Abstract
As a precision goniometer, photoelectric encoder plays an important role in rotational inertial navigation system (RINS). The encoder is used to measure the rotate angle of rotating mechanism for attitude calculation and feedback of motor control. However, the experiment shows that there are position-related errors in the encoder output, so calibration is necessary in high precision applications. This paper presents a calibration method designed by the characteristics of encoder errors and the structure of a tri-axis RINS. In RINS, the gyro sensitive axis can be coincided with the motor axis by gimbals rotation, and then the gyro and the photoelectric encoder measure the same angle, so the error can be calculated as the difference between the encoder output and the integral of gyro output. The error will be analyzed through Fourier method, then the error will be fitted by least squares method and a harmonic model will be established. The verification experiments demonstrate that the angle measurement error is reduced from ± 40″ to ± 2″, and the attitude output error drops 75″. The calibration method is proved to be experimentally effective.
Similar content being viewed by others
References
Chamoun JN, Digonnet MJF (2015) Noise and bias error due to polarization coupling in a fiber optic gyroscope. J Lightwave Technol 33(13):2839–2847
Deng Z, Sun M, Wang B (2014) Error modulation scheme analysis of dual-axis rotating strap-down inertial navigation system based on FOG. In: Proceedings of the 33rd Chinese Control Conference (CCC’14) , pp 692–696, Nanjing, China
Filator YV, Agapov MY, Bournachev MN, Loukianov DP, Pavlov PA (2003) Laser goniometer systems for dynamic calibration of optical encoders. Proc SPIE 5144:381–390
Geller ES (1968) Inertial system platform rotation. IEEE Trans Aerospace Electron Sys AES-4(4):557–568
Gerberding O, Cervantes FG, Melcher J, Pratt JR, Taylor JM (2015) Opt-mechanical reference accelerometer. Metrologia 52(5):654–665
Hai YU, Qiuhua WAN, Shujie WANG, Xinran LU, Yingcai DU (2015) High-precision real-time angle reference in dynamic measurement of photoelectric encoder. Chin Opt 8(3):447–455
Hong LI, You FC, Hui DL (2005) Dynamic evaluation method for interpolation errors in photoelectric encoder. J Translocat Technol 18(4):927–930
Huang Z, Qin S, Wang X et al (2007a) Error analysis of optical angular encoder and its calibration with ring laser gyro. Chin J Sci Instrum 10:27
Huang Z, Qin S, Wang X et al (2007b) Error analysis of optical angular encoder and its calibration with ring laser gyro. Chin J Sci Instrum 28:1866
Jianhua C, Mingyue L, Daidai C, Li C, Junyu S (2011) Research of strapdown inertial navigation system monitor technique based on dual-axis consequential rotation. In: Proceedings of the International Conference on Information and Automation (ICIA’11), pp 203–208
Johnson N, Mohan KJ, Janson KE et al (2013) Optimization of incremental optical encoder pulse processing. In: IEEE international mutli-conference on automation, computing, communication, control and compressed sensing (iMac4s), pp 769–773
Li K, Gao P, Wang L et al (2015) Analysis and improvement of attitude output accuracy in rotation inertial navigation system. Math Probl Eng 2015(1):1–10
Lu, Li X, Feng H et al (2005) A simulated evaluation method for interpolation errors in photoelectric encoder. Control Autom 21(10-1):109–110
Morrow Jr RB, Heckman DW (1998) High precision IFOG insertion into the strategic submarine navigation system. In Proceedings of the IEEE Position Location and Navigation Symposium, pp 332–338, IEEE, Palm Springs, Calif, USA
Qin S, Huang Z, Wang X (2010) Optical angular encoder installation error measurement and calibration by ring laser gyroscope. IEEE Trans Instrum Meas 59(3):506–511
Ren Q, Wang B, Deng Z et al (2014) A multi-position self-calibration method for dual-axis rotational inertial navigation system. Sens Actuators A Phys 219:24–31
Savage PG (2013) Blazing gyros: the evolution of strap-down inertial navigation technology for aircraft. J Guid Control Dyn 36(3):637–655
Stockton JK, Takase K, Kasevich MA (2011) Absolute geodetic rotation measurement using atom interferometry. Phys Rev Lett 107(13):133001
Su D, Xu Z, Jia J, Liu B, Li D (2013) Read-head design for improving the precision of circular grating angular measuring system. J Electron Meas Instrum 27(7):653–657
Sun W, Wang D, Xu L, Xu L (2013) MEMS-based rotary strap-down inertial navigation system. Measurement 46(8):2585–2596
Waldmann J, Silva RIG, Chagas RAJ (2016) Observability analysis of inertial navigation errors from optical flow subspace constraint. Inf Sci 327:300–326
Wang XJ (2012) Errors and precision analysis of subdivision signals for photoelectric angle encoders. Opt Precis Eng 20(2):379–386
Wang C, Zhang G, Guo S, Jiang J (1996) Auto correction of interpolation errors in optical encoders. Proc SPIE 2718:439–447
Wang X, Wu J, Xu T, Wang W (2013) Analysis and verification of rotation modulation effects on inertial navigation system based on MEMS sensors. J Navig 66(5):751–772
Wang L, Wang W, Zhang Q, Gao P (2014) Self-calibration method based on navigation in high-precision inertial navigation system with fiber optic gyro. Opt Eng 53(6):064103
Wang Z, Zhao H, Qiu S et al (2015) Stance-phase detection for ZUPT-aided foot-mounted pedestrian navigation system. IEEE/ASME Trans Mechatron 20(6):3170–3181
Wu Z, Hu X, Wu M, Mu H, Cao J, Zhang K, Tuo Z (2013) An experimental evaluation of autonomous underwater vehicle localization on geomagnetic map. Appl Phys Lett 103(10):104102
Ying S, Wan QH, Wang SJ et al (2010) Design of signal process system for spaceborne photoelectric encoder. Opt Precis Eng 18(5):1182–1188
Yuan B, Liao D, Han S (2012) Error compensation of an optical gyro INS by multi-axis rotation. Meas Sci Technol 23(2):025102
Zhang Q, Wang L, Liu Z, Feng P (2015) An accurate calibration method based on velocity in a rotational inertial navigation system. Sens (Basel) 15(8):18443–18458
Zheng Z, Han S, Zheng K (2015) An eight-position self-calibration method for a dual-axis rotational inertial navigation system. Sens Actuator A Phys 232:39–48
Acknowledgements
This work was supported by the Aeronautical Science Foundation of China (Grant No. 20175851030).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lu, L., Wang, L., Wang, W. et al. A self-calibration method for error of photoelectric encoder based on gyro in rotational inertial navigation system. Microsyst Technol 25, 2145–2152 (2019). https://doi.org/10.1007/s00542-018-4139-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-018-4139-0