Abstract

Aircraft wake is a pair of strong counter-rotating vortices generated behind a flying aircraft. It might be very hazardous to a following aircraft and the real-time detection of it is of great interest in aviation safety field. Vortex-core positions and velocity circulations, which respectively represent the location and strength of a wake, are two characteristic parameters that have attracted the main attention in wake vortex detection. This paper introduces a new algorithm, the Path Integration (PI) method, to retrieve the characteristic parameters of wake vortex. The method uses Doppler velocity distribution to locate the vortex-core positions, and the integration of Doppler velocity along a LOS (line-of-sight) is derived as a linear expression about the circulations. From this expression, the circulations can be solved with the least square method. Moreover, an vortex-core position adjusting method is proposed to compensate the compressing and expanding effects of wake vortex caused by the scanning of Lidar beam. Basically, the use of Doppler velocity integration can improve the method’s adaptability in turbulence environment and mitigate the impact of noise. Numerical examples and field detection data from Hong Kong international airport and Tsingtao Liuting airport have well verified the good performance of the method, in terms of both accuracy and efficiency.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]

2018 (3)

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[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]

H. Gao, J. Li, P. W. Chan, K. K. Hon, and X. Wang, “Parameter-retrieval of dry-Air wake vortices with a scanning Doppler Lidar,” Opt. Express 26(13), 16377–16392 (2018).
[Crossref]

2017 (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]

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]

L. Thobois, “Next generation scanning Lidar systems for optimizing wake turbulence separation minima,” J. Radar 6(6), 689–698 (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), 660–672 (2017).
[Crossref]

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

J. Schneider, G. Beauquet, and F. Barbaresco, “Circulation retrieval of wake vortices under rainy conditions with an X band Radar,” J. Radar 6(6), 673–699 (2017).
[Crossref]

J. Liu, L. Ma, Z. Chen, and Y. Cai, “Radar target detection method of aircraft wake vortices based on matrix information geometry,” J. Radar 6(6), 660–672 (2017).
[Crossref]

2016 (3)

F. Barbaresco, V. Brion, and N. Jeannin, “Radar wake-vortices cross-section/Doppler signature characterisation based on simulation and field tests trials,” IET Radar Sonar Nav. 10(1), 82–96 (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]

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 (3)

2011 (2)

C. Breitsamter, “Wake vortex characteristics of transport aircraft,” Prog. Aerospace Sci. 47(2), 89–134 (2011).
[Crossref]

J. Li, X. S. Wang, and T. Wang, “Modeling of Aircraft Wake Vortices’ Dielectric Constant Distribution for Radar Detection,” IEEE Trans. Aerosp. Electron. Syst. 47(2), 820–831 (2011).
[Crossref]

2009 (1)

Z. C. Zheng, X. Ying, and D. K. Wilson, “Behaviors of vortex wake in random atmospheric turbulence,” J. Aircraft. 46(6), 2139–2144 (2009).
[Crossref]

2008 (1)

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

2007 (1)

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

2005 (1)

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

2003 (2)

F. Holzäpfel, “Probabilistic Two-Phase wake vortex decay and transport model,” J. Aircraft. 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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

2002 (1)

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38(3), 181–208 (2002).
[Crossref]

2001 (1)

R. E. Robins, D. P. Delisi, and G. C. Greene, “Algorithm for prediction of trailing vortex evolution,” J. Aircraft. 38(5), 911–917 (2001).
[Crossref]

1979 (2)

P. G. Saffman, “The approach of a vortex pair to a plane surface in inviscid fluid,” J. Fluid Mech. 92(3), 497–503 (1979).
[Crossref]

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. 17(4), 113–128 (1979).
[Crossref]

Banakh, V.

V. Banakh and I. N. Smalikho, Coherent Doppler wind Lidars in a turbulence atmosphere (Artech House, 2013), Chap. 2.

Banakh, V. A.

Barbaresco, F.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

J. Schneider, G. Beauquet, and F. Barbaresco, “Circulation retrieval of wake vortices under rainy conditions with an X band Radar,” J. Radar 6(6), 673–699 (2017).
[Crossref]

F. Barbaresco, V. Brion, and N. Jeannin, “Radar wake-vortices cross-section/Doppler signature characterisation based on simulation and field tests trials,” IET Radar Sonar Nav. 10(1), 82–96 (2016).
[Crossref]

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 Sci. Days (URSI-France, 2015), pp. 81–110.

