Abstract

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).

© 2014 Optical Society of America

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    [Crossref]
  29. S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
    [Crossref]
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  31. G. Evensen, “The ensemble Kalman filter: theoretical formulation and practical implementation,” Ocean Dynamics 53, 343–367 (2003).
    [Crossref]
  32. C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review 129, 420–436 (2001).
    [Crossref]
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    [Crossref]
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    [Crossref]
  35. P. Sakov and P. R. Oke, “Implications of the form of the ensemble transformation in the ensemble square root filters,” Monthly Weather Review 136, 1042–1053 (2008).
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  36. M. Bocquet, “Ensemble Kalman filtering without the intrinsic need for inflation,” Nonlinear Processes in Geophysics 18, 735–750 (2011).
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  39. R. Conan and C. Correia, “Object-oriented matlab adaptive optics,” Proc. SPIE 9148, 91486C (2014).
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  41. D. Gratadour, “COMPASS: an efficient, scalable and versatile numerical platform for the development of ELT AO systems,” Proc. SPIE 9148, 91486O (2014).
  42. M. Bocquet and P. Sakov, “Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems,” Nonlinear Processes in Geophysics 19, 383–399 (2012).
    [Crossref]
  43. P. Sakov, G. Evensen, and L. Bertino, “Asynchronous data assimilation with the EnKF,” Tellus 62A, 24–29 (2010).
    [Crossref]

2014 (2)

R. Conan and C. Correia, “Object-oriented matlab adaptive optics,” Proc. SPIE 9148, 91486C (2014).

D. Gratadour, “COMPASS: an efficient, scalable and versatile numerical platform for the development of ELT AO systems,” Proc. SPIE 9148, 91486O (2014).

2013 (2)

2012 (6)

M. Bocquet and P. Sakov, “Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems,” Nonlinear Processes in Geophysics 19, 383–399 (2012).
[Crossref]

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

L. Stepp, “Thirty Meter Telescope project update,” Proc. SPIE 8444, 84441G (2012).
[Crossref]

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

M. Gray and B. Le Roux, “ETKF, a non-stationary control law for complex adaptive optics systems on ELTs: theoretical aspects and first simulation results,” Proc. SPIE 8447, 84471T (2012).
[Crossref]

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt. 51, 4520–4535 (2012).
[Crossref] [PubMed]

2011 (2)

M. Bocquet, “Ensemble Kalman filtering without the intrinsic need for inflation,” Nonlinear Processes in Geophysics 18, 735–750 (2011).
[Crossref]

P. Massioni, C. Kulcsár, H.-F. Raynaud, and J.-M. Conan, “Fast computation of an optimal controller for large-scale adaptive optics,” J. Opt. Soc. Am. A 28, 2298–2309 (2011).
[Crossref]

2010 (5)

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

P. Sakov and L. Bertino, “Relation between two common localisation methods for the EnKF,” Computational Geoscience 15, 225–237 (2010).
[Crossref]

P. Sakov, G. Evensen, and L. Bertino, “Asynchronous data assimilation with the EnKF,” Tellus 62A, 24–29 (2010).
[Crossref]

S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
[Crossref]

2009 (2)

2008 (4)

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[Crossref] [PubMed]

P. Sakov and P. R. Oke, “Implications of the form of the ensemble transformation in the ensemble square root filters,” Monthly Weather Review 136, 1042–1053 (2008).
[Crossref]

C. Correia, C. Kulcsár, J.-M. Conan, and H.-F. Raynaud, “Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics,” Proc. SPIE 7015, 701551 (2008).
[Crossref]

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

2007 (3)

2006 (1)

2005 (1)

2004 (2)

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

2003 (2)

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

G. Evensen, “The ensemble Kalman filter: theoretical formulation and practical implementation,” Ocean Dynamics 53, 343–367 (2003).
[Crossref]

2002 (1)

2001 (1)

C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review 129, 420–436 (2001).
[Crossref]

1998 (1)

G. Burgers, P. J. V. Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review 126, 1719–1724 (1998).
[Crossref]

1993 (1)

1974 (1)

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence, and separation in stochastic control,” Automatic Control, IEEE Transactions on 19, 494–500 (1974).
[Crossref]

Anderson, D. J.

