Abstract

The calibration of an inertial measurement unit (IMU) is a key technique to improve the preciseness of the inertial navigation system (INS) for missile, especially for the calibration of accelerometer scale factor. Traditional calibration method is generally based on the high accuracy turntable, however, it leads to expensive costs and the calibration results are not suitable to the actual operating environment. In the wake of developments in multi-axis rotational INS (RINS) with optical inertial sensors, self-calibration is utilized as an effective way to calibrate IMU on missile and the calibration results are more accurate in practical application. However, the introduction of multi-axis RINS causes additional calibration errors, including non-orthogonality errors of mechanical processing and non-horizontal errors of operating environment, it means that the multi-axis gimbals could not be regarded as a high accuracy turntable. As for its application on missiles, in this paper, after analyzing the relationship between the calibration error of accelerometer scale factor and non-orthogonality and non-horizontal angles, an innovative calibration procedure using the signals of fiber optic gyro and photoelectric encoder is proposed. The laboratory and vehicle experiment results validate the theory and prove that the proposed method relaxes the orthogonality requirement of rotation axes and eliminates the strict application condition of the system.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  2. D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).
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    [Crossref]
  4. P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
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  5. Z. Ding, C. Hong, and H. Yang, “An improved multi-position calibration method for low cost micro-electro mechanical systems inertial measurement units,” J. Aerosp. Eng. 229(10), 1919–1930 (2015).
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  9. B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  24. N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
    [Crossref]
  25. Q. Nie, X. Gao, and Z. Liu, “Research on accuracy improvement of INS with continuous rotation,” in Proceedings of IEEE Conference on Information and Automation (IEEE, 2009), pp. 849–853.

2015 (6)

Z. Ding, C. Hong, and H. Yang, “An improved multi-position calibration method for low cost micro-electro mechanical systems inertial measurement units,” J. Aerosp. Eng. 229(10), 1919–1930 (2015).

B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
[Crossref]

W. Gao, Y. Zhang, and J. Wang, “Research on initial alignment and self-calibration of rotary strapdown inertial navigation systems,” Sensors (Basel) 15(2), 3154–3171 (2015).
[Crossref] [PubMed]

Z. Shang, X. Ma, M. Li, and Y. Liu, “A High-Precision Calibration Method for MEMS Gyroscopes,” Int. J. Precis. Eng. Manuf. 16(8), 1711–1716 (2015).
[Crossref]

G. Rao, G. Wang, S. Han, and W. Zhang, “Calibration of Laser Inertial Navigator with Dual-axis Rotation,” Int. J. Control Autom. 13(4), 960–966 (2015).
[Crossref]

Y. Xu, X. H. Zhu, and Y. Su, “A novel network calibration method for inertial measurement units,” J. Aerosp. Eng. 229(7), 1336–1348 (2015).

2014 (6)

M. S. Kim, S. B. Yu, and W. S. Lee, “Development of a high-precision calibration method for inertial measurement unit,” Int. J. Precis. Eng. Manuf. 15(3), 567–575 (2014).
[Crossref]

Q. Ren, B. Wang, Z. Deng, and M. Fu, “A multi-position self-calibration method for dual-axis rotational inertial navigation system,” Sensor. Actuat. A. 219, 24–31 (2014).

P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
[Crossref]

J. Pan, C. Zhang, and Q. Cai, “An accurate calibration method for accelerometer nonlinear scale factor on a low-cost three-axis turntable,” Meas. Sci. Technol. 25(2), 025102 (2014).
[Crossref]

J. Pan, C. Zhang, Y. Niu, and Z. Fan, “Accurate calibration for drift of fiber optic gyroscope in multi-position north-seeking phase,” Optik (Stuttg.) 125(24), 7244–7246 (2014).
[Crossref]

D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).

