Abstract

Rotation modulation technology could effectively improve the accuracy of the inertial navigation system (INS) by compensating for the biases of the inertial sensors automatically. However, the carrier angular motion and rotation control error could reduce the rotation modulation effect and then decrease the navigation accuracy. To address this problem, for the single-axis rotation INS, a novel rotation control scheme is presented. The control scheme employs the fiber optic gyros to control the inertial measurement unit (IMU) rotation angular velocity so that the INS with both rotation modulation and azimuth motion insulation functions. Furthermore, in order to reduce the control error, this study adopts two ways: optimizing the control strategy and shortening the delay time. The former way is to control the IMU rotating about the z-axis of the platform frame with respect to the navigation frame, rather than the up-axis of the navigation frame. The latter way is to apply interrupt mode rather than inquiry mode to complete the data transfer between the navigation and the control processors. The simulation and experimental results demonstrate that: the proposed method would not only realize the rotation modulation of the biases of the inertial sensors, but also achieve the insulation of the azimuth motion. The steady-state control error of the control system is less than 10” and the overshoot control error is less than 50”. Compared to the traditional SRINS, the navigation position error in the single-axis rotation/azimuth-motion insulation INS could reduce 50% in some navigation application.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  3. L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).
  4. F. Liu, W. Wang, L. Wang, and P. Feng, “Error analyses and calibration methods with accelerometers for optical angle encoders in rotational inertial navigation systems,” Appl. Opt. 52(32), 7724–7731 (2013).
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  6. Q. Zhang, L. Wang, Z. Liu, and Y. Zhang, “Innovative self-calibration method for accelerometer scale factor of the missile-borne RINS with fiber optic gyro,” Opt. Express 24(19), 21228–21243 (2016).
    [PubMed]
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  21. K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).
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2017 (3)

T. X. Song, K. Li, L. Wang, J. Sui, and L. C. Wang, “A rapid and high-precision initial alignment scheme for dual-axis rotational inertial navigation system,” Microsyst. Technol. 23(12), 5515–5525 (2017).

L. C. Wang, K. Li, L. Wang, and J. X. Gao, “Identifying Z-axis gyro drift and scale factor error using azimuth measurement in fiber optic gyroscope single-axis rotation inertial navigation system,” Opt. Eng. 56(2), 024102 (2017).

L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).

2016 (4)

P. Y. Gao, K. Li, L. Wang, and Q. Zhang, “Four-position heading effect calibration algorithm for rotation inertial navigation system based on fiber optic gyro,” Opt. Eng. 55(7), 074105 (2016).

P. Y. Gao, K. Li, and L. Wang, “A Self-Calibration Method for Non-Orthogonal Angles of Gimbals in Tri-Axis Rotational Inertial Navigation System,” IEEE Sens. J. 16(24), 8998–9005 (2016).

Y. Hao, G. Q. Wu, F. Gao, and Q. Y. Tan, “Implementation of the Carrier-Insulated Control for the 2-Axis FOG Strapdown Inertial Navigation System,” Nav. Pos. Timing 3(4), 9–12 (2016).

Q. Zhang, L. Wang, Z. Liu, and Y. Zhang, “Innovative self-calibration method for accelerometer scale factor of the missile-borne RINS with fiber optic gyro,” Opt. Express 24(19), 21228–21243 (2016).
[PubMed]

2015 (1)

K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).

2014 (2)

X. Z. Gao, “Research on the influence of rotation inertial navigation due to gyro angle random walk error,” Ship Sci. Technol. 36(9), 122–124 (2014).

L. Wang, W. Wang, X. Y. Wang, and G. L. Yang, “Design and implementation of digital position stabilization loop for fiber optic gyroscope based rotational inertial navigation system,” Control Decis. 464(1), 195–200 (2014).

2013 (4)

J. N. Xu, F. Zha, J. S. Li, and H. Y. He, “Analysis and compensation for heading-coupling effect of single-axis rotating INS,” J. Chin. Inertial Tech. 21(1), 26–30 (2013).

J. Liu and W. Wang, “Motor control of self-calibration of rotation inertial navigation system,” Autom. Instrum. 18(1), 55–62 (2013).

