Abstract

A wake vortex is a form of irregular airflow generated by a flying aircraft, which can cause a severe hazard for aviation. To quantify the hazard of a wake after fully roll-up and before rebound, this paper proposes an algorithm to retrieve its characteristic parameters (circulations, vortex-core positions, and vortex-core radii) with a scanning Doppler Lidar. In the algorithm, a governing equation related to the Doppler velocities and characteristic parameters is established based on the aerosols’ weak inertia, from which the target parameters are solved with an optimization method. During the process, the distortion of Doppler velocity caused by the scanning of the Lidar beam is adjusted by the Doppler acceleration to achieve better estimations of the target characteristic parameters. Good performance of the algorithm has been verified by simulation and field detection data.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. P. R. Veillette, “Data show that U. S. wake turbulence accidents are most frequent at low altitude and during approach and landing,” Flight Safty Digest 21(3–4), 1–47 (2002).
  2. T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
    [Crossref]
  3. J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).
  4. SESAR Consortium, European Air Traffic Management Master Plan, Edition 1 (2009).
  5. J. Burden, P. A. Curry, D. Roby, and F. Love, “Introduction to the next generation automatic test system (NGATS),” in Proceedings of IEEE Autotestcon (IEEE, 2005), pp. 16–19.
  6. P. A. Curry, J. Burden, and G. A. Lundy, “Next generation automatic test system (NGATS) update,” in Proceedings of IEEE Autotestcon (IEEE, 2006), pp. 318–322.
  7. J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
    [Crossref]
  8. J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
    [Crossref]
  9. J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
    [Crossref]
  10. J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
    [Crossref]
  11. F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.
  12. L. Thobois, “Next generation scanning Lidar systems for optimizing wake turbulence separation minima,” J. Radar 6(6), 689–698 (2017).
  13. S. Rahm, I. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
    [Crossref]
  14. S. Rahm and I. Smalikho, “Aircraft wake vortex measurement with airborne coherent Doppler Lidar,” J. Aircr. 45(4), 1148–1155 (2008).
    [Crossref]
  15. H. Wassaf, D. Burnham, and F. Wang, “Wake vortex tangential velocity adaptive spectral (TVAS) algorithm for pulsed Lidar systems,” presented at the 16th Coherent Laser Radar Conference, Long Beach, CA, 20–24 Jun. 2011.
  16. D. J. Ramsey and C. Nguyen, “Characterizing aircraft wake vortices with ground-based pulsed coherent Lidar: effects of vortex circulation strength and Lidar signal-to-noise ratio on the spectral signature,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.
  17. D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.
  18. D. Jacob, D. Y. Lai, and D. P. Delisi, “Development of an improved pulsed Lidar circulation estimation algorithm and performance results for Denver OGE data,” presented at the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, 07–10 Jan. 2013.
  19. D. Jacob, M. J. Pruis, D. Y. Lai, and D. P. Delisi, “WakeMod 4: A new standalone wake vortex algorithm for estimating circulation strength and position,” presented at the 7th AIAA Atmospheric and Space Environments Conference, Dallas, Texas, 22–26 Jun. 2015.
  20. I. N. Smalikho, V. A. Banakh, F. Holzäpfel, and S. Rahm, “Method of radial velocities for the estimation of aircraft wake vortex parameters from data measured by coherent Doppler Lidar,” Opt. Express 23(19), A1194–A1207 (2015).
    [Crossref] [PubMed]
  21. I. N. Smalikho and V. A. Banakh, “Estimation of aircraft wake vortex parameters from data measured by a stream line Lidar,” Proc. SPIE 9680, 968037 (2015).
    [Crossref]
  22. R. Frehlich and R. Sharman, “Maximum likelihood estimates of vortex parameters from simulated coherent Doppler Lidar data,” J. Atmos. Ocean. Technol. 22(2), 117–130 (2005).
    [Crossref]
  23. A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.
  24. E. Yoshikawa and N. Matayoshi, “Aircraft wake vortex retrieval method on Lidar lateral range-height indicator observation,” AIAA J. 55(7), 2269–2278 (2017).
    [Crossref]
  25. W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, 1999).
  26. D. C. Burnham and J. N. Hallock, “Chicago monostatic acoustic vortex sensing system,” U.S. Department of Transportation. Report No. DOT-TSC-FAA-79-103. 1982. 206 pp.
  27. D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
    [Crossref]
  28. F. Holzäpfel, “Probabilistic two-phase wake vortex decay and transport model,” J. Aircr. 40(2), 323–331 (2003).
    [Crossref]
  29. F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
    [Crossref]
  30. K. K. Hon and P. W. Chan, “Aircraft wake vortex observations in Hong Kong,” J. Radar 6(6), 709–718 (2017).
  31. T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38, 181–208 (2002).
    [Crossref]

2018 (1)

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

2017 (5)

L. Thobois, “Next generation scanning Lidar systems for optimizing wake turbulence separation minima,” J. Radar 6(6), 689–698 (2017).