Anderson, J. L.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

Bar-Shalom, Y.

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence, and separation in stochastic control,” Automatic Control, IEEE Transactions on 19, 494–500 (1974).
[Crossref]

Basden, A.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Bertino, L.

P. Sakov, G. Evensen, and L. Bertino, “Asynchronous data assimilation with the EnKF,” Tellus 62A, 24–29 (2010).
[Crossref]

P. Sakov and L. Bertino, “Relation between two common localisation methods for the EnKF,” Computational Geoscience 15, 225–237 (2010).
[Crossref]

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

Bishop, C. H.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review 129, 420–436 (2001).
[Crossref]

Bocquet, M.

M. Bocquet and P. Sakov, “Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems,” Nonlinear Processes in Geophysics 19, 383–399 (2012).
[Crossref]

M. Bocquet, “Ensemble Kalman filtering without the intrinsic need for inflation,” Nonlinear Processes in Geophysics 18, 735–750 (2011).
[Crossref]

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

Bouchez, A.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Brase, J. M.

Brunetto, E.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Burgers, G.

G. Burgers, P. J. V. Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review 126, 1719–1724 (1998).
[Crossref]

Cassali, M.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Conan, J.-M.

P. Massioni, C. Kulcsár, H.-F. Raynaud, and J.-M. Conan, “Fast computation of an optimal controller for large-scale adaptive optics,” J. Opt. Soc. Am. A 28, 2298–2309 (2011).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “LQG control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[Crossref] [PubMed]

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

C. Correia, C. Kulcsár, J.-M. Conan, and H.-F. Raynaud, “Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics,” Proc. SPIE 7015, 701551 (2008).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[Crossref] [PubMed]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” in Proc. of the first AO4ELT conference (2010), p. 07003.

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation ?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (Optical Society of America, 2007), p. PMA1.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Conan, R.

R. Conan and C. Correia, “Object-oriented matlab adaptive optics,” Proc. SPIE 9148, 91486C (2014).

Corazza, M.

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Correia, C.

R. Conan and C. Correia, “Object-oriented matlab adaptive optics,” Proc. SPIE 9148, 91486C (2014).

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010).
[Crossref]

C. Correia, C. Kulcsár, J.-M. Conan, and H.-F. Raynaud, “Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics,” Proc. SPIE 7015, 701551 (2008).
[Crossref]

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” in Proc. of the first AO4ELT conference (2010), p. 07003.

Costille, A.

de Lesegno, P. V.

Dierickx, P.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Dipper, N.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Ellerbroek, B.

Etherton, B. J.

C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review 129, 420–436 (2001).
[Crossref]

Evensen, G.

P. Sakov, G. Evensen, and L. Bertino, “Asynchronous data assimilation with the EnKF,” Tellus 62A, 24–29 (2010).
[Crossref]

G. Evensen, “The ensemble Kalman filter: theoretical formulation and practical implementation,” Ocean Dynamics 53, 343–367 (2003).
[Crossref]

G. Burgers, P. J. V. Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review 126, 1719–1724 (1998).
[Crossref]

Farahani, A.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
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Fedrigo, E.

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

Filgueira, J.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Fusco, T.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[Crossref] [PubMed]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

Gavel, D. T.

Gendron, E.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Gilles, L.

Gratadour, D.

D. Gratadour, “COMPASS: an efficient, scalable and versatile numerical platform for the development of ELT AO systems,” Proc. SPIE 9148, 91486O (2014).

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Gray, M.

M. Gray and B. Le Roux, “ETKF, a non-stationary control law for complex adaptive optics systems on ELTs: theoretical aspects and first simulation results,” Proc. SPIE 8447, 84471T (2012).
[Crossref]

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

Guesalaga, A.