2013 (5)

Q. Wang, Z. Qi, and F. Sun, “Six-position calibration for the fiber optic gyro based on a double calculating program,” Opt. Eng. 52(4), 043603 (2013).
[Crossref]

Q. Cai, N. Song, G. Yang, and Y. Liu, “Accelerometer calibration with nonlinear scale factor based on multi-position observation,” Meas. Sci. Technol. 24(10), 105002 (2013).
[Crossref]

W. Sun and Y. Gao, “Fiber-based rotary strapdown inertial navigation system,” Opt. Eng. 52(7), 076106 (2013).
[Crossref]

W. Sun, D. Wang, L. Xu, and L. Xu, “MEMS-based rotary strapdown inertial navigation system,” Meas. 46(8), 2585–2596 (2013).
[Crossref]

N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
[Crossref]

2012 (2)

B. Yuan, D. Liao, and S. Han, “Error compensation of an optical gyro INS by multi-axis rotation,” Meas. Sci. Technol. 23(2), 025102 (2012).
[Crossref]

J. Li, J. Fang, and M. Du, “Error Analysis and Gyro-Bias Calibration of Analytic Coarse Alignment for Airborne POS,” IEEE. Trans. Instrum. Meas. 61(11), 3058–3064 (2012).
[Crossref]

2008 (1)

H. G. Wang and T. C. Williams, “Strategic inertial navigation systems – High-accuracy inertially stabilized platforms for hostile environments,” IEEE Contr. Syst. Mag. 28(1), 65–85 (2008).
[Crossref]

2007 (1)

D. Jurman, M. Jankovec, R. Kamnik, and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sensor. Actuat. A. 138, 411–420 (2007).

2003 (1)

T. C. Lin, “Development of U.S. Air Force intercontinental ballistic missile,” J. Spacecr. Rockets 40(4), 491–509 (2003).
[Crossref]

Cai, Q.

J. Pan, C. Zhang, and Q. Cai, “An accurate calibration method for accelerometer nonlinear scale factor on a low-cost three-axis turntable,” Meas. Sci. Technol. 25(2), 025102 (2014).
[Crossref]

Q. Cai, N. Song, G. Yang, and Y. Liu, “Accelerometer calibration with nonlinear scale factor based on multi-position observation,” Meas. Sci. Technol. 24(10), 105002 (2013).
[Crossref]

N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
[Crossref]

Deng, Z.

B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
[Crossref]

Q. Ren, B. Wang, Z. Deng, and M. Fu, “A multi-position self-calibration method for dual-axis rotational inertial navigation system,” Sensor. Actuat. A. 219, 24–31 (2014).

Ding, Z.

Z. Ding, C. Hong, and H. Yang, “An improved multi-position calibration method for low cost micro-electro mechanical systems inertial measurement units,” J. Aerosp. Eng. 229(10), 1919–1930 (2015).

Du, M.

J. Li, J. Fang, and M. Du, “Error Analysis and Gyro-Bias Calibration of Analytic Coarse Alignment for Airborne POS,” IEEE. Trans. Instrum. Meas. 61(11), 3058–3064 (2012).
[Crossref]

Fan, Z.

J. Pan, C. Zhang, Y. Niu, and Z. Fan, “Accurate calibration for drift of fiber optic gyroscope in multi-position north-seeking phase,” Optik (Stuttg.) 125(24), 7244–7246 (2014).
[Crossref]

Fang, J.

J. Li, J. Fang, and M. Du, “Error Analysis and Gyro-Bias Calibration of Analytic Coarse Alignment for Airborne POS,” IEEE. Trans. Instrum. Meas. 61(11), 3058–3064 (2012).
[Crossref]

Fu, M.

B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
[Crossref]

Q. Ren, B. Wang, Z. Deng, and M. Fu, “A multi-position self-calibration method for dual-axis rotational inertial navigation system,” Sensor. Actuat. A. 219, 24–31 (2014).

Gao, W.

W. Gao, Y. Zhang, and J. Wang, “Research on initial alignment and self-calibration of rotary strapdown inertial navigation systems,” Sensors (Basel) 15(2), 3154–3171 (2015).
[Crossref] [PubMed]

Gao, X.

Q. Nie, X. Gao, and Z. Liu, “Research on accuracy improvement of INS with continuous rotation,” in Proceedings of IEEE Conference on Information and Automation (IEEE, 2009), pp. 849–853.

Gao, Y.

W. Sun and Y. Gao, “Fiber-based rotary strapdown inertial navigation system,” Opt. Eng. 52(7), 076106 (2013).
[Crossref]

Han, S.

