Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor

doi:10.23919/JSEE.2020.000055

Journal of Systems Engineering and Electronics ›› 2020, Vol. 31 ›› Issue (4): 804-814.doi: 10.23919/JSEE.2020.000055

• Control Theory and Application • Previous Articles Next Articles

Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor

Yu HUANG^1,^2,*(), Lihua WU²(), Qiang YU³()

¹ Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 150001, China
² Key Lab of In-fiber Integrated Optics, Ministry Education of China, College of Physics and Optoelectronic Engineering, Harbin Engineering University, Harbin 150001, China
³ College of Automation, Harbin Engineering University, Harbin 150001, China

Received:2019-11-07 Online:2020-08-25 Published:2020-08-25
Contact: Yu HUANG E-mail:huangyu@hrbeu.edu.cn;wulihua@hrbeu.edu.cn;yuqiang@hrbeu.edu.cn
About author:HUANG Yu was born in 1976. He received his Ph.D. degree in engineering in 2011. He is currently an associate professor in the College of Physics and Optoelectronic Engineering at Harbin Engineering University. He has authored over 60 papers in journals or conferences and has authorized more than 10 Chinese invention patents. His main research interests include magnetic field detection and geomagnetic field navigation. E-mail: huangyu@hrbeu.edu.cn|WU Lihua was born in 1979. She received her Ph.D. degree in engineering in 2010. She is currently a lecturer in the College of Physics and Optoelectronic Engineering at Harbin Engineering University. She has authored over 20 papers in journals or conferences and has authorized seven Chinese invention patents. Her main research interests are in the field of precise magnetic field measurement. E-mail: wulihua@hrbeu.edu.cn|YU Qiang was born in 1977. He is a lecturer of the College of Automation, Harbin Engineering University. He obtained his Ph.D. degree majoring in navigation guidance and control from Harbin Engineering University in 2011. He has more than 10 academic papers published, and 30 invention patents applied. The main research directions are inertial navigation technology and magnetic detection technology. E-mail: yuqiang@hrbeu.edu.cn
Supported by:
the National Natural Science Foundation of China(11405035);the National Natural Science Foundation of China(61004130);the National Natural Science Foundation of China(60834005);the Natural Science Foundation of Heilongjiang Province of China(F201414);the Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province(LBHQ15034);the Stable Supporting Fund of Acoustic Science and Technology Laboratory(JCKYS2019604SSJS002);the Fundamental Research Funds for the Central Universities;This work was supported by the National Natural Science Foundation of China (11405035; 61004130; 60834005), the Natural Science Foundation of Heilongjiang Province of China (F201414), the Postdoctoral Scientific Research Developmental Fund of Heilongjiang Province (LBHQ15034), the Stable Supporting Fund of Acoustic Science and Technology Laboratory (JCKYS2019604SSJS002), and the Fundamental Research Funds for the Central Universities

Abstract

Abstract:

This paper presents a kind of attitude estimation algorithm based on quaternion-vector switching and square-root cubature Kalman filter for autonomous underwater vehicle (AUV). The filter formulation is based on geomagnetic field tensor measurement dependent on the attitude and a gyro-based model for attitude propagation. In this algorithm, switching between the quaternion and the three-component vector is done by a couple of the mathematical transformations. Quaternion is chosen as the state variable of attitude in the kinematics equation to time update, while the mean value and covariance of the quaternion are computed by the three-component vector to avoid the normalization constraint of quaternion. The square-root forms enjoy a continuous and improved numerical stability because all the resulting covariance matrices are guaranteed to stay positively semi-definite. The entire square-root cubature attitude estimation algorithm with quaternion-vector switching for the nonlinear equality constraint of quaternion is given. The numerical simulation of simultaneous swing motions in the three directions is performed to compare with the three kinds of filters and the results indicate that the proposed filter provides lower attitude estimation errors than the other two kinds of filters and a good convergence rate.