J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

E. Yoshikawa and N. Matayoshi, “Aircraft wake vortex retrieval method on Lidar lateral range-height indicator observation,” AIAA J. 55(7), 2269–2278 (2017).
[Crossref]

K. K. Hon and P. W. Chan, “Aircraft wake vortex observations in Hong Kong,” J. Radar 6(6), 709–718 (2017).

2016 (2)

J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
[Crossref]

J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
[Crossref]

2015 (2)

2008 (1)

S. Rahm and I. Smalikho, “Aircraft wake vortex measurement with airborne coherent Doppler Lidar,” J. Aircr. 45(4), 1148–1155 (2008).
[Crossref]

2007 (1)

S. Rahm, I. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
[Crossref]

2005 (2)

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

R. Frehlich and R. Sharman, “Maximum likelihood estimates of vortex parameters from simulated coherent Doppler Lidar data,” J. Atmos. Ocean. Technol. 22(2), 117–130 (2005).
[Crossref]

2004 (1)

D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
[Crossref]

2003 (2)

F. Holzäpfel, “Probabilistic two-phase wake vortex decay and transport model,” J. Aircr. 40(2), 323–331 (2003).
[Crossref]

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

2002 (2)

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38, 181–208 (2002).
[Crossref]

P. R. Veillette, “Data show that U. S. wake turbulence accidents are most frequent at low altitude and during approach and landing,” Flight Safty Digest 21(3–4), 1–47 (2002).

Auvermann, H. J.

D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
[Crossref]

Banakh, V. A.

Barbaresco, F.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Barr, K. S.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Besson, L.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Brion, V.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Brusquet, L. Le

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

Bryant, W.

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

Burden, J.

J. Burden, P. A. Curry, D. Roby, and F. Love, “Introduction to the next generation automatic test system (NGATS),” in Proceedings of IEEE Autotestcon (IEEE, 2005), pp. 16–19.

P. A. Curry, J. Burden, and G. A. Lundy, “Next generation automatic test system (NGATS) update,” in Proceedings of IEEE Autotestcon (IEEE, 2006), pp. 318–322.

Burnham, D.

H. Wassaf, D. Burnham, and F. Wang, “Wake vortex tangential velocity adaptive spectral (TVAS) algorithm for pulsed Lidar systems,” presented at the 16th Coherent Laser Radar Conference, Long Beach, CA, 20–24 Jun. 2011.

Burnham, D. C.

D. C. Burnham and J. N. Hallock, “Chicago monostatic acoustic vortex sensing system,” U.S. Department of Transportation. Report No. DOT-TSC-FAA-79-103. 1982. 206 pp.

Cariou, J. P.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Chan, P. W.

K. K. Hon and P. W. Chan, “Aircraft wake vortex observations in Hong Kong,” J. Radar 6(6), 709–718 (2017).

Chandrasekar, V.

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

Curry, P. A.

P. A. Curry, J. Burden, and G. A. Lundy, “Next generation automatic test system (NGATS) update,” in Proceedings of IEEE Autotestcon (IEEE, 2006), pp. 318–322.

J. Burden, P. A. Curry, D. Roby, and F. Love, “Introduction to the next generation automatic test system (NGATS),” in Proceedings of IEEE Autotestcon (IEEE, 2005), pp. 16–19.

Darracq, D.

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38, 181–208 (2002).
[Crossref]

Delisi, D. P.

D. Jacob, M. J. Pruis, D. Y. Lai, and D. P. Delisi, “WakeMod 4: A new standalone wake vortex algorithm for estimating circulation strength and position,” presented at the 7th AIAA Atmospheric and Space Environments Conference, Dallas, Texas, 22–26 Jun. 2015.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

D. Jacob, D. Y. Lai, and D. P. Delisi, “Development of an improved pulsed Lidar circulation estimation algorithm and performance results for Denver OGE data,” presented at the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, 07–10 Jan. 2013.