W. Sun and Y. Gao, “Fiber-based rotary strapdown inertial navigation system,” Opt. Eng. 52(82), 585–2596 (2013).

F. Liu, W. Wang, L. Wang, and P. Feng, “Error analyses and calibration methods with accelerometers for optical angle encoders in rotational inertial navigation systems,” Appl. Opt. 52(32), 7724–7731 (2013).
[PubMed]

2012 (2)

F. Liu, W. Wei, and Z. Y. Zhang, “Motor rotation control method for rotation–modulation SINS,” Electric Machines Control 16(11), 17–21 (2012).

L. D. Zhang, J. X. Lian, M. Wu, and X. P. Hu, “Research on yaw angle isolation method of inertial navigation system based on single–axis rotation,” Yiqi Yibiao Xuebao 33(6), 1247–1253 (2012).

2011 (2)

S. Chen, L. Wang, and Y. F. Xu, “A High-Precision Control System of DC Motor Based On DSP,” Procedia Eng. 15(1), 573–577 (2011).

L. D. Zhang, J. X. Lian, and X. P. Hu, “The Effect of Vehicle Angle Motion on Rotation Modulation Technology for Rotating INS,” J. Natl. University Defense Technol. 33(4), 152–156 (2011).

2009 (1)

W. H. Baird, “An Introduction to Inertial Navigation,” Am. J. Phys. 77(9), 844–847 (2009).

Baird, W. H.

W. H. Baird, “An Introduction to Inertial Navigation,” Am. J. Phys. 77(9), 844–847 (2009).

Chen, S.

S. Chen, L. Wang, and Y. F. Xu, “A High-Precision Control System of DC Motor Based On DSP,” Procedia Eng. 15(1), 573–577 (2011).

Chen, Y. P.

L. Wang, K. Li, Y. P. Chen, and R. Guo, “Control implementation for the single-axis rotation and motion-insulated inertial navigation system,” in Proc. of IEEE-CDC (IEEE, 2017), pp. 3172–3177.

Deng, Z. H.

H. R. Wang, Z. H. Deng, and B. Wang, “Analysis of error suppression performance in the carrier angle motion status for rotation for FOG inertial navigation system,” in Proc. of IEEE-CCC (IEEE, 2014), pp.1026–1030.

Ding, Z. X.

L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).

Emanuel, L.

T. Terry and L. Emanuel, ”The AN/WSN–7B marine gyrocompass/navigator,” in Proc. of Conference on National Technical Meeting of the Institute of Navigation (Academic,2000), pp. 348–357.

Feng, P.

Gao, F.

Y. Hao, G. Q. Wu, F. Gao, and Q. Y. Tan, “Implementation of the Carrier-Insulated Control for the 2-Axis FOG Strapdown Inertial Navigation System,” Nav. Pos. Timing 3(4), 9–12 (2016).

Gao, J. X.

L. C. Wang, K. Li, L. Wang, and J. X. Gao, “Identifying Z-axis gyro drift and scale factor error using azimuth measurement in fiber optic gyroscope single-axis rotation inertial navigation system,” Opt. Eng. 56(2), 024102 (2017).

Gao, P. Y.

P. Y. Gao, K. Li, L. Wang, and Q. Zhang, “Four-position heading effect calibration algorithm for rotation inertial navigation system based on fiber optic gyro,” Opt. Eng. 55(7), 074105 (2016).

P. Y. Gao, K. Li, and L. Wang, “A Self-Calibration Method for Non-Orthogonal Angles of Gimbals in Tri-Axis Rotational Inertial Navigation System,” IEEE Sens. J. 16(24), 8998–9005 (2016).

K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).

Gao, X. Z.

X. Z. Gao, “Research on the influence of rotation inertial navigation due to gyro angle random walk error,” Ship Sci. Technol. 36(9), 122–124 (2014).

Gao, Y.

W. Sun and Y. Gao, “Fiber-based rotary strapdown inertial navigation system,” Opt. Eng. 52(82), 585–2596 (2013).

Guo, R.

L. Wang, K. Li, Y. P. Chen, and R. Guo, “Control implementation for the single-axis rotation and motion-insulated inertial navigation system,” in Proc. of IEEE-CDC (IEEE, 2017), pp. 3172–3177.

Hao, Y.

Y. Hao, G. Q. Wu, F. Gao, and Q. Y. Tan, “Implementation of the Carrier-Insulated Control for the 2-Axis FOG Strapdown Inertial Navigation System,” Nav. Pos. Timing 3(4), 9–12 (2016).

He, H. Y.