Guzman, D.

Hamill, T. M.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

Hubert, Z.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Hunt, B. R.

B. R. Hunt, E. J. Kostelich, and I. Szunyogh, “Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter,” Physica D 230, 112–126 (2007).
[Crossref]

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Jacoby, G.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Johns, M.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Kalnay, E.

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Kissler-Patig, M.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Kostelich, E. J.

B. R. Hunt, E. J. Kostelich, and I. Szunyogh, “Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter,” Physica D 230, 112–126 (2007).
[Crossref]

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Kulcsar, C.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
[Crossref]

Kulcsár, C.

L. Gilles, P. Massioni, C. Kulcsár, H.-F. Raynaud, and B. Ellerbroek, “Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes,” J. Opt. Soc. Am. A 30, 898–909 (2013).
[Crossref]

P. Massioni, C. Kulcsár, H.-F. Raynaud, and J.-M. Conan, “Fast computation of an optimal controller for large-scale adaptive optics,” J. Opt. Soc. Am. A 28, 2298–2309 (2011).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “LQG control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[Crossref] [PubMed]

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

C. Correia, C. Kulcsár, J.-M. Conan, and H.-F. Raynaud, “Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics,” Proc. SPIE 7015, 701551 (2008).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[Crossref] [PubMed]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” in Proc. of the first AO4ELT conference (2010), p. 07003.

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation ?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (Optical Society of America, 2007), p. PMA1.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Le Gland, F.

F. Le Gland, V. Monbet, and V. D. Tran, Large Sample Asymptotics for the Ensemble Kalman Filter (Oxford University Press, Oxford, 2011), pp. 598–631.

Le Roux, B.

M. Gray and B. Le Roux, “ETKF, a non-stationary control law for complex adaptive optics systems on ELTs: theoretical aspects and first simulation results,” Proc. SPIE 8447, 84471T (2012).
[Crossref]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

Leeuwen, P. J. V.

G. Burgers, P. J. V. Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review 126, 1719–1724 (1998).
[Crossref]

Looze, D. P.

Macintosh, B. A.

Majumdar, S. J.

C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review 129, 420–436 (2001).
[Crossref]

Martin, O.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Massioni, P.

McCarthy, P.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

McPherson, A.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Meimon, S.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
[Crossref]

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Monbet, V.

F. Le Gland, V. Monbet, and V. D. Tran, Large Sample Asymptotics for the Ensemble Kalman Filter (Oxford University Press, Oxford, 2011), pp. 598–631.

Morris, T.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Mugnier, L. M.

Myers, R.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Neichel, B.

O’Neal, J.

Oke, P. R.

P. Sakov and P. R. Oke, “Implications of the form of the ensemble transformation in the ensemble square root filters,” Monthly Weather Review 136, 1042–1053 (2008).
[Crossref]

Osborn, J.

Ott, E.

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Parisot, A.

A. Parisot, “Calibrations et stratégies de commande tomographiques pour les optiques adaptatives grand champ: validations expérimentales sur le banc Homer,” PhD Thesis, Aix-Marseille University (2012).

Paschall, R. N.

Patil, D.

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Petit, C.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “LQG control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[Crossref] [PubMed]

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[Crossref] [PubMed]

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” in Proc. of the first AO4ELT conference (2010), p. 07003.

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation ?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (Optical Society of America, 2007), p. PMA1.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Piatrou, P.

Poyneer, L. A.

Ramsay, S.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Raybould, K.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Raynaud, H.-F.

