Calibration of Vehicular Three-axis Magnetometer via Truncated Total Least Squares Algorithm

doi:10.3969/j.issn.1000-1093.2015.03.007

Abstract

Abstract: A regularization three-axis magnetometer calibration algorithm is proposed for vehicular navigation. Due to the constrained manoeuvre of the vehicle, a linear observational equation system for calibration of three-axis magnetometer is severely ill-posed. The traditional calibration methods may result in unreliable solutions in the lack of dealing with ill-posed problem. The ill-posed problem is solved by using the truncated total least squares (TTLS) technique. This method can effectively suppress the errors on both sides of the observation equation. Furthermore, the TTLS method is used to solve the ill-posed problems. A vehicular navigation experiment is conducted to validate the effectiveness of the method．The results show that the proposed algorithm can effectively mitigate the ill-posed problem and obtain more stable numerical solutions. The mean value of the heading angles from the calibrated measurements is equal to 1.5°, which meets the vehicular navigation application.

Key words: control science and technology, truncated total least squares, calibration, vehicle navigation

ZHANG Ying， YANG Ren-nong， LI Ming-yang， ZUO Jia-liang， CHEN Xing-yi. Calibration of Vehicular Three-axis Magnetometer via Truncated Total Least Squares Algorithm[J]. Acta Armamentarii, 2015, 36(3): 427-432.

References

［1］ Caruso M J. Applications of magnetic sensors for low cost compass systems[C]∥IEEE 2000 Position Location and Navigation Symposium. San Diego, CA:IEEE, 2000:177-184.
[2] Siddharth S, Ali A S, El-Sheimy N, et al. A game-theoretic approach for calibration of low-cost magnetometers under noise uncertainty[J]. Measurement Science and Technology, 2012, 23(2):025003.
[3] Fang J C, Sun H W, Cao J J, et al. A novel calibration method of magnetic compass based on ellipsoid fitting[J]. IEEE Transactions on Instrumentation and Measurement, 2011， 60(6):2053-2061.
[4] Foster C C, Elkaim G H. Extension of a non-linear,two-step calibration methodology to include non-orthogonal sensor axes[J]. IEEE Transactions on Aerospace Electronic Systems, 2008， 44(3): 1070-1087.
[5] Gebre-Egziabher D, Elkaim G H, Powell J D, et al. A non-linear, two-step estimation algorithm for calibrating solid-state strap down magnetometers[C]∥8th International Conference on Navigation Systems. St. Petersburg, Russia:IEEE/AIAA, 2001:290-297.
[6] 徐玉, 任沁源, 孙文达, 等. 微小型无人直升机地磁导航算法研究[J]. 兵工学报, 2011， 32(3): 337-342.
XU Yu, REN Qin-yuan, SUN Wen-da, et al. A geomagnetic navigation algorithm for miniature unmanned helicopter[J]. Acta Armamentarii, 2011, 32(3):337-342. (in Chinese)
[7] 黄学功, 王炅. 地磁信号检测系统误差分析与补偿方法研究[J]. 兵工学报, 2011, 32(1): 33-36.
HUANG Xue-gong，WANG Jiong． Error analysis and compensation methods for geomagnetic signal detection system[J]. Acta Armamentarii, 2011, 32(1):33-36. (in Chinese)
[8] Renaudin V, Afzal M H, Lachapelle G. Complete triaxis magnetometer calibration in the magnetic domain[J]. Journal of Sensors, 2010, 2010:1-9.
[9] 吴志添, 武元新, 胡小平, 等. 基于总体最小二乘的捷联三轴磁力仪标定与地磁场测量误差补偿[J]. 兵工学报, 2012, 33(10): 1202-1209.
WU Zhi-tian, WU Yuan-xin, HU Xiao-ping, et al. Calibration of strapdown three-axis magnetometer and measurement error compensation of geomagnetic field based on total least squares[J]. Acta Armamentarii, 2012, 33(10):1202-1209.(in Chinese)
[10] Honerkamp J, Weese J. Tikhonovs regularization method for ill-posed problems[J]. Continuum Mechanics and Thermodyna-mics, 1990, 2(1):17-30.
[11] Fierro R D, Golub G H, Hansen P C, et al. Regularization by truncated total least squares[J]. SIAM Journal on Scientific Computing, 1997, 18(4):1223-1241.
[12] Mclean S, Macmillan S. The US/UK world magnetic model for 2005—2010[R]. Nottingham, UK: British Geological Survey, 2004.
[13] Bonnet S, Bassompierre C, Godin C, et al. Calibration methods for inertial and magnetic sensors[J]. Sensors and Actuators A: Physical, 2009, 156(2): 302-311.
[14] Wu Z T, Wu Y X, Hu X P, et al. Calibration of three-axis strapdown magnetometers using particle swarm optimiazation algorithm[C]∥IEEE International Symposium on Robotic and Sensors Environments. Montreal, Canada:IEEE, 2011:160-165.
[15] Golub G H, Van Loan C F. An analysis of the total least squares problem[J]. SIAM Journal on Numerical Analysis, 1980, 17(6): 883-893.
[16] Markovsky I, Van Huffel S. Overview of total least-squares methods[J]. Signal Processing, 2007, 87(10): 2283-2302.
[17] Sima D M, Van Huffel S. Level choice in truncated total least squares[J]. Computational Statistics & Data Analysis, 2007, 52(2): 1103-1118.
[18] Hansen P C, O'Leary D P. The use of the L-curve in the regularization of discrete ill-posed problems[J]. SIAM Journal on Scientific Computing, 1993, 14(6):1487-1803.
[19] 陈希孺, 王松桂. 近代回归分析[M]. 合肥: 安徽教育出版社, 1987.
CHEN Xi-ru, WANG Song-gui. Advanced in regression analysis[M]. Hefei: Anhui Education Press, 1987. (in Chinese)
[20] 张晓明, 赵剡. 基于椭圆约束的新型载体磁场标定及补偿技术[J]. 仪器仪表学报, 2009, 30(11): 2438-2443.
ZHANG Xiao-ming, ZHAO Yan. New auto-calibration and compensation method for vehicle magnetic field based on ellipse restriction[J]. Chinese Journal of Scientific Instrument, 2009, 30(11): 2438-2443. (in Chinese)