J. N. Xu, F. Zha, J. S. Li, and H. Y. He, “Analysis and compensation for heading-coupling effect of single-axis rotating INS,” J. Chin. Inertial Tech. 21(1), 26–30 (2013).

Hu, X. P.

L. D. Zhang, J. X. Lian, M. Wu, and X. P. Hu, “Research on yaw angle isolation method of inertial navigation system based on single–axis rotation,” Yiqi Yibiao Xuebao 33(6), 1247–1253 (2012).

L. D. Zhang, J. X. Lian, and X. P. Hu, “The Effect of Vehicle Angle Motion on Rotation Modulation Technology for Rotating INS,” J. Natl. University Defense Technol. 33(4), 152–156 (2011).

Li, J. S.

J. N. Xu, F. Zha, J. S. Li, and H. Y. He, “Analysis and compensation for heading-coupling effect of single-axis rotating INS,” J. Chin. Inertial Tech. 21(1), 26–30 (2013).

Li, K.

T. X. Song, K. Li, L. Wang, J. Sui, and L. C. Wang, “A rapid and high-precision initial alignment scheme for dual-axis rotational inertial navigation system,” Microsyst. Technol. 23(12), 5515–5525 (2017).

L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).

L. C. Wang, K. Li, L. Wang, and J. X. Gao, “Identifying Z-axis gyro drift and scale factor error using azimuth measurement in fiber optic gyroscope single-axis rotation inertial navigation system,” Opt. Eng. 56(2), 024102 (2017).

P. Y. Gao, K. Li, and L. Wang, “A Self-Calibration Method for Non-Orthogonal Angles of Gimbals in Tri-Axis Rotational Inertial Navigation System,” IEEE Sens. J. 16(24), 8998–9005 (2016).

P. Y. Gao, K. Li, L. Wang, and Q. Zhang, “Four-position heading effect calibration algorithm for rotation inertial navigation system based on fiber optic gyro,” Opt. Eng. 55(7), 074105 (2016).

K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).

L. Wang, K. Li, Y. P. Chen, and R. Guo, “Control implementation for the single-axis rotation and motion-insulated inertial navigation system,” in Proc. of IEEE-CDC (IEEE, 2017), pp. 3172–3177.

Lian, J. X.

L. D. Zhang, J. X. Lian, M. Wu, and X. P. Hu, “Research on yaw angle isolation method of inertial navigation system based on single–axis rotation,” Yiqi Yibiao Xuebao 33(6), 1247–1253 (2012).

L. D. Zhang, J. X. Lian, and X. P. Hu, “The Effect of Vehicle Angle Motion on Rotation Modulation Technology for Rotating INS,” J. Natl. University Defense Technol. 33(4), 152–156 (2011).

Liu, F.

F. Liu, W. Wang, L. Wang, and P. Feng, “Error analyses and calibration methods with accelerometers for optical angle encoders in rotational inertial navigation systems,” Appl. Opt. 52(32), 7724–7731 (2013).
[PubMed]

F. Liu, W. Wei, and Z. Y. Zhang, “Motor rotation control method for rotation–modulation SINS,” Electric Machines Control 16(11), 17–21 (2012).

Liu, J.

J. Liu and W. Wang, “Motor control of self-calibration of rotation inertial navigation system,” Autom. Instrum. 18(1), 55–62 (2013).

Liu, Z.

Song, T. X.

T. X. Song, K. Li, L. Wang, J. Sui, and L. C. Wang, “A rapid and high-precision initial alignment scheme for dual-axis rotational inertial navigation system,” Microsyst. Technol. 23(12), 5515–5525 (2017).

Sui, J.

T. X. Song, K. Li, L. Wang, J. Sui, and L. C. Wang, “A rapid and high-precision initial alignment scheme for dual-axis rotational inertial navigation system,” Microsyst. Technol. 23(12), 5515–5525 (2017).

Sun, W.

W. Sun and Y. Gao, “Fiber-based rotary strapdown inertial navigation system,” Opt. Eng. 52(82), 585–2596 (2013).

Tan, Q. Y.

Y. Hao, G. Q. Wu, F. Gao, and Q. Y. Tan, “Implementation of the Carrier-Insulated Control for the 2-Axis FOG Strapdown Inertial Navigation System,” Nav. Pos. Timing 3(4), 9–12 (2016).

Terry, T.

T. Terry and L. Emanuel, ”The AN/WSN–7B marine gyrocompass/navigator,” in Proc. of Conference on National Technical Meeting of the Institute of Navigation (Academic,2000), pp. 348–357.