L. Gilles, P. Massioni, C. Kulcsár, H.-F. Raynaud, and B. Ellerbroek, “Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes,” J. Opt. Soc. Am. A 30, 898–909 (2013).
[Crossref]

P. Massioni, C. Kulcsár, H.-F. Raynaud, and J.-M. Conan, “Fast computation of an optimal controller for large-scale adaptive optics,” J. Opt. Soc. Am. A 28, 2298–2309 (2011).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “LQG control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “First laboratory validation of vibration filtering with LQG control law for adaptive optics,” Opt. Express 16, 87–97 (2008).
[Crossref] [PubMed]

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

C. Correia, C. Kulcsár, J.-M. Conan, and H.-F. Raynaud, “Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics,” Proc. SPIE 7015, 701551 (2008).
[Crossref]

C. Kulcsár, H.-F. Raynaud, C. Petit, J.-M. Conan, and P. V. de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express 14, 7464–7476 (2006).
[Crossref] [PubMed]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” in Proc. of the first AO4ELT conference (2010), p. 07003.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation ?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (Optical Society of America, 2007), p. PMA1.

Rigaut, F.

Rodionov, S.

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

Roggemann, M. C.

Rousset, G.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Sakov, P.

M. Bocquet and P. Sakov, “Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems,” Nonlinear Processes in Geophysics 19, 383–399 (2012).
[Crossref]

P. Sakov, G. Evensen, and L. Bertino, “Asynchronous data assimilation with the EnKF,” Tellus 62A, 24–29 (2010).
[Crossref]

P. Sakov and L. Bertino, “Relation between two common localisation methods for the EnKF,” Computational Geoscience 15, 225–237 (2010).
[Crossref]

P. Sakov and P. R. Oke, “Implications of the form of the ensemble transformation in the ensemble square root filters,” Monthly Weather Review 136, 1042–1053 (2008).
[Crossref]

Shectman, S.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Sheehan, M.

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

Sivo, G.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Spyromilio, J.

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

Stepp, L.

L. Stepp, “Thirty Meter Telescope project update,” Proc. SPIE 8444, 84441G (2012).
[Crossref]

Szunyogh, I.

B. R. Hunt, E. J. Kostelich, and I. Szunyogh, “Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter,” Physica D 230, 112–126 (2007).
[Crossref]

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Talbot, G.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Tippett, M. K.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

Tran, V. D.

F. Le Gland, V. Monbet, and V. D. Tran, Large Sample Asymptotics for the Ensemble Kalman Filter (Oxford University Press, Oxford, 2011), pp. 598–631.

Tse, E.

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence, and separation in stochastic control,” Automatic Control, IEEE Transactions on 19, 494–500 (1974).
[Crossref]

Véran, J.-P.

Vidal, F.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Whitaker, J.

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

Yorke, J. A.

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Younger, E.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

Zimin, A. V.

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Appl. Opt. (4)

Automatic Control, IEEE Transactions on (1)

Y. Bar-Shalom and E. Tse, “Dual effect, certainty equivalence, and separation in stochastic control,” Automatic Control, IEEE Transactions on 19, 494–500 (1974).
[Crossref]

Computational Geoscience (1)

P. Sakov and L. Bertino, “Relation between two common localisation methods for the EnKF,” Computational Geoscience 15, 225–237 (2010).
[Crossref]

J. Opt. Soc. Am. A (10)

L. A. Poyneer, B. A. Macintosh, and J.-P. Véran, “Fourier transform wavefront control with adaptive prediction of the atmosphere,” J. Opt. Soc. Am. A 24, 2645–2660 (2007).
[Crossref]

L. Gilles, P. Massioni, C. Kulcsár, H.-F. Raynaud, and B. Ellerbroek, “Distributed Kalman filtering compared to Fourier domain preconditioned conjugate gradient for laser guide star tomography on extremely large telescopes,” J. Opt. Soc. Am. A 30, 898–909 (2013).
[Crossref]

P. Massioni, C. Kulcsár, H.-F. Raynaud, and J.-M. Conan, “Fast computation of an optimal controller for large-scale adaptive optics,” J. Opt. Soc. Am. A 28, 2298–2309 (2011).
[Crossref]

S. Meimon, C. Petit, T. Fusco, and C. Kulcsar, “Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A 27, 122–132 (2010).
[Crossref]

