Abstract

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

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References

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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]
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  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]

2012 (1)

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]

2011 (2)

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]

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]

2010 (1)

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]

2009 (1)

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]

2004 (1)

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]

2001 (2)

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]

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors J. 1, 332–339 (2001).
[CrossRef]

1997 (2)

Yu. V. Filatov, D. P. Loukianov, and R. Probst, “Angle measurement by laser goniometer,” Metrologia 34, 343–351 (1997).
[CrossRef]

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

1995 (1)

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]

1992 (1)

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]

1989 (1)

L. Pesquera, R. Blanco, and M. A. Rodriguez, “Statistical properties of gas ring lasers with backscattering,” Phys. Rev. A 39, 5777–5784 (1989).
[CrossRef]

1986 (1)

R. Christian and L. Mandel, “Frequency dependence of a ring laser with backscattering,” Phys. Rev. A 34, 3932–3939 (1986).
[CrossRef]

1973 (1)

L. N. Menegozzi and W. E. Lamb, “Theory of a ring laser,” Phys. Rev. A 8, 2103–2125 (1973).
[CrossRef]

1970 (1)

F. Aronowitz and R. J. Collins, “Lock-in and intensity-phase interaction in the ring laser,” J. Appl. Phys. 41, 130–141 (1970).
[CrossRef]

1966 (1)

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]

Allegrini, M.

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]

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]

Aronowitz, F.

F. Aronowitz and R. J. Collins, “Lock-in and intensity-phase interaction in the ring laser,” J. Appl. Phys. 41, 130–141 (1970).
[CrossRef]

F. Aronowitz, “Fundamentals of ring laser gyro,” in Optical Gyros and their Applications, RTO AGARDograph 339 (1999), pp. 23–30.

Barbour, N.

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors J. 1, 332–339 (2001).
[CrossRef]

Belfi, J.

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]

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]

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]

Beverini, N.

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]

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]

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]

Bilger, H. R.

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]

Blanco, R.

L. Pesquera, R. Blanco, and M. A. Rodriguez, “Statistical properties of gas ring lasers with backscattering,” Phys. Rev. A 39, 5777–5784 (1989).
[CrossRef]

Bosi, F.

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]

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]

Bouhadef, B.

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]

Carelli, G.

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]

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]

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]

Cella, G.

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]

Centeno Neelen, R.

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]

Cerdonio, M.

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]

Christian, R.

R. Christian and L. Mandel, “Frequency dependence of a ring laser with backscattering,” Phys. Rev. A 34, 3932–3939 (1986).
[CrossRef]

Collins, R. J.

F. Aronowitz and R. J. Collins, “Lock-in and intensity-phase interaction in the ring laser,” J. Appl. Phys. 41, 130–141 (1970).
[CrossRef]

Di Virgilio, A.

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]

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]

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]

Etrich, C.

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]

Ferrante, I.

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]

Filatov, Yu. V.

Yu. V. Filatov, D. P. Loukianov, and R. Probst, “Angle measurement by laser goniometer,” Metrologia 34, 343–351 (1997).
[CrossRef]

Flannery, B. P.

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).

Gebauer, A.

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]

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]

Goldstein, H.

H. Goldstein, Classical Mechanics (Addison-Wesley, 1980).

Hairer, E.

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration (Springer, 2006).

Hurst, R. B.

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]

Jaznmiski, A. H.

A. H. Jaznmiski, Stochastic Processes and Filtering Theory (Academic, 1970).

King, B. T.

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]

Klügel, T.

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]

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]

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]

Lamb, W. E.

L. N. Menegozzi and W. E. Lamb, “Theory of a ring laser,” Phys. Rev. A 8, 2103–2125 (1973).
[CrossRef]

Li, Z.

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]

Loukianov, D. P.

Yu. V. Filatov, D. P. Loukianov, and R. Probst, “Angle measurement by laser goniometer,” Metrologia 34, 343–351 (1997).
[CrossRef]

Lubich, C.

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration (Springer, 2006).

Maccioni, E.

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]

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]

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]

Mandel, L.

R. Christian and L. Mandel, “Frequency dependence of a ring laser with backscattering,” Phys. Rev. A 34, 3932–3939 (1986).
[CrossRef]

Mandel, P.

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]

Manolakis, D. G.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing (Macmillan, 1992).

McGregor, A. D.

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]

McLeod, D. P.

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]

Menegozzi, L. N.

L. N. Menegozzi and W. E. Lamb, “Theory of a ring laser,” Phys. Rev. A 8, 2103–2125 (1973).
[CrossRef]

Ortolan, A.

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]

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]

Passaquieti, R.

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]

Pesquera, L.

L. Pesquera, R. Blanco, and M. A. Rodriguez, “Statistical properties of gas ring lasers with backscattering,” Phys. Rev. A 39, 5777–5784 (1989).
[CrossRef]

Pizzocaro, M.

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]

Porzio, A.

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]

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]

Press, W. H.

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).

Proakis, J. G.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing (Macmillan, 1992).

Probst, R.

Yu. V. Filatov, D. P. Loukianov, and R. Probst, “Angle measurement by laser goniometer,” Metrologia 34, 343–351 (1997).
[CrossRef]

Rodriguez, M. A.