Wang, B.

H. R. Wang, Z. H. Deng, and B. Wang, “Analysis of error suppression performance in the carrier angle motion status for rotation for FOG inertial navigation system,” in Proc. of IEEE-CCC (IEEE, 2014), pp.1026–1030.

Wang, H. R.

H. R. Wang, Z. H. Deng, and B. Wang, “Analysis of error suppression performance in the carrier angle motion status for rotation for FOG inertial navigation system,” in Proc. of IEEE-CCC (IEEE, 2014), pp.1026–1030.

Wang, L.

L. C. Wang, K. Li, L. Wang, and J. X. Gao, “Identifying Z-axis gyro drift and scale factor error using azimuth measurement in fiber optic gyroscope single-axis rotation inertial navigation system,” Opt. Eng. 56(2), 024102 (2017).

T. X. Song, K. Li, L. Wang, J. Sui, and L. C. Wang, “A rapid and high-precision initial alignment scheme for dual-axis rotational inertial navigation system,” Microsyst. Technol. 23(12), 5515–5525 (2017).

Q. Zhang, L. Wang, Z. Liu, and Y. Zhang, “Innovative self-calibration method for accelerometer scale factor of the missile-borne RINS with fiber optic gyro,” Opt. Express 24(19), 21228–21243 (2016).
[PubMed]

P. Y. Gao, K. Li, L. Wang, and Q. Zhang, “Four-position heading effect calibration algorithm for rotation inertial navigation system based on fiber optic gyro,” Opt. Eng. 55(7), 074105 (2016).

P. Y. Gao, K. Li, and L. Wang, “A Self-Calibration Method for Non-Orthogonal Angles of Gimbals in Tri-Axis Rotational Inertial Navigation System,” IEEE Sens. J. 16(24), 8998–9005 (2016).

K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).

L. Wang, W. Wang, X. Y. Wang, and G. L. Yang, “Design and implementation of digital position stabilization loop for fiber optic gyroscope based rotational inertial navigation system,” Control Decis. 464(1), 195–200 (2014).

F. Liu, W. Wang, L. Wang, and P. Feng, “Error analyses and calibration methods with accelerometers for optical angle encoders in rotational inertial navigation systems,” Appl. Opt. 52(32), 7724–7731 (2013).
[PubMed]

S. Chen, L. Wang, and Y. F. Xu, “A High-Precision Control System of DC Motor Based On DSP,” Procedia Eng. 15(1), 573–577 (2011).

L. Wang, K. Li, Y. P. Chen, and R. Guo, “Control implementation for the single-axis rotation and motion-insulated inertial navigation system,” in Proc. of IEEE-CDC (IEEE, 2017), pp. 3172–3177.

Wang, L. C.

L. C. Wang, K. Li, L. Wang, and J. X. Gao, “Identifying Z-axis gyro drift and scale factor error using azimuth measurement in fiber optic gyroscope single-axis rotation inertial navigation system,” Opt. Eng. 56(2), 024102 (2017).

L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).

T. X. Song, K. Li, L. Wang, J. Sui, and L. C. Wang, “A rapid and high-precision initial alignment scheme for dual-axis rotational inertial navigation system,” Microsyst. Technol. 23(12), 5515–5525 (2017).

Wang, W.

L. Wang, W. Wang, X. Y. Wang, and G. L. Yang, “Design and implementation of digital position stabilization loop for fiber optic gyroscope based rotational inertial navigation system,” Control Decis. 464(1), 195–200 (2014).

J. Liu and W. Wang, “Motor control of self-calibration of rotation inertial navigation system,” Autom. Instrum. 18(1), 55–62 (2013).

F. Liu, W. Wang, L. Wang, and P. Feng, “Error analyses and calibration methods with accelerometers for optical angle encoders in rotational inertial navigation systems,” Appl. Opt. 52(32), 7724–7731 (2013).
[PubMed]

Wang, X. Y.

L. Wang, W. Wang, X. Y. Wang, and G. L. Yang, “Design and implementation of digital position stabilization loop for fiber optic gyroscope based rotational inertial navigation system,” Control Decis. 464(1), 195–200 (2014).

Wei, W.

F. Liu, W. Wei, and Z. Y. Zhang, “Motor rotation control method for rotation–modulation SINS,” Electric Machines Control 16(11), 17–21 (2012).