[1]	WUBULIAISAN Maimaitituersun, WU Yanqing, HOU Xiao, YIN Xinmei, ZHANG Xin. On the Determination of Viscoelastic Model Parameters and Microstructural Damage Evolution of Solid Propellants [J]. Acta Armamentarii, 2024, 45(4): 1038-1046.
[2]	DUAN Hao， CHEN Hui， ZHAI Zhaoyang， HAN Yu， MA Fanhua， CUI Yahui. Performance Prediction of Hydrogen-enriched Compressed Natural Gas Engine Based on Support Vector Machine [J]. Acta Armamentarii, 2022, 43(5): 1002-1011.
[3]	WU Qian， GUO Weiguo. Calibration of Sensitivity Coefficient of Three-dimensional High-g Accelerometer Based on Vector Decomposition [J]. Acta Armamentarii, 2021, 42(7): 1535-1543.
[4]	JING Wenbo, HUANG Bingkun, LIU Jian, YU Hongyang. Calibration of Different-source Cameras for Laser Irradiation Performance Measurement [J]. Acta Armamentarii, 2020, 41(5): 924-931.
[5]	YANG Guanjinzi， LI Jianchen， HUANG Hai， GUO Linna. Non-turntable Field-calibration Method for Gyroscope Based on Optimal Analysis [J]. Acta Armamentarii, 2020, 41(3): 577-584.
[6]	ZHANG Sen， GUO Jinbiao， WU Yuanyuan. Calibration Algorithm for Underwater Navigation System Based on Rodrigues Matrix Transformation [J]. Acta Armamentarii, 2020, 41(2): 342-349.
[7]	WANG Qi, WANG Lixin, LIANG Shuhui, QIN Weiwei, SHEN Qiang. Selection of System Models for Continuous Self-calibration of Hybrid Inertial Navigation System Based on Observability Analysis [J]. Acta Armamentarii, 2020, 41(1): 56-67.
[8]	ZHOU Quan, YAO Minli, SHEN Xiaowei. Research on Field Calibration Method for MEMS Accelerometer Based on Support Ellipsoid Fitting [J]. Acta Armamentarii, 2020, 41(1): 68-74.
[9]	DONG Chunmei， REN Shunqing， CHEN Xijun， LI Wei. A System-level Calibration Method for Laser Gyro SINS [J]. Acta Armamentarii, 2019, 40(8): 1618-1626.
[10]	YUAN Dongming， DING Yalin, ZHANG Jian. Calibration of Seeker Angle-measuring Error with Block Three-order Polynomial [J]. Acta Armamentarii, 2019, 40(10): 2042-2049.
[11]	WANG Da-peng, JIN Xing, ZHOU Wei-jing, LI Nan-lei. Analysis of Plate Non-parallelism Error of Capacitance Displacement Sensor in Thrust Measurement of Space-borneMicro-thruster [J]. Acta Armamentarii, 2018, 39(4): 816-824.
[12]	JU Tan, YU Ji-yan, WANG Xiao-ming, GU Xiao-hui. A Calibration Method of Magnetometer-aided Two-axis Gyro Sensor in the Projectile-borne Environment [J]. Acta Armamentarii, 2018, 39(10): 1919-1926.
[13]	WU Ming, ZHANG Guo-liang, LI Lin-lin, FU Guang-yuan, LI Cheng-jian. Muli-sensor Calibration Optimization Method of Mobile Robot Based on Stationary and Moving Object Observation ConsistencyConstraint [J]. Acta Armamentarii, 2017, 38(8): 1630-1641.
[14]	WANG Kun-ming, XIE Jian, ZHOU Zhao-fa. Calibration Method of Dimension Error of Accelerometer in Single-axial Rotation SINS [J]. Acta Armamentarii, 2017, 38(7): 1314-1321.
[15]	LI Dian-qi， DUAN Yong. Implementation of Active Disturbance Rejection Control of Robot by Tracking Differentiator [J]. Acta Armamentarii, 2016, 37(9): 1721-1729.