G. Rao, G. Wang, S. Han, and W. Zhang, “Calibration of Laser Inertial Navigator with Dual-axis Rotation,” Int. J. Control Autom. 13(4), 960–966 (2015).
[Crossref]

B. Yuan, D. Liao, and S. Han, “Error compensation of an optical gyro INS by multi-axis rotation,” Meas. Sci. Technol. 23(2), 025102 (2012).
[Crossref]

Hong, C.

Z. Ding, C. Hong, and H. Yang, “An improved multi-position calibration method for low cost micro-electro mechanical systems inertial measurement units,” J. Aerosp. Eng. 229(10), 1919–1930 (2015).

Hsu, C. S.

D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).

Jankovec, M.

D. Jurman, M. Jankovec, R. Kamnik, and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sensor. Actuat. A. 138, 411–420 (2007).

Jurman, D.

D. Jurman, M. Jankovec, R. Kamnik, and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sensor. Actuat. A. 138, 411–420 (2007).

Jwo, D. J.

D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).

Kamnik, R.

D. Jurman, M. Jankovec, R. Kamnik, and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sensor. Actuat. A. 138, 411–420 (2007).

Kim, M. S.

M. S. Kim, S. B. Yu, and W. S. Lee, “Development of a high-precision calibration method for inertial measurement unit,” Int. J. Precis. Eng. Manuf. 15(3), 567–575 (2014).
[Crossref]

Lai, J.

P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
[Crossref]

Lee, W. S.

M. S. Kim, S. B. Yu, and W. S. Lee, “Development of a high-precision calibration method for inertial measurement unit,” Int. J. Precis. Eng. Manuf. 15(3), 567–575 (2014).
[Crossref]

Li, J.

J. Li, J. Fang, and M. Du, “Error Analysis and Gyro-Bias Calibration of Analytic Coarse Alignment for Airborne POS,” IEEE. Trans. Instrum. Meas. 61(11), 3058–3064 (2012).
[Crossref]

Li, M.

Z. Shang, X. Ma, M. Li, and Y. Liu, “A High-Precision Calibration Method for MEMS Gyroscopes,” Int. J. Precis. Eng. Manuf. 16(8), 1711–1716 (2015).
[Crossref]

Liao, D.

B. Yuan, D. Liao, and S. Han, “Error compensation of an optical gyro INS by multi-axis rotation,” Meas. Sci. Technol. 23(2), 025102 (2012).
[Crossref]

Lin, T. C.

T. C. Lin, “Development of U.S. Air Force intercontinental ballistic missile,” J. Spacecr. Rockets 40(4), 491–509 (2003).
[Crossref]

Liu, J.

P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
[Crossref]

Liu, Y.

Z. Shang, X. Ma, M. Li, and Y. Liu, “A High-Precision Calibration Method for MEMS Gyroscopes,” Int. J. Precis. Eng. Manuf. 16(8), 1711–1716 (2015).
[Crossref]

Q. Cai, N. Song, G. Yang, and Y. Liu, “Accelerometer calibration with nonlinear scale factor based on multi-position observation,” Meas. Sci. Technol. 24(10), 105002 (2013).
[Crossref]

Liu, Z.

Q. Nie, X. Gao, and Z. Liu, “Research on accuracy improvement of INS with continuous rotation,” in Proceedings of IEEE Conference on Information and Automation (IEEE, 2009), pp. 849–853.

Lv, P.

P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
[Crossref]

Ma, X.

Z. Shang, X. Ma, M. Li, and Y. Liu, “A High-Precision Calibration Method for MEMS Gyroscopes,” Int. J. Precis. Eng. Manuf. 16(8), 1711–1716 (2015).
[Crossref]

Nie, M.

P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
[Crossref]

Nie, Q.

Q. Nie, X. Gao, and Z. Liu, “Research on accuracy improvement of INS with continuous rotation,” in Proceedings of IEEE Conference on Information and Automation (IEEE, 2009), pp. 849–853.

Niu, Y.

