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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 31 — Nov. 1, 2012
  • pp: 7518–7528

Compensation of the laser parameter fluctuations in large ring-laser gyros: a Kalman filter approach

Alessandro Beghi, Jacopo Belfi, Nicolò Beverini, B. Bouhadef, D. Cuccato, Angela Di Virgilio, and Antonello Ortolan  »View Author Affiliations

Applied Optics, Vol. 51, Issue 31, pp. 7518-7528 (2012)

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He–Ne ring-laser gyroscopes are, at present, the most precise devices for absolute angular velocity measurements. Limitations to their performance come from the nonlinear dynamics of the laser. Following Lamb semiclassical theory, we find a set of critical parameters affecting the time stability of the system. We propose a method for estimating the long-term drift of the laser parameters and for filtering out the laser dynamics effects from the rotation measurement. The parameter estimation procedure, based on the perturbative solutions of the laser dynamics, allows us to apply Kalman filter theory for the estimation of the angular velocity. Results of a comprehensive Monte Carlo simulation and results of a preliminary analysis on experimental data from the ring-laser prototype G-Pisa are shown and discussed.

© 2012 Optical Society of America

OCIS Codes
(120.5790) Instrumentation, measurement, and metrology : Sagnac effect
(140.1340) Lasers and laser optics : Atomic gas lasers
(140.3370) Lasers and laser optics : Laser gyroscopes

ToC Category:
Lasers and Laser Optics

Original Manuscript: August 7, 2012
Revised Manuscript: September 20, 2012
Manuscript Accepted: September 24, 2012
Published: October 23, 2012

Alessandro Beghi, Jacopo Belfi, Nicolò Beverini, B. Bouhadef, D. Cuccato, Angela Di Virgilio, and Antonello Ortolan, "Compensation of the laser parameter fluctuations in large ring-laser gyros: a Kalman filter approach," Appl. Opt. 51, 7518-7528 (2012)

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  1. N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors J. 1, 332–339 (2001). [CrossRef]
  2. Yu. V. Filatov, D. P. Loukianov, and R. Probst, “Angle measurement by laser goniometer,” Metrologia 34, 343–351 (1997). [CrossRef]
  3. K. U. Schreiber, A. Velikoseltsev, M. Rothacher, T. Klügel, G. E. Stedman, and D. L. Wiltshire, “Direct measurement of diurnal polar motion by ring laser gyroscopes,” J. Geophys. Res. 109, B06405 (2004). [CrossRef]
  4. K. U. Schreiber, T. Klügel, J.-P. R. Wells, R. B. Hurst, and A. Gebauer, “How to detect the Chandler and the annual wobble of the earth with a large ring laser gyroscope,” Phys. Rev. Lett. 107, 173904 (2011). [CrossRef]
  5. G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997). [CrossRef]
  6. J. Belfi, N. Beverini, F. Bosi, G. Carelli, A. Di Virgilio, E. Maccioni, A. Ortolan, and F. Stefani, “A 1.82  m2 ring laser gyroscope for nano-rotational motion sensing,” Appl. Phys. B 106, 271–281 (2012). [CrossRef]
  7. A. Di Virgilio, M. Allegrini, J. Belfi, N. Beverini, F. Bosi, G. Carelli, E. Maccioni, M. Pizzocaro, A. Porzio, U. Schreiber, S. Solimeno, and F. Sorrentino, “Performances of ‘G-Pisa’: a middle size gyrolaser,” Class. Quantum Grav. 27, 084033 (2010). [CrossRef]
  8. G. Cella, A. Di Virgilio, A. Ortolan, A. Porzio, S. Solimeno, M. Cerdonio, J. P. Zendri, M. Allegrini, N. Beverini, J. Belfi, B. Bouhadef, G. Carelli, I. Ferrante, E. Maccioni, R. Passaquieti, F. Stefani, M. L. Ruggiero, A. Tartaglia, K. U. Schreiber, A. Gebauer, and J.-P. R. Wells, “Measuring gravito-magnetic effects by multi ring-laser gyroscope,” Phys. Rev. D 84, 122002(2011). [CrossRef]
  9. A. Velikoseltsev, “The development of a sensor model for large ring lasers and their application in seismic studies,” Ph.D. thesis (Technische Universität München, 2005) and references therein.
  10. A. H. Jaznmiski, Stochastic Processes and Filtering Theory (Academic, 1970).
  11. L. N. Menegozzi and W. E. Lamb, “Theory of a ring laser,” Phys. Rev. A 8, 2103–2125 (1973). [CrossRef]
  12. F. Aronowitz, “Fundamentals of ring laser gyro,” in Optical Gyros and their Applications, RTO AGARDograph 339 (1999), pp. 23–30.
  13. F. Aronowitz and R. J. Collins, “Lock-in and intensity-phase interaction in the ring laser,” J. Appl. Phys. 41, 130–141 (1970). [CrossRef]
  14. G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, and H. R. Bilger, “Harmonic analysis in a precision ring laser with back-scatter induced pulling,” Phys. Rev. A 51, 4944–4958 (1995). [CrossRef]
  15. R. Christian and L. Mandel, “Frequency dependence of a ring laser with backscattering,” Phys. Rev. A 34, 3932–3939 (1986). [CrossRef]
  16. L. Pesquera, R. Blanco, and M. A. Rodriguez, “Statistical properties of gas ring lasers with backscattering,” Phys. Rev. A 39, 5777–5784 (1989). [CrossRef]
  17. C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, and J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992). [CrossRef]
  18. D. P. McLeod, B. T. King, G. E. Stedman, T. H. Webb, and K. U. Schreiber, “Autoregressive analysis for the detection of earthquakes with a ring laser gyroscope,” Fluct. Noise Lett. 1, R41–R50 (2001). [CrossRef]
  19. H. Goldstein, Classical Mechanics (Addison-Wesley, 1980).
  20. By definition, the interferogram of the two counterpropagating beams is given by S(t)=I1(t)+I2(t)−2I1(t)I2(t) sin(ψ(t)). However, to estimate sin(ψ(t)) directly from S(t), the linear trend I1(t)+I2(t) is removed, and the energy I1(t)I2(t) is normalized to 1 over time intervals that usually correspond to thousands of cycles.
  21. J. G. Proakis and D. G. Manolakis, Digital Signal Processing (Macmillan, 1992).
  22. K. U. Schreiber, T. Klügel, A. Velikoseltsev, W. Schlüter, G. E. Stedman, and J.-P. R. Wells, “The large ring laser G for continuous Earth rotation monitoring,” Pure Appl. Geophys. 166, 1485–1498 (2009). [CrossRef]
  23. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition, The Art of Scientific Computing (Cambridge University, 2007).
  24. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration (Springer, 2006).
  25. P. W. Smith, “Linewidth and saturation parameters for the 6328 Å transition in a He-Ne laser,” J. Appl. Phys. 37, 2089–2093 (1966). [CrossRef]

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