Wu, G. Q.

Y. Hao, G. Q. Wu, F. Gao, and Q. Y. Tan, “Implementation of the Carrier-Insulated Control for the 2-Axis FOG Strapdown Inertial Navigation System,” Nav. Pos. Timing 3(4), 9–12 (2016).

Wu, M.

L. D. Zhang, J. X. Lian, M. Wu, and X. P. Hu, “Research on yaw angle isolation method of inertial navigation system based on single–axis rotation,” Yiqi Yibiao Xuebao 33(6), 1247–1253 (2012).

Xu, J. N.

J. N. Xu, F. Zha, J. S. Li, and H. Y. He, “Analysis and compensation for heading-coupling effect of single-axis rotating INS,” J. Chin. Inertial Tech. 21(1), 26–30 (2013).

Xu, Y. F.

S. Chen, L. Wang, and Y. F. Xu, “A High-Precision Control System of DC Motor Based On DSP,” Procedia Eng. 15(1), 573–577 (2011).

Yang, G. L.

L. Wang, W. Wang, X. Y. Wang, and G. L. Yang, “Design and implementation of digital position stabilization loop for fiber optic gyroscope based rotational inertial navigation system,” Control Decis. 464(1), 195–200 (2014).

Zha, F.

J. N. Xu, F. Zha, J. S. Li, and H. Y. He, “Analysis and compensation for heading-coupling effect of single-axis rotating INS,” J. Chin. Inertial Tech. 21(1), 26–30 (2013).

Zhang, J.

L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).

Zhang, L. D.

L. D. Zhang, J. X. Lian, M. Wu, and X. P. Hu, “Research on yaw angle isolation method of inertial navigation system based on single–axis rotation,” Yiqi Yibiao Xuebao 33(6), 1247–1253 (2012).

L. D. Zhang, J. X. Lian, and X. P. Hu, “The Effect of Vehicle Angle Motion on Rotation Modulation Technology for Rotating INS,” J. Natl. University Defense Technol. 33(4), 152–156 (2011).

Zhang, Q.

Q. Zhang, L. Wang, Z. Liu, and Y. Zhang, “Innovative self-calibration method for accelerometer scale factor of the missile-borne RINS with fiber optic gyro,” Opt. Express 24(19), 21228–21243 (2016).
[PubMed]

P. Y. Gao, K. Li, L. Wang, and Q. Zhang, “Four-position heading effect calibration algorithm for rotation inertial navigation system based on fiber optic gyro,” Opt. Eng. 55(7), 074105 (2016).

K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).

Zhang, Y.

Zhang, Z. Y.

F. Liu, W. Wei, and Z. Y. Zhang, “Motor rotation control method for rotation–modulation SINS,” Electric Machines Control 16(11), 17–21 (2012).

Am. J. Phys. (1)

W. H. Baird, “An Introduction to Inertial Navigation,” Am. J. Phys. 77(9), 844–847 (2009).

Appl. Opt. (1)

Autom. Instrum. (1)

J. Liu and W. Wang, “Motor control of self-calibration of rotation inertial navigation system,” Autom. Instrum. 18(1), 55–62 (2013).

Control Decis. (1)

L. Wang, W. Wang, X. Y. Wang, and G. L. Yang, “Design and implementation of digital position stabilization loop for fiber optic gyroscope based rotational inertial navigation system,” Control Decis. 464(1), 195–200 (2014).

Electric Machines Control (1)

F. Liu, W. Wei, and Z. Y. Zhang, “Motor rotation control method for rotation–modulation SINS,” Electric Machines Control 16(11), 17–21 (2012).

IEEE Sens. J. (2)

L. C. Wang, K. Li, J. Zhang, and Z. X. Ding, “Soft Fault Diagnosis and Recovery Method Based on Model Identification in Rotation FOG Inertial Navigation System,” IEEE Sens. J. 17(17), 5705–5716 (2017).

P. Y. Gao, K. Li, and L. Wang, “A Self-Calibration Method for Non-Orthogonal Angles of Gimbals in Tri-Axis Rotational Inertial Navigation System,” IEEE Sens. J. 16(24), 8998–9005 (2016).

J. Chin. Inertial Tech. (1)

J. N. Xu, F. Zha, J. S. Li, and H. Y. He, “Analysis and compensation for heading-coupling effect of single-axis rotating INS,” J. Chin. Inertial Tech. 21(1), 26–30 (2013).