J. Pan, C. Zhang, Y. Niu, and Z. Fan, “Accurate calibration for drift of fiber optic gyroscope in multi-position north-seeking phase,” Optik (Stuttg.) 125(24), 7244–7246 (2014).
[Crossref]

Pan, J.

J. Pan, C. Zhang, Y. Niu, and Z. Fan, “Accurate calibration for drift of fiber optic gyroscope in multi-position north-seeking phase,” Optik (Stuttg.) 125(24), 7244–7246 (2014).
[Crossref]

J. Pan, C. Zhang, and Q. Cai, “An accurate calibration method for accelerometer nonlinear scale factor on a low-cost three-axis turntable,” Meas. Sci. Technol. 25(2), 025102 (2014).
[Crossref]

Qi, Z.

Q. Wang, Z. Qi, and F. Sun, “Six-position calibration for the fiber optic gyro based on a double calculating program,” Opt. Eng. 52(4), 043603 (2013).
[Crossref]

Rao, G.

G. Rao, G. Wang, S. Han, and W. Zhang, “Calibration of Laser Inertial Navigator with Dual-axis Rotation,” Int. J. Control Autom. 13(4), 960–966 (2015).
[Crossref]

Ren, Q.

B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
[Crossref]

Q. Ren, B. Wang, Z. Deng, and M. Fu, “A multi-position self-calibration method for dual-axis rotational inertial navigation system,” Sensor. Actuat. A. 219, 24–31 (2014).

Shang, Z.

Z. Shang, X. Ma, M. Li, and Y. Liu, “A High-Precision Calibration Method for MEMS Gyroscopes,” Int. J. Precis. Eng. Manuf. 16(8), 1711–1716 (2015).
[Crossref]

Shih, J. H.

D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).

Song, N.

Q. Cai, N. Song, G. Yang, and Y. Liu, “Accelerometer calibration with nonlinear scale factor based on multi-position observation,” Meas. Sci. Technol. 24(10), 105002 (2013).
[Crossref]

N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
[Crossref]

Su, Y.

Y. Xu, X. H. Zhu, and Y. Su, “A novel network calibration method for inertial measurement units,” J. Aerosp. Eng. 229(7), 1336–1348 (2015).

Sun, F.

Q. Wang, Z. Qi, and F. Sun, “Six-position calibration for the fiber optic gyro based on a double calculating program,” Opt. Eng. 52(4), 043603 (2013).
[Crossref]

Sun, W.

W. Sun, D. Wang, L. Xu, and L. Xu, “MEMS-based rotary strapdown inertial navigation system,” Meas. 46(8), 2585–2596 (2013).
[Crossref]

W. Sun and Y. Gao, “Fiber-based rotary strapdown inertial navigation system,” Opt. Eng. 52(7), 076106 (2013).
[Crossref]

Topic, M.

D. Jurman, M. Jankovec, R. Kamnik, and M. Topič, “Calibration and data fusion solution for the miniature attitude and heading reference system,” Sensor. Actuat. A. 138, 411–420 (2007).

Wang, B.

B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
[Crossref]

Q. Ren, B. Wang, Z. Deng, and M. Fu, “A multi-position self-calibration method for dual-axis rotational inertial navigation system,” Sensor. Actuat. A. 219, 24–31 (2014).

Wang, D.

W. Sun, D. Wang, L. Xu, and L. Xu, “MEMS-based rotary strapdown inertial navigation system,” Meas. 46(8), 2585–2596 (2013).
[Crossref]

Wang, G.

G. Rao, G. Wang, S. Han, and W. Zhang, “Calibration of Laser Inertial Navigator with Dual-axis Rotation,” Int. J. Control Autom. 13(4), 960–966 (2015).
[Crossref]

Wang, H. G.

H. G. Wang and T. C. Williams, “Strategic inertial navigation systems – High-accuracy inertially stabilized platforms for hostile environments,” IEEE Contr. Syst. Mag. 28(1), 65–85 (2008).
[Crossref]

Wang, J.

W. Gao, Y. Zhang, and J. Wang, “Research on initial alignment and self-calibration of rotary strapdown inertial navigation systems,” Sensors (Basel) 15(2), 3154–3171 (2015).
[Crossref] [PubMed]

Wang, Q.