C. Petit, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “LQG control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A 26, 1307–1325 (2009).
[Crossref]

B. Le Roux, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptive optics,” J. Opt. Soc. Am. A 21, 1261–1276 (2004).
[Crossref]

D. P. Looze, “LQG control for adaptive optics systems using a hybrid model,” J. Opt. Soc. Am. A 26, 1–9 (2009).
[Crossref]

L. A. Poyneer, D. T. Gavel, and J. M. Brase, “Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform,” J. Opt. Soc. Am. A 19, 2100–2111 (2002).
[Crossref]

A. Costille, C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and T. Fusco, “Wide field adaptive optics laboratory demonstration with closed-loop tomographic control,” J. Opt. Soc. Am. A 27, 469–483 (2010).
[Crossref]

C. Correia, H.-F. Raynaud, C. Kulcsár, and J.-M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A 27, 333–349 (2010).
[Crossref]

Monthly Weather Review (4)

G. Burgers, P. J. V. Leeuwen, and G. Evensen, “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review 126, 1719–1724 (1998).
[Crossref]

C. H. Bishop, B. J. Etherton, and S. J. Majumdar, “Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects,” Monthly Weather Review 129, 420–436 (2001).
[Crossref]

M. K. Tippett, J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, “Ensemble square root filters,” Monthly Weather Review 131, 1485–1490 (2003).
[Crossref]

P. Sakov and P. R. Oke, “Implications of the form of the ensemble transformation in the ensemble square root filters,” Monthly Weather Review 136, 1042–1053 (2008).
[Crossref]

Nonlinear Processes in Geophysics (2)

M. Bocquet, “Ensemble Kalman filtering without the intrinsic need for inflation,” Nonlinear Processes in Geophysics 18, 735–750 (2011).
[Crossref]

M. Bocquet and P. Sakov, “Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems,” Nonlinear Processes in Geophysics 19, 383–399 (2012).
[Crossref]

Ocean Dynamics (1)

G. Evensen, “The ensemble Kalman filter: theoretical formulation and practical implementation,” Ocean Dynamics 53, 343–367 (2003).
[Crossref]

Opt. Express (3)

Physica D (1)

B. R. Hunt, E. J. Kostelich, and I. Szunyogh, “Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter,” Physica D 230, 112–126 (2007).
[Crossref]

Proc. SPIE (8)

R. Conan and C. Correia, “Object-oriented matlab adaptive optics,” Proc. SPIE 9148, 91486C (2014).

C. Petit, T. Fusco, E. Fedrigo, J.-M. Conan, C. Kulcsár, and H.-F. Raynaud, “Optimisation of the control laws for the SPHERE XAO system,” Proc. SPIE 7015, 70151D (2008).
[Crossref]

C. Correia, C. Kulcsár, J.-M. Conan, and H.-F. Raynaud, “Hartmann modelling in the discrete spatial-frequency domain: application to real-time reconstruction in adaptive optics,” Proc. SPIE 7015, 701551 (2008).
[Crossref]

M. Johns, P. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[Crossref]

L. Stepp, “Thirty Meter Telescope project update,” Proc. SPIE 8444, 84441G (2012).
[Crossref]

A. McPherson, J. Spyromilio, M. Kissler-Patig, S. Ramsay, E. Brunetto, P. Dierickx, and M. Cassali, “E-ELT update of project and effect of change to 39m design,” Proc. SPIE 8444, 84441F (2012).
[Crossref]

M. Gray and B. Le Roux, “ETKF, a non-stationary control law for complex adaptive optics systems on ELTs: theoretical aspects and first simulation results,” Proc. SPIE 8447, 84471T (2012).
[Crossref]

D. Gratadour, “COMPASS: an efficient, scalable and versatile numerical platform for the development of ELT AO systems,” Proc. SPIE 9148, 91486O (2014).

Tellus (2)

P. Sakov, G. Evensen, and L. Bertino, “Asynchronous data assimilation with the EnKF,” Tellus 62A, 24–29 (2010).
[Crossref]

E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D. Patil, and J. A. Yorke, “A local ensemble Kalman filter for atmospheric data assimilation,” Tellus 56A, 415–428 (2004).
[Crossref]

Other (6)

C. Correia, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, and C. Petit, “Adapting optimal LQG methods to ELT-sized AO systems,” in Proc. of the first AO4ELT conference (2010), p. 07003.

F. Le Gland, V. Monbet, and V. D. Tran, Large Sample Asymptotics for the Ensemble Kalman Filter (Oxford University Press, Oxford, 2011), pp. 598–631.

A. Parisot, “Calibrations et stratégies de commande tomographiques pour les optiques adaptatives grand champ: validations expérimentales sur le banc Homer,” PhD Thesis, Aix-Marseille University (2012).

M. Gray, C. Petit, S. Rodionov, L. Bertino, M. Bocquet, and T. Fusco, “Local ETKF: a non-stationary control law for complex adaptive optics systems on ELTs,” in Proc. of the third AO4ELT conference (2013).

C. Kulcsár, H.-F. Raynaud, C. Petit, and J.-M. Conan, “Can LQG adaptive optics control cope with actuator saturation ?” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings (Optical Society of America, 2007), p. PMA1.

G. Sivo, C. Kulcsár, J.-M. Conan, H.-F. Raynaud, E. Gendron, A. Basden, F. Vidal, T. Morris, S. Meimon, C. Petit, D. Gratadour, O. Martin, Z. Hubert, G. Rousset, N. Dipper, G. Talbot, E. Younger, and R. Myers, “Full LQG control with vibration mitigation: from theory to first on-sky validation on the CANARY MOAO demonstrator,” in Imaging and Applied Optics (Optical Society of America, 2013), p. OTu2A.2.

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Figures (7)

Fig. 1
Fig. 1 Block diagram of a classical AO system closed-loop.
Fig. 2
Fig. 2 Temporal diagram of the system process.
Fig. 3
Fig. 3 Partition of the actuators domains on a 16 m telescope pupil with a 32×32 SH-WFS.
Fig. 4
Fig. 4 Convergences of the ETKF and the Local ETKF performances to the KF.
Fig. 5
Fig. 5 Coherent energy loss with different partitions and a fixed noise variance.
Fig. 6
Fig. 6 Coherent energy loss with different partitions and 101 members.
Fig. 7
Fig. 7 Cumulative Wave Front Error (in nm rms) with 290 members.

Tables (4)

Tables Icon

Table 1 Numbers of operations with m = 101 during one cycle of the AO loop.

Tables Icon

Table 3 Numbers of multiplications during the update step.

Tables Icon

Table 4 Numbers of operations during the prediction step.

Tables Icon

Table 2 Runtime (in msec) with m = 101 during one cycle of the AO loop.

Equations (32)

