# Multi-geomagnetic-component assisted localization algorithm for hypersonic vehicles

## Abstract

Owing to the lack of information about geomagnetic anomaly fields, conventional geomagnetic matching algorithms in near space are prone to divergence. Therefore, geomagnetic matching navigation algorithms for hypersonic vehicles are also prone to divergence or mismatch. To address this problem, we propose a multi-geomagnetic-component assisted localization (MCAL) algorithm to improve positioning accuracy using only the information of the main geomagnetic field. First, the main components of the geomagnetic field and a mathematical representation of the Earth’s geomagnetic field (World Magnetic Model 2015) are introduced. The mathematical relationships between the geomagnetic components are given, and the source of geomagnetic matching error is explained. We then propose the MCAL algorithm. The algorithm uses the intersections of the isopleths of the geomagnetic components and a decision method to estimate the real position of a carrier with high positioning accuracy. Finally, inertial/geomagnetic integrated navigation is simulated for hypersonic boost-glide vehicles. The simulation results demonstrate that the proposed algorithm can provide higher positioning accuracy than conventional geomagnetic matching algorithms. When the random error range is ±30 nT, the average absolute latitude error and longitude error of the MCAL algorithm are 151 m and 511 m lower, respectively, than those of the Sandia inertial magnetic aided navigation (SIMAN) algorithm.

## 概要

### 方法

1. 给出地磁主磁场模型的数学表达, 分析地磁匹配系统的误差来源. 2. 从理想情况出发, 提出一种MCAL算法, 并通过2~3条地磁分量的等值线对飞行器位置进行估计. 3. 在助推-滑翔高超声速飞行器弹道上进行数字仿真试验, 并与其他几种传统算法进行分析比较.

### 结论

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## Author information

Authors

### Corresponding author

Correspondence to Kai Chen.

## Additional information

Project supported by the Space Science and Technology Innovation Fund of China (No. 2016KC020028) and the Fund of China Space Science and Technology (No. 2017-HT-XG)

### Contributors

Kai CHEN designed the research and provided the funding support. Wen-chao LIANG wrote the first draft of the manuscript and conducted the literature review. Cheng-zhi ZENG processed the data. Rui GUAN revised the final version and developed the software.

### Conflict of interest

Kai CHEN, Wen-chao LIANG, Cheng-zhi ZENG, and Rui GUAN declare that they have no conflict of interest.

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### Cite this article

Chen, K., Liang, Wc., Zeng, Cz. et al. Multi-geomagnetic-component assisted localization algorithm for hypersonic vehicles. J. Zhejiang Univ. Sci. A 22, 357–368 (2021). https://doi.org/10.1631/jzus.A2000524

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### Key words

• Geomagnetic navigation
• Isopleth
• Geomagnetic components
• Integrated navigation
• Kálmán filter

• 地磁导航
• 等值线
• 地磁分量
• 组合导航
• 卡尔曼滤波

• V44