Q. Wang, Z. Qi, and F. Sun, “Six-position calibration for the fiber optic gyro based on a double calculating program,” Opt. Eng. 52(4), 043603 (2013).
[Crossref]

Williams, T. C.

H. G. Wang and T. C. Williams, “Strategic inertial navigation systems – High-accuracy inertially stabilized platforms for hostile environments,” IEEE Contr. Syst. Mag. 28(1), 65–85 (2008).
[Crossref]

Xu, L.

W. Sun, D. Wang, L. Xu, and L. Xu, “MEMS-based rotary strapdown inertial navigation system,” Meas. 46(8), 2585–2596 (2013).
[Crossref]

W. Sun, D. Wang, L. Xu, and L. Xu, “MEMS-based rotary strapdown inertial navigation system,” Meas. 46(8), 2585–2596 (2013).
[Crossref]

Xu, Y.

Y. Xu, X. H. Zhu, and Y. Su, “A novel network calibration method for inertial measurement units,” J. Aerosp. Eng. 229(7), 1336–1348 (2015).

Yang, G.

N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
[Crossref]

Q. Cai, N. Song, G. Yang, and Y. Liu, “Accelerometer calibration with nonlinear scale factor based on multi-position observation,” Meas. Sci. Technol. 24(10), 105002 (2013).
[Crossref]

Yang, H.

Z. Ding, C. Hong, and H. Yang, “An improved multi-position calibration method for low cost micro-electro mechanical systems inertial measurement units,” J. Aerosp. Eng. 229(10), 1919–1930 (2015).

Yin, H.

N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
[Crossref]

Yu, K. L.

D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).

Yu, S. B.

M. S. Kim, S. B. Yu, and W. S. Lee, “Development of a high-precision calibration method for inertial measurement unit,” Int. J. Precis. Eng. Manuf. 15(3), 567–575 (2014).
[Crossref]

Yuan, B.

B. Yuan, D. Liao, and S. Han, “Error compensation of an optical gyro INS by multi-axis rotation,” Meas. Sci. Technol. 23(2), 025102 (2012).
[Crossref]

Zhang, C.

J. Pan, C. Zhang, Y. Niu, and Z. Fan, “Accurate calibration for drift of fiber optic gyroscope in multi-position north-seeking phase,” Optik (Stuttg.) 125(24), 7244–7246 (2014).
[Crossref]

J. Pan, C. Zhang, and Q. Cai, “An accurate calibration method for accelerometer nonlinear scale factor on a low-cost three-axis turntable,” Meas. Sci. Technol. 25(2), 025102 (2014).
[Crossref]

Zhang, W.

G. Rao, G. Wang, S. Han, and W. Zhang, “Calibration of Laser Inertial Navigator with Dual-axis Rotation,” Int. J. Control Autom. 13(4), 960–966 (2015).
[Crossref]

Zhang, Y.

W. Gao, Y. Zhang, and J. Wang, “Research on initial alignment and self-calibration of rotary strapdown inertial navigation systems,” Sensors (Basel) 15(2), 3154–3171 (2015).
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Zhu, X. H.

Y. Xu, X. H. Zhu, and Y. Su, “A novel network calibration method for inertial measurement units,” J. Aerosp. Eng. 229(7), 1336–1348 (2015).

IEEE Contr. Syst. Mag. (1)

H. G. Wang and T. C. Williams, “Strategic inertial navigation systems – High-accuracy inertially stabilized platforms for hostile environments,” IEEE Contr. Syst. Mag. 28(1), 65–85 (2008).
[Crossref]

IEEE. Trans. Ind. Electron. (1)

B. Wang, Q. Ren, Z. Deng, and M. Fu, “A self-calibration method for nonorthogonal angles between gimbals of rotational inertial navigation system,” IEEE. Trans. Ind. Electron. 62(4), 2353–2362 (2015).
[Crossref]

IEEE. Trans. Instrum. Meas. (1)

J. Li, J. Fang, and M. Du, “Error Analysis and Gyro-Bias Calibration of Analytic Coarse Alignment for Airborne POS,” IEEE. Trans. Instrum. Meas. 61(11), 3058–3064 (2012).
[Crossref]