D. Kovalev, D. Vanhoenacker-Janvier, R. Wilson, and F. Barbaresco, “Electromagnetic wind radar simulator validation using meteorological data and a zenith X-band radar,” in Proceedings of European Radar Conference (IEEE, 2016), pp. 121–124.

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.

Beauquet, G.

J. Schneider, G. Beauquet, and F. Barbaresco, “Circulation retrieval of wake vortices under rainy conditions with an X band Radar,” J. Radar 6(6), 673–699 (2017).
[Crossref]

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 Sci. Days (URSI-France, 2015), pp. 81–110.

Breitsamter, C.

C. Breitsamter, “Wake vortex characteristics of transport aircraft,” Prog. Aerospace Sci. 47(2), 89–134 (2011).
[Crossref]

Bricteux, L.

S. Brousmiche, L. Bricteux, G. Winckelmans, B. Macq, and P. Sobieski, Advances in Geoscience and Remote Sensing (Intech, 2009), Chap. 11.

Brion, V.

F. Barbaresco, V. Brion, and N. Jeannin, “Radar wake-vortices cross-section/Doppler signature characterisation based on simulation and field tests trials,” IET Radar Sonar Nav. 10(1), 82–96 (2016).
[Crossref]

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 Sci. Days (URSI-France, 2015), pp. 81–110.

Brousmiche, S.

S. Brousmiche, L. Bricteux, G. Winckelmans, B. Macq, and P. Sobieski, Advances in Geoscience and Remote Sensing (Intech, 2009), Chap. 11.

Brusquet, L. L.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

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. Federal Aviation Administration, Report No. DOT-TSC-FAA-79-103, 1982.

Cai, Y.

J. Liu, L. Ma, Z. Chen, and Y. Cai, “Radar target detection method of aircraft wake vortices based on matrix information geometry,” J. Radar 6(6), 660–672 (2017).
[Crossref]

Cariou, J. 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 Sci. Days (URSI-France, 2015), pp. 81–110.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

Chan, P. W.

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]

Chen, Z.

J. Liu, L. Ma, Z. Chen, and Y. Cai, “Radar target detection method of aircraft wake vortices based on matrix information geometry,” J. Radar 6(6), 660–672 (2017).
[Crossref]

Coustols, E.

L. Jacquin, D. Fabre, P. Geffory, and E. Coustols, “The properties of a transport aircraft wake in the extended near field: an experiment study,” presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8–11 Jan. 2001.

Darracq, D.

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38(3), 181–208 (2002).
[Crossref]

Delisi, D. P.

R. E. Robins, D. P. Delisi, and G. C. Greene, “Algorithm for prediction of trailing vortex evolution,” J. Aircraft. 38(5), 911–917 (2001).
[Crossref]

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, 7–10 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.

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 Sci. Days (URSI-France, 2015), pp. 81–110.

Dolfi-Bouteyre, A.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 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 Sci. Days (URSI-France, 2015), pp. 81–110.

Doviak, R. J.

R. J. Doviak and D. S. Zrnic, Doppler Radar and Weather Observations (Academic Press, 1993).

Duponcheel, M.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

Fabre, D.

L. Jacquin, D. Fabre, P. Geffory, and E. Coustols, “The properties of a transport aircraft wake in the extended near field: an experiment study,” presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8–11 Jan. 2001.

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 Sci. Days (URSI-France, 2015), pp. 81–110.

Fleury, G.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

Frehlich, R.

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

Gao, H.

H. Gao, J. Li, P. W. Chan, K. K. Hon, and X. Wang, “Parameter-retrieval of dry-Air wake vortices with a scanning Doppler Lidar,” Opt. Express 26(13), 16377–16392 (2018).
[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, 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), 660–672 (2017).
[Crossref]

H. Gao, “Parameter-retrieval of dry-air wake vortices with a scanning Doppler Lidar,” Master Degree Thesis, NUDT (National University of Defense technology), 2018.

Geffory, P.

L. Jacquin, D. Fabre, P. Geffory, and E. Coustols, “The properties of a transport aircraft wake in the extended near field: an experiment study,” presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8–11 Jan. 2001.

Gerz, T.

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. Oceanic Technol. 20(8), 1183–1195 (2003).
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T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38(3), 181–208 (2002).
[Crossref]

Greene, G. C.

R. E. Robins, D. P. Delisi, and G. C. Greene, “Algorithm for prediction of trailing vortex evolution,” J. Aircraft. 38(5), 911–917 (2001).
[Crossref]

Haan, S. D.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

Hallermeyer, A.

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 Sci. Days (URSI-France, 2015), pp. 81–110.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

Hallock, J. N.