J. Natl. University Defense Technol. (1)

L. D. Zhang, J. X. Lian, and X. P. Hu, “The Effect of Vehicle Angle Motion on Rotation Modulation Technology for Rotating INS,” J. Natl. University Defense Technol. 33(4), 152–156 (2011).

Math. Probl. Eng. (1)

K. Li, P. Y. Gao, L. Wang, and Q. Zhang, “Analysis and Improvement of Attitude Output Accuracy in Rotation Inertial Navigation System,” Math. Probl. Eng. 2015(1), 1–10 (2015).

Microsyst. Technol. (1)

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Figures (11)

Fig. 1
Fig. 1 Configuration of the SRAINS.
Fig. 2
Fig. 2 The control scheme diagram.
Fig. 3
Fig. 3 (a) Root locus of the control system with the different delay-time. (b) Step response of the control system with the different delay-time.
Fig. 4
Fig. 4 Configuration of the control system of the SRAINS.
Fig. 5
Fig. 5 Detailed implementation of the control system of the SRAINS.
Fig. 6
Fig. 6 Software flowchart of the control DSP. (a) Inquiry mode. (b) Interrupt mode.
Fig. 7
Fig. 7 (a) Attitude in the motion. (b) Motor control rotation velocities with the traditional and improved strategy.
Fig. 8
Fig. 8 (a) Control outputs with different control strategy. (b) Control outputs with different delay time. (c) Control outputs with different control strategy and different delay time.
Fig. 9
Fig. 9 The experimental equipment.
Fig. 10
Fig. 10 Performance verification of the control system of the SRAINS Control error with different implementation (b) Rotation/azimuth-insulation function verification.
Fig. 11
Fig. 11 Azimuth motion insulation effect verification. (a) Attitude of the vehicle test; (b) Attitude of the ship test; (c) Attitude of this test;(d) position errors in the east and north before and after the azimuth motion insulated.

Tables (1)

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Table 1 Parameters of the motor.

Equations (34)