Int. J. Control Autom. (1)

G. Rao, G. Wang, S. Han, and W. Zhang, “Calibration of Laser Inertial Navigator with Dual-axis Rotation,” Int. J. Control Autom. 13(4), 960–966 (2015).
[Crossref]

Int. J. Precis. Eng. Manuf. (2)

M. S. Kim, S. B. Yu, and W. S. Lee, “Development of a high-precision calibration method for inertial measurement unit,” Int. J. Precis. Eng. Manuf. 15(3), 567–575 (2014).
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Z. Shang, X. Ma, M. Li, and Y. Liu, “A High-Precision Calibration Method for MEMS Gyroscopes,” Int. J. Precis. Eng. Manuf. 16(8), 1711–1716 (2015).
[Crossref]

J. Aerosp. Eng. (2)

Y. Xu, X. H. Zhu, and Y. Su, “A novel network calibration method for inertial measurement units,” J. Aerosp. Eng. 229(7), 1336–1348 (2015).

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D. J. Jwo, J. H. Shih, C. S. Hsu, and K. L. Yu, “Development of a strapdown inertial navigation system simulation platform,” J. Mar. Sci. Technol. 22(3), 381–391 (2014).

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P. Lv, J. Lai, J. Liu, and M. Nie, “The compensation effects of gyros’ stochastic errors in a rotational inertial navigation system,” J. Navig. 67(06), 1069–1088 (2014).
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W. Sun, D. Wang, L. Xu, and L. Xu, “MEMS-based rotary strapdown inertial navigation system,” Meas. 46(8), 2585–2596 (2013).
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Meas. Sci. Technol. (4)

N. Song, Q. Cai, G. Yang, and H. Yin, “Analysis and calibration of the mounting errors between inertial measurement unit and turntable in dual-axis rotational inertial navigation system,” Meas. Sci. Technol. 24(11), 115002 (2013).
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Q. Wang, Z. Qi, and F. Sun, “Six-position calibration for the fiber optic gyro based on a double calculating program,” Opt. Eng. 52(4), 043603 (2013).
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J. Pan, C. Zhang, Y. Niu, and Z. Fan, “Accurate calibration for drift of fiber optic gyroscope in multi-position north-seeking phase,” Optik (Stuttg.) 125(24), 7244–7246 (2014).
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Q. Ren, B. Wang, Z. Deng, and M. Fu, “A multi-position self-calibration method for dual-axis rotational inertial navigation system,” Sensor. Actuat. A. 219, 24–31 (2014).

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K. Kou, B. Li, and D. Tang, “An INS Error Estimation Method Based on Passive Observation to single Feature Target for Cruise Missile,” in Proceedings of IEEE Chinese Guidance, Navigation and Control Conference (IEEE 2014), pp. 2488–2493.
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Figures (16)

Fig. 1
Fig. 1 The structure of RINS.
Fig. 2
Fig. 2 The x accelerometer axis points up.
Fig. 3
Fig. 3 The x accelerometer axis points down.
Fig. 4
Fig. 4 The actual situation of the gimbals.
Fig. 5
Fig. 5 The error of accelerometer scale factor.
Fig. 6
Fig. 6 Schematic of non- orthogonality angle.
Fig. 7
Fig. 7 Rotation along with the Z i -axis.
Fig. 8
Fig. 8 Rotation along with the X m -axis.
Fig. 9
Fig. 9 Rotation along with the Y b -axis.
Fig. 10
Fig. 10 Rotation along with the Y b -axis.
Fig. 11
Fig. 11 The laboratory experimental equipment.
Fig. 12
Fig. 12 Comparison of traditional and improved method.
Fig. 13
Fig. 13 The vehicle experiment device.
Fig. 14
Fig. 14 Trajectory of the navigation result in vehicle experiment.
Fig. 15
Fig. 15 The camparition of velocity error.
Fig. 16
Fig. 16 The camparition of position error.

Tables (3)

Tables Icon

Table 1 Specification of the IMU.

Tables Icon

Table 2 The calibration results.

