技术,2017,(3):17-21.(Huang Shiyong,Wen Yue.Reasearch for Atmospheric Density and Wind Field from 20km to 85km[J].Missiles and Space Vehicles,2017,(3):17-21.)
[17]Torrieri D J.Statistical Theory of Passive Location System[J].IEEE Transaction on Aerospace and Electronic Systems,1984,20(2):183-198.
[18]李晓宇,田康生,郑玉军,等.基于关机点状态的弹道导弹落点估计及误差分析[J].舰船电子对抗,2014,37(5):71-74.(Li Xiaoyu,Tian Kangsheng,Zheng Yujun,et al.Estimation and Error Analysis of Ballistic Missile Fall Point[J].Shipboard Electronic Countermeasure,2014,37(5):71-74.)