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ϕ ˙ = ω i n n × ϕ + δ ω i n n C b 0 n C b b 0 [ ( δ K G + δ G ) ω i p p + ε ] ,
δ V ˙ n = f n × ϕ n + C b 0 n C b b 0 [ ( δ K A + δ A ) f b + ] + δ V n × ( 2 ω i e n + ω e n n ) + V n × ( 2 δ ω i e n + δ ω e n n ) + δ g n .
ϕ ˙ = ω i n n × ϕ + δ ω i n n C b 0 n C b b 0 C p b [ ( δ K G + δ G ) ω i p p + ε ] ,
δ V ˙ n = f n × ϕ n + C b 0 n C b b 0 C p b [ ( δ K A + δ A ) f p + ] + δ V n × ( 2 ω i e n + ω e n n ) + V n × ( 2 δ ω i e n + δ ω e n n ) + δ g n .
C p b = [ cos φ z sin φ z 0 sin φ z cos φ z 0 0 0 1 ] ,
{ ε X = ε x cos φ z ε y sin φ z ε Y = ε x sin φ z + ε y cos φ z ,
C b b 0 = [ cos ( Δ ψ ) sin ( Δ ψ ) 0 sin ( Δ ψ ) cos ( Δ ψ ) 0 0 0 1 ] ,
{ ε X = ε x cos ( Δ ψ + φ z ) ε y sin ( Δ ψ + φ z ) ε Y = ε x sin ( Δ ψ + φ z ) + ε y cos ( Δ ψ + φ z ) .
C b b 0 ( δ K G + δ G ) ω i p p C b b 0 ( δ K G + δ G ) ( C b p ω n b b + ω b p p ) = [ ( ω n b z b + ω c ) [ δ G 31 cos ( φ z ψ ) δ G 32 sin ( φ z ψ ) ] ( ω n b z b + ω c ) [ δ G 31 sin ( φ z ψ ) + δ G 32 cos ( φ z ψ ) ] ( ω n b z b + ω c ) δ K G z ] = [ [ δ G 31 ( sin ( ψ + φ z ) ) ' + δ G 32 ( cos ( ψ + φ z ) ) ' ] [ δ G 31 ( cos ( ψ + φ z ) ) ' + δ G 32 ( sin ( ψ + φ z ) ) ' ] ( ω n b z b + ω c ) δ K G z ] .
θ ( t ) = 0 t w ( τ ) d τ ,
E { w ( τ 1 ) w ( τ 2 ) } = { 0 , τ 1 = τ 2 K , τ 1 τ 2 .
σ ( t ) = E ( θ ( t ) ) 2 = E { 0 t w ( τ 1 ) d τ 1 0 t w ( τ 2 ) d τ 2 } = K t ,
{ Δ S E = R ε z sin L cos L ( t sin ω e t / ω e ) Δ S N = R ε z cos L ( 1 cos ω e t ) / ω e .
{ σ Δ S E 2 = R σ ε z 2 sin L cos L ( t sin ω e t / ω e ) σ Δ S N 2 = R σ ε z 2 cos L ( 1 cos ω e t ) / ω e .
E X = 0 2 π ε x cos φ z ε y sin φ z d t = ε x k = 1 N sin ( k Δ φ z ) sin [ ( k 1 ) Δ φ z ] ω k + ε y k = 1 N cos ( k Δ φ z ) cos [ ( k 1 ) Δ φ z ] ω k = ε x ( sin ( 2 π ) ω N sin 0 ω 1 ) ε x k = 1 N 1 sin ( k Δ φ z ) ( 1 ω k + 1 1 ω k ) + ε y ( cos ( 2 π ) ω N cos 0 ω 1 ) ε y k = 1 N 1 cos ( k Δ φ z ) ( 1 ω k + 1 1 ω k )
E X ε x k = 1 N 1 sin ( k Δ φ z ) ( 1 ω k + 1 1 ω k ) ε y k = 1 N 1 cos ( k Δ φ z ) ( 1 ω k + 1 1 ω k ) .
E Y ε x k = 1 N 1 cos ( k Δ φ z ) ( 1 ω k + 1 1 ω k ) ε y k = 1 N 1 sin ( k Δ φ z ) ( 1 ω k + 1 1 ω k ) .
Δ ϕ b = 1 ω c ( 0 2 π + α C p b ε d θ + α 2 π + β C p b ε d θ + β 0 C p b ε d θ ) ,
{ Δ ϕ X = 2 ω c [ ( sin α + sin β ) ε x + ( cos α cos β ) ε y ] Δ ϕ Y = 2 ω c [ ( cos α cos β ) ε x + ( sin α + sin β ) ε y ] .
G ( s ) = C m ( L s + R ) ( J s + B ) + C e C m ,
C 1 ( s ) = K p + K I s + K I I s 2 = 4.8 + 129 s + 860 s 2 ,
C ( s ) = C 1 ( s ) G ( s ) e τ s 1 + C 1 ( s ) G ( s ) e τ s .
ω n p n = ω n b n + ω b p n = C b n ( ω n b b + ω b p b ) ,
ω n b b = [ cos γ 0 sin γ cos θ 0 1 sin θ sin γ 0 cos γ cos θ ] [ θ ˙ γ ˙ ψ ˙ ] , ω b p b = [ 0 0 ω c ( t ) ] ,
ω n p z n = Ω .
Ω = C b n ( 3 , 1 ) ω n b x b + C b n ( 3 , 2 ) ω n b y b + C b n ( 3 , 3 ) ( ω n b z b + ω c ) ,
ω c = Ω C b n ( 3 , 1 ) ω n b x b + C b n ( 3 , 2 ) ω n b y b C b n ( 3 , 3 ) ω n b z b ,
C b n = [ cos γ cos ψ sin γ sin θ sin ψ cos θ sin ψ sin γ cos ψ + cos γ sin θ sin ψ cos γ sin ψ + sin γ sin θ cos ψ cos θ cos ψ sin γ sin ψ cos γ sin θ cos ψ sin γ sin θ sin θ cos γ cos θ ] .
ω c = Ω cos θ cos γ + sin γ ( tan θ 1 ) θ ˙ + tan θ cos γ γ ˙ + ( sin 2 γ cos γ sin θ sin 2 θ cos θ cos γ + cos θ cos γ ) ψ ˙ .
ω n p z p = ( ω n b z b + ω c ) .
ω c = Ω ω n b z b = Ω θ ˙ sin γ + cos γ cos θ ψ ˙ .
ω n p p = ω i p p C n p ( ω i e n + ω e n n ) ,
U C = K p Δ ω + K I Δ ω d t + K I I ( Δ ω d t ) d t ) ,
θ , γ , ψ = 1 n i = 1 n A i sin ( ω i t + φ i ) ,

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