L. Pesquera, R. Blanco, and M. A. Rodriguez, “Statistical properties of gas ring lasers with backscattering,” Phys. Rev. A 39, 5777–5784 (1989).
[CrossRef]

Rothacher, M.

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]

Rowe, C. H.

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]

Ruggiero, M. L.

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]

Schlüter, W.

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]

Schmidt, G.

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors J. 1, 332–339 (2001).
[CrossRef]

Schreiber, K. U.

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]

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]

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]

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]

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]

Schreiber, U.

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]

Smith, P. W.

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]

Solimeno, S.

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]

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]

Sorrentino, F.

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]

Spreeuw, R. J. C.

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]

Stedman, G. E.

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]

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]

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]

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

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]

Stefani, F.

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]

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]

Tartaglia, A.

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]

Teukolsky, S. A.

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).

Velikoseltsev, A.

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]

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]

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.

Vetterling, W. T.

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).

Wanner, G.

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration (Springer, 2006).

Webb, T. H.

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]

Wells, J.-P. R.

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]

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]

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]

Wiltshire, D. L.

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]

Woerdman, J. P.

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]

Zendri, J. P.

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]

Appl. Phys. B (1)

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]

Class. Quantum Grav. (1)

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]

Fluct. Noise Lett. (1)

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]

IEEE Sensors J. (1)

N. Barbour and G. Schmidt, “Inertial sensor technology trends,” IEEE Sensors J. 1, 332–339 (2001).
[CrossRef]

J. Appl. Phys. (2)

F. Aronowitz and R. J. Collins, “Lock-in and intensity-phase interaction in the ring laser,” J. Appl. Phys. 41, 130–141 (1970).
[CrossRef]

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]

J. Geophys. Res. (1)

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]

Metrologia (1)

Yu. V. Filatov, D. P. Loukianov, and R. Probst, “Angle measurement by laser goniometer,” Metrologia 34, 343–351 (1997).
[CrossRef]

Phys. Rev. A (5)

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]

R. Christian and L. Mandel, “Frequency dependence of a ring laser with backscattering,” Phys. Rev. A 34, 3932–3939 (1986).
[CrossRef]

L. Pesquera, R. Blanco, and M. A. Rodriguez, “Statistical properties of gas ring lasers with backscattering,” Phys. Rev. A 39, 5777–5784 (1989).
[CrossRef]

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]

L. N. Menegozzi and W. E. Lamb, “Theory of a ring laser,” Phys. Rev. A 8, 2103–2125 (1973).
[CrossRef]

Phys. Rev. D (1)

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]

Phys. Rev. Lett. (1)

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]

Pure Appl. Geophys. (1)

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]

Rep. Prog. Phys. (1)

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[CrossRef]

Other (8)

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.

A. H. Jaznmiski, Stochastic Processes and Filtering Theory (Academic, 1970).

H. Goldstein, Classical Mechanics (Addison-Wesley, 1980).

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.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing (Macmillan, 1992).

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).

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration (Springer, 2006).

F. Aronowitz, “Fundamentals of ring laser gyro,” in Optical Gyros and their Applications, RTO AGARDograph 339 (1999), pp. 23–30.

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Figures (11)

Fig. 1.
Fig. 1.

Simulated Allan deviations of the estimated rotation rate. See the text for details.

Fig. 2.
Fig. 2.

G-Pisa experimental setup. The cavity vacuum chamber is entirely filled with a mixture of He–Ne and does not contain any intracavity element except for the four mirrors. S{n}, Sagnac interference signal; I1{n}, counterclockwise single beam intensity; I2{n}, clockwise single beam intensity; IB, optical beat intensity; RFD, radio frequency discharge; IBS, intensity beam splitter; HW, half-wave plate; PZT, piezoelectric transducer.

Fig. 3.
Fig. 3.

Schematic of the parameter estimation procedure. LP, lowpass Butterworth filter; BP, bandpass Butterworth filter; ZD, zoom and decimation routine; HT, Hilbert transform (see text).

Fig. 4.
Fig. 4.

Histograms of the relative errors (α^1,2α1,2)/α1,2 that affect the estimation of gain minus losses parameters calculated with 2×104 realizations of the ring-laser dynamics. (a) Histogram relative to α1: mean 1.4×103 and standard deviation 2.9×103 and (b) histogram relative to α2: mean 2.5×104 and standard deviation 3.9×103.

Fig. 5.
Fig. 5.

Histograms of the relative errors (r^1,2r1,2)/r1,2 that affect the estimation of backscattering coefficients calculated with 2×104 realizations of the ring-laser dynamics. (a) Histogram relative to r1: mean 1.1×103 and standard deviation 4.6×103 and (b) histogram relative to r2: mean 1.3×103 and standard deviation 3.2×103.

Fig. 6.
Fig. 6.

Histogram of the absolute errors ε^ε that affect the estimation of backscattering phase calculated with 2×104 realizations of the ring-laser dynamics; mean 4.3×104rad and standard deviation 2.8×103rad.

Fig. 7.
Fig. 7.

