Abstract
The normal gravity model of a hypersonic boost-glide vehicle in near space is studied in this paper with the aim of alleviating the influence of the gravity model error on the precision of the inertial navigation system (INS) during flight. First, a spherical harmonic model of the Earth’s gravitational field is introduced and the normal gravity of the Earth is derived from it. Then, the coordinate transformation needed for the application of the gravity model to the near-space navigation algorithm is formulated. Subsequently, the gravity disturbance in near space and the impact of J2 and J4 gravity truncation errors are analyzed. Finally, different normal gravity models and different precisions of inertial measurement unit (IMU) are exploited to simulate the near-space navigation algorithm. Based on this, the influence of the independent and combined effects caused by the interference factors is analyzed, and the applicable conditions of the normal gravity model are discussed.
概要
目的
地球真实重力场建模复杂, 惯性导航通常使用正常重力模型近似地球真实重力。这种做法能满足大部分高超声速助推滑翔(HBG)飞行器导航系统的精度要求, 但在一些已出现的高精度惯性导航系统中, 传统重力模型的误差已不可忽略, 甚至成为主要的误差来源。本文旨在研究导航系统需要的实用误差更小的重力模型。
创新点
1. 讨论球谐模型建立的高精度地球重力场以及正常重力场在HBG飞行器上的应用;2. 将重力模型用于基准飞行轨迹生成和导航仿真;3. 比较各常用重力模型的误差及计算量, 并给出不同精度惯性导航系统对不同精度重力模型的选择依据。
方法
1. 通过理论推导, 梳理球谐模型和正常重力模型之间的关系, 并给出重力计算公式和坐标转换公式;2. 在计算基准飞行轨迹时使用最高精度的球谐模型;3. 在导航时试验不同重力模型, 并通过结果分析各模型精度;4. 同时加入惯性器件误差和重力模型误差, 并与重力模型单独作用时进行对比, 给出不同精度惯性导航系统选择重力模型的依据。
结论
1. 临近空间大部分区域的重力扰动在0.01 mg到0.10 mg之间;2. 正常重力模型中J4模型接近正常重力精度极限, 较J2模型精度有小幅提升;3. 惯性器件精度优于0.10 mg时, 要使用比正常重力模型精度更高的重力模型, 如中低阶球谐模型。
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Kai CHEN designed the research. Cheng-zhi ZENG processed the corresponding data and wrote the first draft of the manuscript. Sen-sen PEI helped to organize the manuscript. Wen-chao LIANG revised and edited the final version.
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Kai CHEN, Cheng-zhi ZENG, Sen-sen PEI, and Wenchao LIANG declare that they have no conflict of interest.
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Chen, K., Zeng, Cz., Pei, Ss. et al. Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle. J. Zhejiang Univ. Sci. A 23, 55–67 (2022). https://doi.org/10.1631/jzus.A2100133
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DOI: https://doi.org/10.1631/jzus.A2100133