Key words: attitude estimator, geomagnetic field tensor, quaternion-vector switching, square-root cubature Kalman filter, autonomous underwater vehicle (AUV)

Yu HUANG, Lihua WU, Qiang YU. Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor[J]. Journal of Systems Engineering and Electronics, 2020, 31(4): 804-814.

Figures/Tables 5

Table 1

Fig 1

Fig 2

Table 2

Table 3

References 32

1	XIA Y Q, ZHU Z, FU M Y, et al. Attitude tracking of rigid spacecraft with bounded disturbances. IEEE Trans. on Industrial Electronics, 2011, 58 (2): 647- 659. doi: 10.1109/TIE.2010.2046611
2	ZHENG B, ZHONG Y S. Robust attitude regulation of a 3-DOF helicopter benchmark: theory and experiments. IEEE Trans. on Industrial Electronics, 2011, 58 (2): 660- 670. doi: 10.1109/TIE.2010.2046579
3	HECTOR G M, FERNANDO J P, JOSE M G, et al. UAV attitude estimation using unscented Kalman filter and TRIAD. IEEE Trans. on Industrial Electronics, 2012, 59 (11): 4465- 4474. doi: 10.1109/TIE.2011.2163913
4	MOHD Z H, AMRAN A, ABU H A, et al. Review on attitude estimation algorithm of attitude determination system. ARPN Journal of Engineering and Applied Sciences, 2016, 11 (7): 4455- 4460.
5	SHUSTER M D, OH S D. Three-axis attitude determination from vector observations. Journal of Guidance, Control and Dynamics, 1981, 4 (1): 70- 77.
6	MARKELY F L. Attitude determination using vector observations and the singular value decomposition. The Journal of the Astronautical Sciences, 1988, 36 (3): 245- 258.
7	MARKELY F L. Attitude determination using vector observations: a fast optimal matrix algorithm. The Journal of the Astronautical Sciences, 1993, 41 (2): 261- 280.
8	SHUSTER M D. Approximate algorithms for fast optimal attitude computation. Proc. of the AIAA Guidance and Control Conference, 1978, 88- 95.
9	SHUSTER M D. Constraint in attitude estimation Part Ⅰ: constrained estimation. Journal of the Astronautical Sciences, 2003, 51 (1): 51- 101.
10	MARKLEY F L. Attitude error representations for Kalman filtering. Journal of Guidance, Control and Dynamics, 2003, 63 (2): 311- 317.
11	CRASSIDIS J L, MARKLEY F L. Unscented filtering for spacecraft attitude estimation. Journal of Guidance, Control and Dynamics, 2003, 26 (4): 536- 542.
12	RICHARDS P W. Constrained Kalman filtering using pseudo-measurements. Proc. of the IEE Colloquium on Algorithms for Target Tracking, 1995, 75- 79.
13	SIMON D, CHIA T. Kalman filtering with state equality constraint. IEEE Trans. on Aerospace and Electronics Systems, 2002, 38 (1): 128- 136. doi: 10.1109/7.993234
14	JULIER S J, LAVIOLA JR J J. On Kalman filtering with nonlinear equality constraints. IEEE Trans. on Signal Processing, 2007, 55 (6): 2774- 2784.
15	ZANETTI R, MAJJI M, BISHOP R H, et al. Norm-constrained Kalman filtering. Journal of Guidance, Control and Dynamics, 2009, 32 (5): 1458- 1465.
16	OSHMAN Y, CARMI A. Attitude estimation from vector observations using genetic algorithm embedded quaternion particle filter. Journal of Guidance, Control and Dynamics, 2006, 29 (4): 879- 891.
