Full Text:   <627>

Summary:  <356>

CLC number: 

On-line Access: 2022-01-26

Received: 2021-03-26

Revision Accepted: 2021-09-17

Crosschecked: 0000-00-00

Cited: 0

Clicked: 432

Citations:  Bibtex RefMan EndNote GB/T7714


Kai Chen


Cheng-zhi ZENG


-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2022 Vol.23 No.1 P.55-67


Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle

Author(s):  Kai CHEN, Cheng-zhi ZENG, Sen-sen PEI, Wen-chao LIANG

Affiliation(s):  School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China

Corresponding email(s):   chenkai@nwpu.edu.cn

Key Words:  Hypersonic boost-glide vehicle, Inertial navigation system (INS), Normal gravity, Gravity disturbance

Kai CHEN, Cheng-zhi ZENG, Sen-sen PEI, Wen-chao LIANG. Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle[J]. Journal of Zhejiang University Science A, 2022, 23(1): 55-67.

@article{title="Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle",
author="Kai CHEN, Cheng-zhi ZENG, Sen-sen PEI, Wen-chao LIANG",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle
%A Cheng-zhi ZENG
%A Sen-sen PEI
%A Wen-chao LIANG
%J Journal of Zhejiang University SCIENCE A
%V 23
%N 1
%P 55-67
%@ 1673-565X
%D 2022
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A2100133

T1 - Normal gravity model for inertial navigation of a hypersonic boost-glide vehicle
A1 - Kai CHEN
A1 - Cheng-zhi ZENG
A1 - Sen-sen PEI
A1 - Wen-chao LIANG
J0 - Journal of Zhejiang University Science A
VL - 23
IS - 1
SP - 55
EP - 67
%@ 1673-565X
Y1 - 2022
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A2100133

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.


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。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]BahmC, BaumannE, MartinJ, et al., 2005. The X-43A Hyper-X Mach 7 flight 2 guidance, navigation, and control overview and flight test results. Proceedings of the AIAA/CIRA 13th International Space Planes and Hypersonics Systems and Technologies Conference, p.3275.

[2]BeckaS, NovackM, SlivinskyS, et al., 2008. A high reliability solid state accelerometer for ballistic missile inertial guidance. Proceedings of AIAA Guidance, Navigation and Control Conference and Exhibit, p.7300.

[3]BykerkT, VerstraeteD, SteelantJ, 2020. Low speed longitudinal aerodynamic, static stability and performance analysis of a hypersonic waverider. Aerospace Science and Technology, 96:105531.

[4]ChachanY, StevensonDJ, 2019. A linear approximation for the effect of cylindrical differential rotation on gravitational moments: application to the non-unique interpretation of Saturn’s gravity. ICARUS, 323:87-98.

[5]ChangLB, QinFJ, WuMP, 2019. Gravity disturbance compensation for inertial navigation system. IEEE Transactions on Instrumentation and Measurement, 68(10):3751-3765.

[6]ChatfieldAB, BennettMM, ChenT, 1975. Effect of gravity model inaccuracy on navigation performance. AIAA Journal, 13(11):1494-1501.

[7]ChenK, ZhouJ, ShenFQ, et al., 2020a. Hypersonic boost–glide vehicle strapdown inertial navigation system/global positioning system algorithm in a launch-centered Earth-fixed frame. Aerospace Science and Technology, 98:105679.

[8]ChenK, ShenFQ, ZhouJ, et al., 2020b. Simulation platform for SINS/GPS integrated navigation system of hypersonic vehicles based on flight mechanics. Sensors, 20(18):5418.

[9]ChenK, ShenFQ, ZhouJ, et al., 2020c. SINS/BDS integrated navigation for hypersonic boost-glide vehicles in the launch-centered inertial frame. Mathematical Problems in Engineering, 2020:7503272.

[10]ChenQ, PoropatL, ZhangLJ, et al., 2018. Validation of the EGSIEM GRACE gravity fields using GNSS coordinate timeseries and in-situ ocean bottom pressure records. Remote Sensing, 10(12):1976.

[11]ClaessensSJ, HirtC, 2015. A surface spherical harmonic expansion of gravity anomalies on the ellipsoid. Journal of Geodesy, 89(10):1035-1048.

[12]FoersteC, BruinsmaSL, AbrykosovO, et al., 2014. EIGEN-6C4 the Latest Combined Global Gravity Field Model Including GOCE Data Up to Degree and Order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services.

[13]GuyM, KeithRD, 1998. On the efficient calculation of ordinary and generalized spherical harmonics. Geophysical Journal International, 135(1):307-309.

[14]HsuDY, 1996. Comparison of four gravity models. Proceedings of Position, Location and Navigation Symposium, p.631-635.

[15]PavlisNK, HolmesSA, KenyonSC, et al., 2012. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research, 117:B04406.

[16]SlobbeC, KleesR, FarahaniHH, et al., 2019. The impact of noise in a GRACE/GOCE global gravity model on a local quasi-geoid. Journal of Geophysical Research, 124(3):3219-3237.

[17]SteffesSR, 2013. Development and Analysis of SHEFEX-2 Hybrid Navigation System Experiment. MS Thesis, University of Bremen, Bremen, Germany.

[18]TodorokiharaM, SatoK, KobayashiY, 2018. A resonant frequency shift quartz accelerometer with 1st order frequency ΔΣ modulators for a high performance MEMS IMU. Proceedings of DGON Inertial Sensors and Systems, p.1-15.

[19]TsoulisD, PatlakisK, 2014. Spectral assessment of isostatic gravity models against CHAMP, GRACE, GOCE satellite-only and combined gravity models. Acta Geophysica, 62(4):679-698.

[20]WalkerS, SherkJ, ShellD, et al., 2008. The DARPA/AF falcon program: the hypersonic technology vehicle #2 (HTV-2) flight demonstration phase. Proceedings of the 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, p.2539.

[21]YounisGKA, JägerR, BeckerM, 2013. Transformation of global spherical harmonic models of the gravity field to a local adjusted spherical cap harmonic model. Arabian Journal of Geosciences, 6(2):375-381.

[22]ZhangCX, WangX, SongLL, et al., 2021. Temperature hysteresis mechanism and compensation of quartz flexible accelerometer in aerial inertial navigation system. Sensors, 21(1):294.

[23]ZhuZS, TanH, JiaY, et al., 2020. Research on the gravity disturbance compensation terminal for high-precision position and orientation system. Sensors, 20(17):4932.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE