Abstract

Traditional compensation methods using temperature-related parameters have little effect when the ring laser gyroscope (RLG) bias changes rapidly. To solve this problem, a novel RLG bias temperature compensation method using readout signals is proposed in this paper. Combined with the least squares support vector machine (LS-SVM) algorithm, the novel method can improve the precision of the RLG bias. Experiments show that by utilizing the readout signals in the LS-SVM model, the RLG bias stability can be significantly raised compared to the original data. The novel method proposed in this paper is shown to be feasible, even when the RLG bias changes rapidly.

© 2015 Optical Society of America

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References

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  1. J. Lahham and J. Brazell, “Acoustic noise reduction in the MK49 Ship’s Inertial Navigation System (SINS),” in Proceedings of IEEE Conference on Position Location and Navigation Symposium (Institute of Electrical and Electronics Engineers, California, 1992), pp. 32–39.
    [Crossref]
  2. J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
    [Crossref]
  3. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
    [Crossref]
  4. Sh. Mohammad-Nejad, M. Pourmahyabadi, and A. Lajevardizadeh, “Performance modeling of ring laser gyro in inertial navigation system,” Iran. J. Electron. Electr. Eng. 2(3), 82–90 (2006).
  5. C. Guo, Y. Xu, and X. Zhao, “Investigation on the temperature compensating model for ring laser gyroscope,” Chin. Opt. Lett. 4, 576–579 (2006).
  6. H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.
  7. G. Y. Wu and Q. T. Gu, “Thermal characteristics and thermal compensation of four frequency ring laser gyro,” in Proceedings of IEEE Conference on Position Location and Navigation Symposium (EEE, 2002), pp. 271–276.
  8. G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
    [Crossref]
  9. X. D. Yu, Y. Wang, G. Wei, P. F. Zhang, and X. W. Long, “Novel temperature modeling and compensation method for bias of ring laser gyroscope based on least-square support vector machine,” Chin. Opt. Lett. 9(5), 051201 (2011).
    [Crossref]
  10. P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).
  11. R. A. Mitchell, “Ring laser gyroscope output optics detection system,” U.S. patent 5,116,132 (26 May 1992).
  12. J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
    [Crossref]
  13. V. N. Vapnik, The Nature of Statistical Learning Theory (Springer, 1995).
  14. V. Vapnik and O. Chapelle, “Bounds on error expectation for support vector machines,” Neural Comput. 12(9), 2013–2036 (2000).
    [Crossref] [PubMed]
  15. J. W. Diesel and G. P. Dunn, “Method for in-field updating of the gyro thermal calibration of an inertial navigation system,” U.S. patent 5,527,003 (18 Jun 1996).
  16. R. J. Buchler, R. Moeller, S. W. Fann, D. A. Tazartes, and J. G. Mark, “Temperature compensation method for strapdown inertial navigation system,” U.S. patent 6,175,807 B1 (16 Jan 2001).

2014 (1)

J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
[Crossref]

2011 (3)

G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
[Crossref]

X. D. Yu, Y. Wang, G. Wei, P. F. Zhang, and X. W. Long, “Novel temperature modeling and compensation method for bias of ring laser gyroscope based on least-square support vector machine,” Chin. Opt. Lett. 9(5), 051201 (2011).
[Crossref]

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

2008 (1)

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
[Crossref]

2006 (2)

Sh. Mohammad-Nejad, M. Pourmahyabadi, and A. Lajevardizadeh, “Performance modeling of ring laser gyro in inertial navigation system,” Iran. J. Electron. Electr. Eng. 2(3), 82–90 (2006).

C. Guo, Y. Xu, and X. Zhao, “Investigation on the temperature compensating model for ring laser gyroscope,” Chin. Opt. Lett. 4, 576–579 (2006).

2000 (1)

V. Vapnik and O. Chapelle, “Bounds on error expectation for support vector machines,” Neural Comput. 12(9), 2013–2036 (2000).
[Crossref] [PubMed]

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Chapelle, O.

V. Vapnik and O. Chapelle, “Bounds on error expectation for support vector machines,” Neural Comput. 12(9), 2013–2036 (2000).
[Crossref] [PubMed]

Cheng, J. C.

J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
[Crossref]

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Fang, J. C.

J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
[Crossref]

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Gu, Q. T.

G. Y. Wu and Q. T. Gu, “Thermal characteristics and thermal compensation of four frequency ring laser gyro,” in Proceedings of IEEE Conference on Position Location and Navigation Symposium (EEE, 2002), pp. 271–276.

Guo, C.

Hyun, S.

H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.

Lajevardizadeh, A.

Sh. Mohammad-Nejad, M. Pourmahyabadi, and A. Lajevardizadeh, “Performance modeling of ring laser gyro in inertial navigation system,” Iran. J. Electron. Electr. Eng. 2(3), 82–90 (2006).

Li, G.

G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
[Crossref]

Li, J. L.

J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
[Crossref]

Long, X.

G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
[Crossref]

Long, X. W.

Mohammad-Nejad, Sh.

Sh. Mohammad-Nejad, M. Pourmahyabadi, and A. Lajevardizadeh, “Performance modeling of ring laser gyro in inertial navigation system,” Iran. J. Electron. Electr. Eng. 2(3), 82–90 (2006).

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Pourmahyabadi, M.

Sh. Mohammad-Nejad, M. Pourmahyabadi, and A. Lajevardizadeh, “Performance modeling of ring laser gyro in inertial navigation system,” Iran. J. Electron. Electr. Eng. 2(3), 82–90 (2006).

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Seon, H. W.

H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.

Soo, L. K.

H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.

Soo, P. B.

H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.

Tang, J. X.

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

Vapnik, V.

V. Vapnik and O. Chapelle, “Bounds on error expectation for support vector machines,” Neural Comput. 12(9), 2013–2036 (2000).
[Crossref] [PubMed]

Wang, Y.

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

X. D. Yu, Y. Wang, G. Wei, P. F. Zhang, and X. W. Long, “Novel temperature modeling and compensation method for bias of ring laser gyroscope based on least-square support vector machine,” Chin. Opt. Lett. 9(5), 051201 (2011).
[Crossref]

Wei, G.

X. D. Yu, Y. Wang, G. Wei, P. F. Zhang, and X. W. Long, “Novel temperature modeling and compensation method for bias of ring laser gyroscope based on least-square support vector machine,” Chin. Opt. Lett. 9(5), 051201 (2011).
[Crossref]

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
[Crossref]

Wu, G. Y.

G. Y. Wu and Q. T. Gu, “Thermal characteristics and thermal compensation of four frequency ring laser gyro,” in Proceedings of IEEE Conference on Position Location and Navigation Symposium (EEE, 2002), pp. 271–276.

Wu, W. R.

J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
[Crossref]

Wu, Y.

G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
[Crossref]

Xu, Y.

Youp, H. J.

H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.

Yu, X. D.

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

X. D. Yu, Y. Wang, G. Wei, P. F. Zhang, and X. W. Long, “Novel temperature modeling and compensation method for bias of ring laser gyroscope based on least-square support vector machine,” Chin. Opt. Lett. 9(5), 051201 (2011).
[Crossref]

Yuan, J.

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
[Crossref]

Zhang, P. F.

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

X. D. Yu, Y. Wang, G. Wei, P. F. Zhang, and X. W. Long, “Novel temperature modeling and compensation method for bias of ring laser gyroscope based on least-square support vector machine,” Chin. Opt. Lett. 9(5), 051201 (2011).
[Crossref]

Zhao, X.

Chin. Opt. Lett. (2)

Infra. Laser Eng. (1)

P. F. Zhang, Y. Wang, X. D. Yu, G. Wei, and J. X. Tang, “Effect of temperature characteristic of light path on RLG’s bias,” Infra. Laser Eng. 40, 2393–2397 (2011).

Iran. J. Electron. Electr. Eng. (1)

Sh. Mohammad-Nejad, M. Pourmahyabadi, and A. Lajevardizadeh, “Performance modeling of ring laser gyro in inertial navigation system,” Iran. J. Electron. Electr. Eng. 2(3), 82–90 (2006).

Measurement (2)

J. C. Cheng, J. C. Fang, W. R. Wu, and J. L. Li, “Temperature drift modeling and compensation of RLG based on PSO tuning SVM,” Measurement 55, 246–254 (2014).
[Crossref]

G. Wei, G. Li, Y. Wu, and X. Long, “Application of least squares-support vector machine in system level temperature compensation of ring laser gyroscope,” Measurement 44(10), 1898–1903 (2011).
[Crossref]

Neural Comput. (1)

V. Vapnik and O. Chapelle, “Bounds on error expectation for support vector machines,” Neural Comput. 12(9), 2013–2036 (2000).
[Crossref] [PubMed]

Opt. Commun. (1)

J. Yuan and X. W. Long, “Optical-axis perturbation in nonplanar ring resonators,” Opt. Commun. 281(5), 1204–1210 (2008).
[Crossref]

Rev. Mod. Phys. (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Other (7)

J. Lahham and J. Brazell, “Acoustic noise reduction in the MK49 Ship’s Inertial Navigation System (SINS),” in Proceedings of IEEE Conference on Position Location and Navigation Symposium (Institute of Electrical and Electronics Engineers, California, 1992), pp. 32–39.
[Crossref]

R. A. Mitchell, “Ring laser gyroscope output optics detection system,” U.S. patent 5,116,132 (26 May 1992).

H. W. Seon, L. K. Soo, P. B. Soo, H. J. Youp, and S. Hyun, “ The compensation method for thermal bias of ring laser gyro,” in Proceedings of IEEE Conference on Laser and Electro-Optics Society (EEE, 2008), pp. 724.

G. Y. Wu and Q. T. Gu, “Thermal characteristics and thermal compensation of four frequency ring laser gyro,” in Proceedings of IEEE Conference on Position Location and Navigation Symposium (EEE, 2002), pp. 271–276.

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer, 1995).

J. W. Diesel and G. P. Dunn, “Method for in-field updating of the gyro thermal calibration of an inertial navigation system,” U.S. patent 5,527,003 (18 Jun 1996).

R. J. Buchler, R. Moeller, S. W. Fann, D. A. Tazartes, and J. G. Mark, “Temperature compensation method for strapdown inertial navigation system,” U.S. patent 6,175,807 B1 (16 Jan 2001).

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Figures (10)

Fig. 1
Fig. 1 The combining prism and readout system of the ring laser gyroscope (RLG). CW: clockwise; CCW: counter-clockwise.
Fig. 2
Fig. 2 The fringe pattern of two beams (a) with coherency and (b) with slightly incoherency.
Fig. 3
Fig. 3 The circuit of processing the readout signals used for the ring laser gyroscope (RLG) bias compensation.
Fig. 4
Fig. 4 The hardware structure of ring laser gyroscope (RLG) bias compensation using readout signals.
Fig. 5
Fig. 5 The ring laser gyroscope (RLG) aircraft strapdown inertial navigation system used in the temperature experiment.
Fig. 6
Fig. 6 The original data of the ring laser gyroscope (RLG) bias and temperature.
Fig. 7
Fig. 7 The comparison between different parameters used for the ring laser gyroscope (RLG) bias compensation.
Fig. 8
Fig. 8 Compensation results of the ring laser gyroscope (RLG) bias using different parameters based on the least squares (LS) fitting. LS fitting model of the RLG bias compensation using (a) temperature, (b) temperature variation rate, (c) light intensity, and (d) difference of readout signals.
Fig. 9
Fig. 9 Compensation result of ring laser gyroscope (RLG) bias using different parameters based on the least squares support vector machine (LS-SVM) model. LS-SVM model of the RLG bias compensation using (a) temperature, (b) temperature variation, (c) light intensity, and (d) difference of readout signals.
Fig. 10
Fig. 10 Compensation result of ring laser gyroscope (RLG) bias using all parameters based on the least squares support vector machine (LS-SVM) model.

Tables (4)

Tables Icon

Table 1 The correlation coefficients of three parameters to the RLG bias.

Tables Icon

Table 2 The ring laser gyroscope (RLG) bias compensation effect of the least squares (LS) fitting model using different parameters.

Tables Icon

Table 3 The ring laser gyroscope (RLG) bias compensation effect of the least squares support vector machine (LS-SVM) model using different parameters.

Tables Icon

Table 4 Compensation result between different methods and input vectors.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

ΔL= 4AΩ c ,
Δf=KΩ=4AΩ/λL,
I= I 0 [1+cos(2πΔft+2π γx λ + ϕ 0 )],
N= 0 t Δfdt=4A/λL 0 t Ωdt=4Aθ/λL ,
wx+b=0,
y i [(w x i )+b]10,i=1,2,...,n.
minφ(w)= 1 2 w 2 .
K(x,y) φ(x)φ(y)dxdy>0
φ 2 (x)dx <.
maxQ(a)= i=1 n a i 1 2 i=1 n j=1 n a i a j y i y j K( x i , x j ) , s.t. i=1 n y i a i =0 0 a i C i=1,2,...,n,
f(x)=sgn[ j=1 n a i * y i K( x i ,x) + b * ],
min w,b,ξ, ξ * 1 2 w T w+ c 2 i=1 n ξ i 2 , s.t. y i [ w T φ( x i )+b]= ξ i ,
L= 1 2 w T w+c i=1 n ξ i 2 i=1 n a i { ξ i +[ w T φ( x i )+b] y i } .
{ L w T =0 w T = i=1 n a i φ( x i ) L b =0 i=1 n a i = 0 L ξ i =0 ξ i = a i c L a i =0 w T φ( x i )+b+ ξ i = y i .
K( x i , x j )=exp( x i x j 2 /2 σ 2 ),
( 0 1 1 1 K( x 1 , x 1 )+1/c K( x 1 , x n ) 1 K( x n , x 1 ) K( x n , x n )+1/c )( b a 1 a n )=( 0 y 1 y n ).
f(x)= i=1 n a i K( x i ,x) +b.
B= c 0 + c 1 X+ c 2 X 2 + c 3 X 3 ,

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