17	MARKLEY F L. Attitude error representations for Kalman filtering. Journal of Guidance, Control and Dynamics, 2003, 26 (2): 311- 317.
18	TANG X J, LIU Z B, ZHANG J S. Square-root quaternion cubature Kalman filtering for spacecraft attitude estimation. Acta Astronautica, 2012, 76, 84- 94. doi: 10.1016/j.actaastro.2012.02.009
19	HUANG W, XIE H S, SHEN C, et al. A robust strong tracking cubature Kalman filter for spacecraft attitude estimation with quaternion constraint. Acta Astronautica, 2016, 121, 153- 163. doi: 10.1016/j.actaastro.2016.01.009
20	SCHMIDT P W, CLARK D A. The magnetic gradient tensor: its properties and uses in source characterization. The Leading Edge, 2006, 25 (1): 75- 78.
21	MIOARA M, MICHAEL P. Observing, modeling, and interpreting magnetic fields of the solid earth. Surveys in Geophysics, 2005, 26 (4): 415- 459. doi: 10.1007/s10712-005-3857-x
22	STOLZ R, ZAKOSARENKO V, SCHULZ M, et al. Magnetic full-tensor SQUID gradiometer system for geophysical applications. The Leading Edge, 2006, 25 (2): 178- 180.
23	SCHMIDT P, CLARK D, LESLIE K, et al. GETMAG-a SQUID magnetic tensor gradiometer for mineral and oil exploration. Exploration Geophysics, 2004, 35 (4): 297- 305.
24	KEENAN S T, YOUNG J A, FOLEY C P, et al. A high-T_c flip-chip SQUID gradiometer for mobile underwater magnetic sensing. Superconductor Science and Technology, 2010, 23 (2): 025029.
25	SUI Y Y, LI G, WANG S L, et al. Compact fluxgate magnetic full-tensor gradiometer with spherical feedback coil. Review of Scientific Instruments, 2014, 85 (1): 014701. doi: 10.1063/1.4856675
26	HUANG Y, HAO Y L. Comparison of two configuration schemes in vector magnetometer's underwater geomagnetic field anomaly localization. Journal of Chinese Inertial Technology, 2009, 17 (6): 677- 682.
27	HUANG Y, WU L H, LI D Q. Theoretical research on full attitude determination using geomagnetic gradient tensor. Journal of Navigation, 2015, 68 (5): 951- 961. doi: 10.1017/S0373463315000259
28	LIU Y Q, JIANG X Y, MA G F. Marginalized particle filter for spacecraft attitude estimation from vector measurements. Journal of Control Theory and Applications, 2007, 5 (1): 60- 66.
29	CRASSIDIS J L. Sigma-point Kalman filtering for integrated GPS and inertial navigation. IEEE Trans. on Aerospace and Electronic Systems, 2006, 42 (2): 750- 756. doi: 10.1109/TAES.2006.1642588
30	CHANDRA K, GU D, POSTLETHWAITE I. square root cubature information filter. IEEE Sensors Journal, 2013, 13 (2): 750- 758.
31	FU J G, WANG X T, JIN L A, et al. A new quaternion-based attitude estimation algorithm using the gravitational field and geomagnetic field observation. Acta Electronic Sinca, 2005, 33 (3): 567- 570.
32	FOBERT A S. Estimating optimal tracking filter performance for manned maneuvering targets. IEEE Trans. on Aerospace and Electronic Systems, 1970, AES-6 (4): 473- 483. doi: 10.1109/TAES.1970.310128