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

x k 1 Δ T ( k 1 ) Δ T k Δ T x ( t ) d t ,
J ( u ) lim n + 1 n k = 1 n ϕ k res 2 .
y k = D ϕ k 1 + w k ,
ϕ k cor = N u k 1 .
x k = ( ( φ k tur ) T ( φ k 1 tur ) T ( u k 1 ) T ( u k 2 ) T ) T .
x k + 1 = A × x k + B × u k + v k y k = C × x k + w k .
x k + 1 = ( A tur 0 0 0 Id 0 0 0 0 0 0 0 0 0 Id 0 ) x k + ( 0 0 Id 0 ) u k + ( Id 0 0 0 ) v k .
y k = [ 0 D 0 D × N ] x k + w k .
x ^ k / k = x ^ k / k 1 + H k ( y k y ^ k / k 1 ) ,
Σ k / k = ( Id H k C 1 ) Σ k / k 1 ,
H k = Σ k / k 1 C 1 T ( C 1 Σ k / k 1 C 1 T + Σ w ) 1 .
Σ k + 1 / k = A 1 Σ k / k 1 A 1 T A 1 H k C 1 Σ k / k 1 A 1 T + Σ v ,
Σ = Z × Z T with Z = [ x 1 x ¯ ; ; x m x ¯ ] / m 1 ,
Z k / k = Z k / k 1 × T k ,
T k = [ Id + ( C 1 Z k / k 1 ) T × Σ w 1 × ( C 1 Z k / k 1 ) ] 1 / 2 .
T k = Q k × Γ k 1 / 2 × Q k T ,
x ^ k / k = x ¯ k / k 1 + Z k / k 1 S c z T ( S inov S c z Q k Γ k 1 Q k T S c z T S inov ) .
X k / k = m 1 × Z k / k + [ x ^ k / k ; ; x ^ k / k ] .
x k + 1 / k i = A 1 × x k / k i + v k + 1 i ( for 1 i m ) ,
O ( m 3 + m 2 × ( n + p ) ) ,
x ¯ ˜ k / k 1 ( n d , 1 ) and Z ˜ k / k 1 ( n d , m )
S ˜ inov = Σ ˜ w 1 / 2 ( y ˜ k y ¯ ˜ k / k 1 ) ( p d , 1 ) and S ˜ c z = Σ ˜ w 1 / 2 C ˜ 1 Z k / k 1 ( p d , m )
EVD of ( Id + S ˜ c z T × S ˜ c z ) Q ˜ k ( m , m ) and Γ ˜ k ( m , m )
x ^ ˜ k / k = x ¯ ˜ k / k 1 + Z ˜ k / k 1 S ˜ c z T ( S ˜ i n o v S ˜ c z × Q ˜ k Γ ˜ k 1 Q ˜ k T × S ˜ c z T S ˜ inov ) ( n d , 1 )
X ˜ k / k = m 1 × Z ˜ k / k 1 × Q ˜ k Γ ˜ k 1 / 2 Q ˜ k T + [ x ^ ˜ k / k ; ; x ^ ˜ k / k ] ( n d , m ) .
x ^ ˜ k / k = x ¯ ˜ k / k 1 + H ˜ k × ( y ˜ k y ¯ ˜ k / k 1 ) with H ˜ k = Z ˜ k / k 1 S ˜ c z T ( I S ˜ c z Q ˜ k Γ ˜ k 1 Q ˜ k T S ˜ c z T ) Σ ˜ w 1 / 2
loss = ( E coh K F E coh Local ETKF ) / E coh K F × 100 .
( U × U T + S × S T ) 1 = ( S 1 ) T { S 1 ( S 1 U ) [ Id + ( S 1 U ) T ( S 1 U ) ] 1 ( S 1 U ) T S 1 } .
x ^ k / k = x ¯ k / k 1 + Z k / k 1 Z k / k 1 T C 1 T ( C 1 Z k / k 1 Z k / k 1 T C 1 T + Σ w ) 1 ( y k y ¯ k / k 1 ) .
x ^ k / k = x ¯ k / k 1 + Z k / k 1 ( Σ w 1 / 2 C 1 Z k / k 1 ) T { Σ w 1 / 2 ( y k y ¯ k / k 1 ) Σ w 1 / 2 C 1 Z k / k 1 × [ Id + ( Σ w 1 / 2 C 1 Z k / k 1 ) T ( Σ w 1 / 2 C 1 Z k / k 1 ) ] 1 ( Σ w 1 / 2 C 1 Z k / k 1 ) T Σ w 1 / 2 ( y k y ¯ k / k 1 ) } .
x ^ k / k = x ¯ k / k 1 + Z k / k 1 S c z T { S inov S c z [ Id + S c z T S c z ] 1 S c z T S inov } .
x ^ k / k = x ¯ k / k 1 + Z k / k 1 S c z T { S inov S c z Q k Γ k 1 Q k T S c z T S inov } .

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