Allan standard deviation of the rotation rate estimated by AR(2) method (circles) and EKF (open diamonds) using 2×104s of the Monte Carlo simulation with random walk of Lamb parameters. For comparison, we also plot the Allan standard deviation of the simulated rotational drift (open triangles), and the Allan standard deviation of the EKF estimation after the subtraction of the rotational drift (dash dotted line).

Fig. 8.
Fig. 8.

EKF estimation of I1(n), I2(n), and sinψ(n). Circles: G-Pisa raw data sampled at 5 kHz. Continuous line: filter output.

Fig. 9.
Fig. 9.

Time series of α1,2, r1,2, and ε and of β, respectively estimated and calibrated using 6 h of experimental data of G-Pisa.

Fig. 10.
Fig. 10.

Power spectrum of the interferogram data around the Sagnac frequency 107.3Hz.

Fig. 11.
Fig. 11.

Allan standard deviation of the rotation rate estimated by AR(2) method (circles) and EKF (open diamonds) using 2×104s of experimental data of G-Pisa.

Tables (3)

Tables Icon

Table 1. Main Nominal Characteristics of the “G-Pisa” Apparatusa

Tables Icon

Table 2. Typical Values of Lamb Parameters Used in the Simulations of G-Pisa Dynamics with G3·105a

Tables Icon

Table 3. G-Pisa Laser Parameters

Equations (24)

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

νs=4AλLn·Ω,
I˙1=cL[α1I1β1I12θ12I1I2+2r2I1I2cos(ψ+ε)],I˙2=cL[α2I2β2I22θ21I1I2+2r1I1I2cos(ψε)],ψ˙=ωs+σ2σ1+τ21I1τ12I2cL[r1I1I2sin(ψε)+r2I2I1sin(ψ+ε)],
ψ˙=ωscL[r1ksin(ψε)+r2ksin(ψ+ε)],
ψ(t)=2arctan[ΩL1+Ωptan(12Ωpt)ωs+ΩL2],
ω(t)ωsΩL2cosωstΩL1sinωst=ωs+ωBS(t),
I˙1=cL[α1I1βI12+2r2I1I2cos(ψ+ε)],I˙2=cL[α2I2βI22+2r1I1I2cos(ψε)],ψ˙=ωscL[r1I1I2sin(ψε)+r2I2I1sin(ψ+ε)].
{I1(t)=α1βI2(t)=α2βψ(t)=ωst,
{I1(λ,t)=k=0λkk!I1(k)(t)I2(λ,t)=k=0λkk!I2(k)(t)Ψ(λ,t)=k=0λkk!ψ(k)(t).
{I1(t)α1β+2r2α1α2α1cos(ε+ωst)+(ωsc/L)sin(ε+ωst)β(α12+(ωsc/L)2)2r1r2(c/L)βωssin(2ε)I2(t)α2β+2r1α1α2α2cos(εωst)(ωsc/L)sin(εωst)β(α12+(ωsc/L)2)+2r1r2(c/L)βωssin(2ε)Ψ(t)(ωs2r1r2(c/L)2cos(2ε)ωs)t+(c/L)r1α1α2cos(εωst)+r2α2α1cos(ε+ωst)ωs,
{I1(t)=I1+i1sin(ωt+ϕ1)I2(t)=I2+i2sin(ωt+ϕ2)Ψ(t)=ωt,
{ϕ1=εϕ2=ε.
ε^=ϕ1ϕ22,
Λ(α1,α2,r1,r2)=2πω02π/ω{I˙1cL[α1I1βI12+2r2I1I2cos(ωt+ε^)]}2+{I˙2cL[α2I2βI22+2r1I1I2cos(ωtε^)]}2dt,
α^1=β(I1+i124I1)+i1i2ω4(c/L)I2sin2ε^,
α^2=β(I2+i224I2)i1i2ω4(c/L)I1sin2ε^,
r^1=i2ω2(c/L)I1I2,
r^2=i1ω2(c/L)I1I2,
ω^BS=cL[r^1I^1I^2sin(ψ^ε^)+r^2I^2I^1sin(ψ^+ε^)],
I1,2(t)=cLambV1,2(t)GphaeffcLambPout1,2,
I1,2=|μab|2(γa+γb)42γaγbγabE1,22=|μab|2(γa+γb)42γaγbγab·Pout1,22cϵ0sbTcLambPout1,2,
μab=πϵ0λ3(2π)3Aik
Z(ξ1,2)=2i0ex22ηx2iξ1,2xdx,
ZI(ξ)πeξ22η,ZR(ξ)2ξeξ2,
α1,2=GZI(0)[kZI(ξ1,2)+kZI(ξ1,2)]μ1,2,β1,2=α1,2+μ1,2,σ1,2=f02GZI(0)[kZR(ξ1,2)+kZR(ξ1,2)],θ12=ΓGZI(0)[kZI(ξ1,2)1+(ξm/η)2+kZI(ξ1,2)1+(ξm/η)2],τ12=Γf02GZI(0)[kZI(ξ1,2)ξm/η1+(ξm/η)2+kZI(ξ1,2)ξm/η1+(ξm/η)2],

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