Dolfi, D.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Dolfi-Bouteyre, A.

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Duponcheel, M.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

Feneyrou, P.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Fleury, G.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

Frech, M.

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

Frehlich, R.

R. Frehlich and R. Sharman, “Maximum likelihood estimates of vortex parameters from simulated coherent Doppler Lidar data,” J. Atmos. Ocean. Technol. 22(2), 117–130 (2005).
[Crossref]

Gao, H.

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

Gerz, T.

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38, 181–208 (2002).
[Crossref]

Goedecke, G. H.

D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
[Crossref]

Hallermeyer, A.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Hallock, J. N.

D. C. Burnham and J. N. Hallock, “Chicago monostatic acoustic vortex sensing system,” U.S. Department of Transportation. Report No. DOT-TSC-FAA-79-103. 1982. 206 pp.

Harris, M.

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

Hinds, W. C.

W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, 1999).

Holzäpfel, F.

I. N. Smalikho, V. A. Banakh, F. Holzäpfel, and S. Rahm, “Method of radial velocities for the estimation of aircraft wake vortex parameters from data measured by coherent Doppler Lidar,” Opt. Express 23(19), A1194–A1207 (2015).
[Crossref] [PubMed]

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

F. Holzäpfel, “Probabilistic two-phase wake vortex decay and transport model,” J. Aircr. 40(2), 323–331 (2003).
[Crossref]

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38, 181–208 (2002).
[Crossref]

Hon, K. K.

K. K. Hon and P. W. Chan, “Aircraft wake vortex observations in Hong Kong,” J. Radar 6(6), 709–718 (2017).

Hutton, D. A.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Jacob, D.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

D. Jacob, M. J. Pruis, D. Y. Lai, and D. P. Delisi, “WakeMod 4: A new standalone wake vortex algorithm for estimating circulation strength and position,” presented at the 7th AIAA Atmospheric and Space Environments Conference, Dallas, Texas, 22–26 Jun. 2015.

D. Jacob, D. Y. Lai, and D. P. Delisi, “Development of an improved pulsed Lidar circulation estimation algorithm and performance results for Denver OGE data,” presented at the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, 07–10 Jan. 2013.

Jeannin, N.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Köpp, F.

S. Rahm, I. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
[Crossref]

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

Lai, D. Y.

D. Jacob, D. Y. Lai, and D. P. Delisi, “Development of an improved pulsed Lidar circulation estimation algorithm and performance results for Denver OGE data,” presented at the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, 07–10 Jan. 2013.

D. Jacob, M. J. Pruis, D. Y. Lai, and D. P. Delisi, “WakeMod 4: A new standalone wake vortex algorithm for estimating circulation strength and position,” presented at the 7th AIAA Atmospheric and Space Environments Conference, Dallas, Texas, 22–26 Jun. 2015.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Leviandier, L.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Li, J.

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).

J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
[Crossref]

J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
[Crossref]

Li, Y.

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

Liu, J.

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

Liu, Z.

J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
[Crossref]

Love, F.

J. Burden, P. A. Curry, D. Roby, and F. Love, “Introduction to the next generation automatic test system (NGATS),” in Proceedings of IEEE Autotestcon (IEEE, 2005), pp. 16–19.

Lundy, G. A.

P. A. Curry, J. Burden, and G. A. Lundy, “Next generation automatic test system (NGATS) update,” in Proceedings of IEEE Autotestcon (IEEE, 2006), pp. 318–322.

Matayoshi, N.

E. Yoshikawa and N. Matayoshi, “Aircraft wake vortex retrieval method on Lidar lateral range-height indicator observation,” AIAA J. 55(7), 2269–2278 (2017).
[Crossref]

Nguyen, C.

D. J. Ramsey and C. Nguyen, “Characterizing aircraft wake vortices with ground-based pulsed coherent Lidar: effects of vortex circulation strength and Lidar signal-to-noise ratio on the spectral signature,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Ostashev, V. E.

D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
[Crossref]

Philip, G.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Pillet, G.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Pruis, M. J.

D. Jacob, M. J. Pruis, D. Y. Lai, and D. P. Delisi, “WakeMod 4: A new standalone wake vortex algorithm for estimating circulation strength and position,” presented at the 7th AIAA Atmospheric and Space Environments Conference, Dallas, Texas, 22–26 Jun. 2015.

Qu, L.

J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
[Crossref]

Rahm, S.

I. N. Smalikho, V. A. Banakh, F. Holzäpfel, and S. Rahm, “Method of radial velocities for the estimation of aircraft wake vortex parameters from data measured by coherent Doppler Lidar,” Opt. Express 23(19), A1194–A1207 (2015).
[Crossref] [PubMed]

S. Rahm and I. Smalikho, “Aircraft wake vortex measurement with airborne coherent Doppler Lidar,” J. Aircr. 45(4), 1148–1155 (2008).
[Crossref]

S. Rahm, I. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
[Crossref]

Ramsey, D. J.

D. J. Ramsey and C. Nguyen, “Characterizing aircraft wake vortices with ground-based pulsed coherent Lidar: effects of vortex circulation strength and Lidar signal-to-noise ratio on the spectral signature,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Roby, D.

J. Burden, P. A. Curry, D. Roby, and F. Love, “Introduction to the next generation automatic test system (NGATS),” in Proceedings of IEEE Autotestcon (IEEE, 2005), pp. 16–19.

Shald, S.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Sharman, R.

R. Frehlich and R. Sharman, “Maximum likelihood estimates of vortex parameters from simulated coherent Doppler Lidar data,” J. Atmos. Ocean. Technol. 22(2), 117–130 (2005).
[Crossref]

Smalikho, I.

S. Rahm and I. Smalikho, “Aircraft wake vortex measurement with airborne coherent Doppler Lidar,” J. Aircr. 45(4), 1148–1155 (2008).
[Crossref]

S. Rahm, I. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
[Crossref]

Smalikho, I. N.

Stephen, M. H.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

Stumpf, E.

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

Tafferner, A.

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

Thobois, L.

L. Thobois, “Next generation scanning Lidar systems for optimizing wake turbulence separation minima,” J. Radar 6(6), 689–698 (2017).

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

Valla, M.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Veillette, P. R.

P. R. Veillette, “Data show that U. S. wake turbulence accidents are most frequent at low altitude and during approach and landing,” Flight Safty Digest 21(3–4), 1–47 (2002).

Wang, F.

H. Wassaf, D. Burnham, and F. Wang, “Wake vortex tangential velocity adaptive spectral (TVAS) algorithm for pulsed Lidar systems,” presented at the 16th Coherent Laser Radar Conference, Long Beach, CA, 20–24 Jun. 2011.

Wang, T.

J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
[Crossref]

J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
[Crossref]

Wang, X.

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).

J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
[Crossref]

J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
[Crossref]

Wassaf, H.

H. Wassaf, D. Burnham, and F. Wang, “Wake vortex tangential velocity adaptive spectral (TVAS) algorithm for pulsed Lidar systems,” presented at the 16th Coherent Laser Radar Conference, Long Beach, CA, 20–24 Jun. 2011.

Wilson, D. K.

D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
[Crossref]

Wilson, R.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

Winckelmans, G.

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

Yoshikawa, E.

E. Yoshikawa and N. Matayoshi, “Aircraft wake vortex retrieval method on Lidar lateral range-height indicator observation,” AIAA J. 55(7), 2269–2278 (2017).
[Crossref]

Young, R. I.

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

AIAA J. (1)

E. Yoshikawa and N. Matayoshi, “Aircraft wake vortex retrieval method on Lidar lateral range-height indicator observation,” AIAA J. 55(7), 2269–2278 (2017).
[Crossref]

Appl. Acoust. (1)

D. K. Wilson, V. E. Ostashev, G. H. Goedecke, and H. J. Auvermann, “Quasi-wavelet calculations of sound scattering behind barriers,” Appl. Acoust. 65(6), 605–627 (2004).
[Crossref]

C. R. Phys. (1)

T. Gerz, F. Holzäpfel, W. Bryant, F. Köpp, M. Frech, A. Tafferner, and G. Winckelmans, “Research towards a wake-vortex advisory system for optimal aircraft spacing,” C. R. Phys. 6(4), 501–523 (2005).
[Crossref]

Flight Safty Digest (1)

P. R. Veillette, “Data show that U. S. wake turbulence accidents are most frequent at low altitude and during approach and landing,” Flight Safty Digest 21(3–4), 1–47 (2002).

IEEE Trans. Aerosp. Electron. Syst. (4)

J. Li, X. Wang, T. Wang, J. Liu, H. Gao, and V. Chandrasekar, “Circulation retrieval of wake vortex under rainy condition with a vertically pointing radar,” IEEE Trans. Aerosp. Electron. Syst. 53(4), 1893–1906 (2017).
[Crossref]

J. Li, H. Gao, Y. Li, V. Chandrasekar, and X. Wang, “Circulation retrieval of simulated wake vortices under rainy condition with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 54(2), 569–584 (2018).
[Crossref]

J. Li, T. Wang, L. Qu, and X. Wang, “Circulation retrieval of wake vortex in fog with an upward-looking monostatic radar,” IEEE Trans. Aerosp. Electron. Syst. 52(1), 169–180 (2016).
[Crossref]

J. Li, T. Wang, Z. Liu, and X. Wang, “Circulation retrieval of wake vortex in fog with a side-looking scanning radar,” IEEE Trans. Aerosp. Electron. Syst. 52(5), 2242–2254 (2016).
[Crossref]

J. Aircr. (3)

S. Rahm, I. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
[Crossref]

S. Rahm and I. Smalikho, “Aircraft wake vortex measurement with airborne coherent Doppler Lidar,” J. Aircr. 45(4), 1148–1155 (2008).
[Crossref]

F. Holzäpfel, “Probabilistic two-phase wake vortex decay and transport model,” J. Aircr. 40(2), 323–331 (2003).
[Crossref]

J. Atmos. Ocean. Technol. (2)

F. Holzäpfel, T. Gerz, F. Köpp, E. Stumpf, M. Harris, R. I. Young, and A. Dolfi-Bouteyre, “Strategies for circulation evaluation of aircraft wake vortices measured by Lidar,” J. Atmos. Ocean. Technol. 20, 1183–1195 (2003).
[Crossref]

R. Frehlich and R. Sharman, “Maximum likelihood estimates of vortex parameters from simulated coherent Doppler Lidar data,” J. Atmos. Ocean. Technol. 22(2), 117–130 (2005).
[Crossref]

J. Radar (3)

K. K. Hon and P. W. Chan, “Aircraft wake vortex observations in Hong Kong,” J. Radar 6(6), 709–718 (2017).

L. Thobois, “Next generation scanning Lidar systems for optimizing wake turbulence separation minima,” J. Radar 6(6), 689–698 (2017).

J. Li, H. Gao, T. Wang, and X. Wang, “A survey of the scattering characteristics and detection of aircraft wake vortices,” J. Radar 6(6), 653–672 (2017).

Opt. Express (1)

Proc. SPIE (1)

I. N. Smalikho and V. A. Banakh, “Estimation of aircraft wake vortex parameters from data measured by a stream line Lidar,” Proc. SPIE 9680, 968037 (2015).
[Crossref]

Prog. Aerospace Sci. (1)

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38, 181–208 (2002).
[Crossref]

Other (12)

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. Le Brusquet, G. Fleury, L. Thobois, J. P. Cariou, M. Duponcheel, and G. Winckelmans, “Development and assessment of a wake vortex characterization algorithm based on a hybrid Lidar signal processing,” presented at the 8th AIAA Atmospheric and Space Environments Conference, Washington, DC, 13–17 Jun. 2016.

W. C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles (Wiley, 1999).

D. C. Burnham and J. N. Hallock, “Chicago monostatic acoustic vortex sensing system,” U.S. Department of Transportation. Report No. DOT-TSC-FAA-79-103. 1982. 206 pp.

H. Wassaf, D. Burnham, and F. Wang, “Wake vortex tangential velocity adaptive spectral (TVAS) algorithm for pulsed Lidar systems,” presented at the 16th Coherent Laser Radar Conference, Long Beach, CA, 20–24 Jun. 2011.

D. J. Ramsey and C. Nguyen, “Characterizing aircraft wake vortices with ground-based pulsed coherent Lidar: effects of vortex circulation strength and Lidar signal-to-noise ratio on the spectral signature,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

D. Jacob, D. Y. Lai, D. P. Delisi, K. S. Barr, D. A. Hutton, S. Shald, M. H. Stephen, and G. Philip, “Assessment of Lockheed Martin’s aircraft wake vortex circulation estimation algorithms using simulated Lidar data,” presented at the 3rd AIAA Atmospheric Space Environments Conference, Honolulu, Hawaii, 27–30 Jun. 2011.

D. Jacob, D. Y. Lai, and D. P. Delisi, “Development of an improved pulsed Lidar circulation estimation algorithm and performance results for Denver OGE data,” presented at the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, Texas, 07–10 Jan. 2013.

D. Jacob, M. J. Pruis, D. Y. Lai, and D. P. Delisi, “WakeMod 4: A new standalone wake vortex algorithm for estimating circulation strength and position,” presented at the 7th AIAA Atmospheric and Space Environments Conference, Dallas, Texas, 22–26 Jun. 2015.

SESAR Consortium, European Air Traffic Management Master Plan, Edition 1 (2009).

J. Burden, P. A. Curry, D. Roby, and F. Love, “Introduction to the next generation automatic test system (NGATS),” in Proceedings of IEEE Autotestcon (IEEE, 2005), pp. 16–19.

P. A. Curry, J. Burden, and G. A. Lundy, “Next generation automatic test system (NGATS) update,” in Proceedings of IEEE Autotestcon (IEEE, 2006), pp. 318–322.

F. Barbaresco, L. Thobois, A. Dolfi-Bouteyre, N. Jeannin, R. Wilson, M. Valla, A. Hallermeyer, P. Feneyrou, V. Brion, L. Besson, J. P. Cariou, L. Leviandier, G. Pillet, and D. Dolfi, “Monitoring wind, turbulence and aircraft wake vortices by high resolution radar and Lidar remote sensors in all weather conditions,” in Proceedings of URSI-France, wakenet.eu (2015), pp. 81–110.

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Figures (11)

Fig. 1
Fig. 1 Geometry setup of the Lidar, runway and wake vortices.
Fig. 2
Fig. 2 Illustration of vortex-core positions’ preliminary estimation: distribution of Doppler velocity (a) and the corresponding velocity gradient (b).
Fig. 3
Fig. 3 Sketch of global and local optimization values (a), and illustration of determining the trajectories of vortices, where the local optimization results for point D are presented (b).
Fig. 4
Fig. 4 Simulated Doppler velocity distribution: the first scan (a) and the last scan (b).
Fig. 5
Fig. 5 Vortex-core trajectory and circulations retrieved from simulated Doppler velocity distribution. Results of the new method without adjusting the Doppler velocity: vortex-core positions (a), circulations (b); Results of the new method with the Doppler velocity adjusted: vortex-core positions (c), circulations (d); Results of the TV method: vortex-core positions (e), circulations (f).
Fig. 6
Fig. 6 The estimated vortex-core trajectories (a) and circulations (b) for different background turbulence.
Fig. 7
Fig. 7 Layout of Lidar and the north runway (25RA) in HKIA, where the vertical scanning plane is the solid line in red (a), and a detailed setup of the Lidar (b).
Fig. 8
Fig. 8 Doppler velocity RHI of wake vortex obtained in HKIA at 07:17:46–07:17:51 (UTC) on August 3, 2014, where the origin is the Lidar position (at a height of 19 m to the ground).
Fig. 9
Fig. 9 Vortex-core position retrieval results from four sets of data on August 3, 2014, where the range is the horizontal distance to the Lidar, and the height is relative to the ground, Airbus A300F4-200 at 00:38:22–00:39:36 (UTC) (a); Boeing 747-400 at 00:52:47–00:54:07 (UTC) (b); Boeing 777-300ER at 07:17:25–07:18:23 (UTC) (c); Airbus A330-300 at 08:35:46–08:36:39 (UTC) (d).
Fig. 10
Fig. 10 Circulation retrieval results from four sets of data on August 3, 2014. Airbus A300F4-200 at 00:38:22–00:39:36 (UTC) (a); Boeing 747-400 at 00:52:47–00:54:07 (UTC) (b); Boeing 777-300ER at 07:17:25–07:18:23 (UTC) (c); Airbus A330-300 at 08:35:46–08:36:39 (UTC) (d).
Fig. 11
Fig. 11 Retrieval results of vortex-core radii from the four sets of data.

Tables (2)

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Table 1 Average relative errors and relative RMSE of the estimated parameters

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Table 2 Main parameters of the pulsed Lidar in HKIA

Equations (17)

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V D ( i ) = V flow , ( i ) | r = V wind , ( i ) | r + V wake , ( i ) | r ,
( i ) = V wind , ( i ) | r + V wake , ( i ) | r + V D ( i ) = 0 .
V wake | θ = Γ V ˜ wake , ( i ) | θ = Γ 2 π r r 2 r 2 + r c 2 ,
V ˜ Lw ( i ) = [ V ˜ L ( i ) | x V ˜ L ( i ) | y ] T = V ˜ L ( i ) | θ R L [ y i O L y ( x i O L x ) ] T
V ˜ Rw ( i ) = [ V ˜ R ( i ) | x V ˜ R ( i ) | y ] T = V ˜ R ( i ) | θ R R [ ( y i O R y ) x i O R x ] T
V wake , ( i ) | r = k [ Γ L V ˜ Lw ( i ) ( O L , O R , r c ) + Γ R V ˜ Rw ( i ) ( O L , O R , r c ) ]
V D ( i ) ( t ¯ ) = V D ( i ) ( t i ) + t i t ¯ A D ( i ) ( τ ) d τ ,
V D ( i ) ( t ) = V r ( i ) ( t ) = [ cos α i sin α i ] · [ ( Γ L V ˜ Lw ( i ) + Γ R V ˜ Rw ( i ) ) + V wind ] ,
A D ( i ) = V D ( i ) ( t ) t 1 2 π [ cos α i sin α i ] · [ Γ L Ψ L ( i ) Γ R Ψ R ( i ) Γ L Φ L ( i ) + Γ R Φ R ( i ) ] ,
Ψ L ( i ) = V L down , ( i ) | y ( y i O L y ) 2 ( x i O L x ) 2 r c 2 ( R L 2 + r c 2 ) 2 + V L wind , ( i ) | x 2 ( x i O L x ) ( y i O L y ) ( R L 2 + r c 2 ) 2 ,
Ψ R ( i ) = V R down , ( i ) | y ( y i O R y ) 2 ( x i O R x ) 2 r c 2 ( R R 2 + r c 2 ) 2 + V R wind , ( i ) | x 2 ( x i O R x ) ( y i O R y ) ( R R 2 + r c 2 ) 2 ,
Φ L ( i ) = V L wind , ( i ) | x ( x i O L x ) 2 ( y i O L y ) 2 r c 2 ( R L 2 + r c 2 ) 2 + V L down , ( i ) | y 2 ( x i O L x ) ( y i O L y ) ( R L 2 + r c 2 ) 2 ,
Φ R ( i ) = V R wind , ( i ) | x ( x i O R x ) 2 ( y i O R y ) 2 r c 2 ( R R 2 + r c 2 ) 2 + V R down , ( i ) | y 2 ( x i O R x ) ( y i O R y ) ( R R 2 + r c 2 ) 2 .
V L down , ( i ) | y = ( O R x O L x ) Γ R 2 π ( b 0 2 + r c 2 ) , V R down , ( i ) | y = ( O R x O L x ) Γ L 2 π ( b 0 2 + r c 2 ) ,
( i ) ( Γ L , Γ R , O L , O R , r c ; V D ( i ) , x i , y i ) = V wind , ( i ) | r + V wake , ( i ) ( Γ L , Γ R , O L , O R , r c ) | r + V D ( i ) = 0
[ Γ ^ L , Γ ^ R , O ^ L , O ^ R , r ^ c ] = arg min Γ L , Γ R , O L , O R , r c i = 1 M | ( i ) ( Γ L , Γ R , O L , O R , r c ; V D ( i ) , x i , y i ) | 2 s . t . O ^ L ( O ^ L + [ 20 , 20 ] × [ 20 , 20 ] ) , O ^ R ( O ^ R + [ 20 , 20 ] × [ 20 , 20 ] ) , Γ ^ L [ 0 , 800 ] , Γ ^ R [ 0 , 800 ] , r ^ c [ 0 , 6 ] ,
E r = 1 N i = 1 N 1 P T ( i ) | P E ( i ) P T ( i ) | × 100 % ( Relative error ) R M S E r = 1 N i = 1 N ( 1 Γ 0 ( P E ( i ) P T ( i ) ) 2 ) × 100 % ( Relative RMSE of circulation ) R M S E r = 1 N i = 1 N ( 1 b 0 ( P E ( i ) P T ( i ) ) 2 ) × 100 % ( Relative RMSE of vortex core height )

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