Sphere					Rectangle
$r$/m	$M$/(A/m)	$I$/(°)	$D$/(°)	$P$/(m×m×m)	$S$/(m×m×m)	$M$/(A/m)	$I$/(°)	$D$/(°)	$P/$(m×m×m)
410	1 800	-55	28	430×1 500×1 300	600×400×56	1.1	80	30	1 100×700×110
450	1 600	-40	-35	3 180×3 170×1 400	400×700×48	1.2	-50	25	2 600×2 500×128
380	1 200	45	-15	1 800×2 800×1 260	600×600×45	1.3	40	55	1 200×1 400×140
390	1 700	35	36	2 000×1 800×1 490	700×600×30	0.9	30	-35	2 400×1 000×130
480	2 200	70	-45	1 080×2 300×1 390
280	1 500	-15	55	2 800×1 820×1 180

Time/s	CKF			ISQCKF			ISQSRCKF
Time/s	$\delta_\psi$/(°)	$\delta_\theta $/(°)	$\delta_\gamma $/(°)	$\delta _\psi$/(°)	$\delta_\theta$/(°)	$\delta _\gamma $/ (°)	$\delta_\psi$/(°)	$\delta_\theta $/(°)	$\delta_\gamma$/(°)
2.50	0.004 97	0.009 06	0.002 16	0.346 73	0.211 11	0.077 31	0.116 95	0.080 94	0.024 6
2.51	0.000 15	0.005 47	0.011 36	0.322 59	0.189 01	0.066 84	0.107 17	0.076 35	0.024 97
2.52	0.018 42	0.014 66	0.018 14	0.299 47	0.179 11	0.058 08	0.095 41	0.066 85	0.024 65
2.53	0.006 72	0.004 86	0.017 78	0.272 04	0.161 6	0.053 46	0.086 73	0.062 38	0.023 7
2.54	0.025 27	0.002 36	0.002 28	0.253 9	0.141 94	0.054 27	0.073 81	0.057 93	0.020 59
2.55	0.015 36	0.001 15	0.012 95	0.226 38	0.128 76	0.045 34	0.065 47	0.051 44	0.021 19
2.56	0.006 01	0.011 19	0.000 98	0.196 92	0.119 86	0.046 51	0.058 8	0.044 35	0.018 65
2.57	0.004 97	0.001 33	0.014 03	0.174 29	0.102 69	0.049 56	0.049 56	0.038 94	0.014 75
2.58	0.012 68	0.007 1	0.006 13	0.153 68	0.084 46	0.042 89	0.038 98	0.034 92	0.013 87
2.59	0.009 57	0.007 62	0.000 81	0.128 23	0.076 07	0.036 4	0.030 54	0.027 08	0.013 79

Filter	$\delta_\psi $/(°)		$\delta_\theta $/(°)		$\delta _\gamma $/(°)
Filter	Mean value	STD	Mean value	STD	Mean value	STD
CKF	0.010 855	0.009 59	0.000 697 83	0.005 477 1	0.007 630 7	0.005 891 5
ISQCKF	0.007 846 2	0.006 48	0.005 784 3	0.004 379	0.006 307 3	0.004 804 6
ISQSRCKF	0.005 236 7	0.004 931 3	0.002 767 9	0.002 157 2	0.002 990 1	0.002 350 2

[1]	Wanping SONG, Zengqiang CHEN, Mingwei SUN, Qinglin SUN. Reinforcement learning based parameter optimization of active disturbance rejection control for autonomous underwater vehicle [J]. Journal of Systems Engineering and Electronics, 2022, 33(1): 170-179.
[2]	Hong Li, Mingyong Liu, and Kun Liu. Bio-inspired geomagnetic navigation method for autonomous underwater vehicle#br# [J]. Journal of Systems Engineering and Electronics, 2017, 28(6): 1203-1209.
[3]	Qingwei Liang, Tianyuan Sun, and Dongdong Wang. Time-varying reliability indexes for multi-AUV cooperative system [J]. Systems Engineering and Electronics, 2017, 28(2): 401-406.
[4]	Qingwei Liang, Tianyuan Sun, and Dongdong Wang. Reliability indexes for multi-AUV cooperative systems [J]. Systems Engineering and Electronics, 2017, 28(1): 179-.
[5]	An Zhang, Shuida Bao, Wenhao Bi, and Yuan Yuan. Low-cost adaptive square-root cubature Kalman filter for systems with process model uncertainty [J]. Journal of Systems Engineering and Electronics, 2016, 27(5): 945-953.
[6]	Mingyong Liu, Baogui Xu, and Xingguang Peng. Cooperative path planning for multi-AUV in time-varying ocean flows [J]. Systems Engineering and Electronics, 2016, 27(3): 612-618.

Underwater square-root cubature attitude estimator by use of quaternion-vector switching and geomagnetic field tensor

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