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Table 3 The navigation performance indicatorsa

Equations (26)

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( 0 0 g )= R X (90) R Z (90)( a xu a yu a zu )=( 1 0 0 0 0 1 0 1 0 )( 0 1 0 1 0 0 0 0 1 )( a xu a yu a zu )=( a yu a zu a xu )
( 0 0 g )= R X (90) R Z (90)( a xu a yu a zu )=( 1 0 0 0 0 1 0 1 0 )( 0 1 0 1 0 0 0 0 1 )( a xu a yu a zu )=( a yu a zu a xu )
{ K ax (g+ x )= N ¯ axu K ax (g+ x )= N ¯ axd
K ax = N ¯ axu N ¯ axd 2g .
( a xu a yu a zu )= R Y (η) R Y (γ) R Z (90) R X (90)( 0 0 g )=( g(sinηsinγcosηcosγ) 0 g(sinηcosγ+cosηsinγ) )
( a xd a yd a zd )= R Y (η) R Y (γ) R Z (90) R X (90)( 0 0 g )=( g(sinηsinγcosηcosγ) 0 g(sinηcosγ+cosηsinγ) )
K ax = N ¯ axu N ¯ axd 2gcosηcosγ
Δ K ax = 10 6 N ¯ axu N ¯ axd 2gcosηcosγ N ¯ axu N ¯ axd 2g N ¯ axu N ¯ axd 2gcosηcosγ .
γ= θ GzGx X θ Gz Y β Gx Y
{ ω x + ¯ =( Ω+ ω ex ) β Gx Y +Δ ε x ω x ¯ =( Ω+ ω ex ) β Gx Y +Δ ε x
β Gx Y = ω x + ¯ ω x ¯ 2Ω
{ ω z + ¯ =( Ω+ ω ez ) θ Gz Y +Δ ε z ω z ¯ =( Ω+ ω ez ) θ Gz Y +Δ ε z
θ Gz Y = ω z + ¯ ω z ¯ 2Ω .
{ ω z + ¯ =( Ω+ ω ez ) θ Gz X +Δ ε z ω z ¯ =( Ω+ ω ez ) θ Gz X +Δ ε z
θ Gz X = ω z + ¯ ω z ¯ 2Ω
{ ω x + ¯ =( Ω+ ω ex ) θ Gx X +Δ ε x ω x ¯ =( Ω+ ω ex ) θ Gx X +Δ ε x
θ Gx X = ω x + ¯ ω x ¯ 2Ω
θ GzGx X = θ Gx X θ Gz X
C i b =[ cos ϕ ZR sin ϕ ZR 0 sin ϕ ZR cos ϕ ZR 0 0 0 1 ]
[ Δ θ x b Δ θ y b Δ θ z b ]=[ cos ϕ ZR sin ϕ ZR 0 sin ϕ ZR cos ϕ ZR 0 0 0 1 ][ Δ θ x i Δ θ y i Δ θ z i ]
[ Δ V x b Δ V y b Δ V z b ]=[ cos ϕ ZR sin ϕ ZR 0 sin ϕ ZR cos ϕ ZR 0 0 0 1 ][ Δ V x i Δ V y i Δ V z i ]
ω ¯ b =[ ω x b ω y b ω z b ]= 1 2T [ Δ θ x b Δ θ y b Δ θ z b ]
f ¯ b =[ f x b f y b f z b ]= 1 2T [ Δ V x b Δ V y b Δ V z b ]
[ ω x b ω y b ω z b f x b f y b f z b ]=[ 0 ω ie cosφ ω ie sinφ 0 0 g ] C b n
{ T 31 = f x b g T 32 = f y b g T 33 = f z b g T 21 = ω x b T 31 ω ie sinφ ω ie cosφ T 22 = ω x b T 32 ω ie sinφ ω ie cosφ T 23 = ω x b T 33 ω ie sinφ ω ie cosφ T 11 = T 22 T 33 T 23 T 32 T 12 = T 23 T 31 T 21 T 33 T 13 = T 21 T 32 T 22 T 31
{ θ= sin 1 ( T 23 ) ϕ= tan 1 ( T 13 T 33 ) ψ= tan 1 ( T 21 T 22 )

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