D. C. Burnham and J. N. Hallock, “Chicago monostatic acoustic vortex sensing system,” U. S. Federal Aviation Administration, Report No. DOT-TSC-FAA-79-103, 1982.

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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

Hinton, D. A.

D. A. Hinton and C. R. Tatnall, “A candidate wake vortex strength definition for application to the NASA aircraft vortex spacing system (AVOSS),” Technical Report, NASA Langley Technical Report Server, 1997.

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]

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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

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

T. Gerz, F. Holzäpfel, and D. Darracq, “Commercial aircraft wake vortices,” Prog. Aerospace Sci. 38(3), 181–208 (2002).
[Crossref]

Hon, K. K.

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, 7–10 Jan. 2013.

Jacquin, L.

L. Jacquin, D. Fabre, P. Geffory, and E. Coustols, “The properties of a transport aircraft wake in the extended near field: an experiment study,” presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8–11 Jan. 2001.

Jeannin, N.

F. Barbaresco, V. Brion, and N. Jeannin, “Radar wake-vortices cross-section/Doppler signature characterisation based on simulation and field tests trials,” IET Radar Sonar Nav. 10(1), 82–96 (2016).
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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 Sci. Days (URSI-France, 2015), pp. 81–110.

Köpp, F.

S. Rahm, I. N. Smalikho, and F. Köpp, “Characterization of aircraft wake vortices by airborne coherent Doppler Lidar,” J. Aircr. 44(3), 799–805 (2007).
[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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

Kovalev, D.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
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D. Kovalev, “Radar signature simulator based on large eddy simulation of wake vortices in turbulent and stratified atmospheres,” PhD Report, UCL (Université Catholique de Louvain), 2019.

D. Kovalev, D. Vanhoenacker-Janvier, R. Wilson, and F. Barbaresco, “Electromagnetic wind radar simulator validation using meteorological data and a zenith X-band radar,” in Proceedings of European Radar Conference (IEEE, 2016), pp. 121–124.

Krasnov, O.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

Lai, D. Y.

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, 7–10 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.

Lamb, H.

H. Lamb, Hydrodynamics (Cambridge University Press, 1932), Chap. 11.

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 Sci. Days (URSI-France, 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]

H. Gao, J. Li, P. W. Chan, K. K. Hon, and X. Wang, “Parameter-retrieval of dry-Air wake vortices with a scanning Doppler Lidar,” Opt. Express 26(13), 16377–16392 (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), 660–672 (2017).
[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, 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).
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J. Li, X. S. Wang, and T. Wang, “Modeling of Aircraft Wake Vortices’ Dielectric Constant Distribution for Radar Detection,” IEEE Trans. Aerosp. Electron. Syst. 47(2), 820–831 (2011).
[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]

J. Liu, L. Ma, Z. Chen, and Y. Cai, “Radar target detection method of aircraft wake vortices based on matrix information geometry,” J. Radar 6(6), 660–672 (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]

Ma, L.

J. Liu, L. Ma, Z. Chen, and Y. Cai, “Radar target detection method of aircraft wake vortices based on matrix information geometry,” J. Radar 6(6), 660–672 (2017).
[Crossref]

Macq, B.

S. Brousmiche, L. Bricteux, G. Winckelmans, B. Macq, and P. Sobieski, Advances in Geoscience and Remote Sensing (Intech, 2009), Chap. 11.

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).
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Nijhuis, A. O.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[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 Sci. Days (URSI-France, 2015), pp. 81–110.

Ploumhans, P.

G. S. Winckelmans, F. Thirifay, and P. Ploumhans, “Effect of non-uniform wind shear onto vortex wakes: parametetric models for operational systems and comparison with CFD studies,” presented at the 4th WakeNet Workshop on “Wake Vortex Encounter”, Amsterdam, The Netherlands, 16-17 Oct. 2000.

Proctor, F. H.

F. H. Proctor, “The NASA-Langley wake vortex modelling effort in support of an operational aircraft spacing system,” presented at the 36th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 12–15 Jan. 1998.

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]

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

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

Robins, R. E.

R. E. Robins, D. P. Delisi, and G. C. Greene, “Algorithm for prediction of trailing vortex evolution,” J. Aircraft. 38(5), 911–917 (2001).
[Crossref]

Saffman, P. G.

P. G. Saffman, “The approach of a vortex pair to a plane surface in inviscid fluid,” J. Fluid Mech. 92(3), 497–503 (1979).
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Schneider, J.

J. Schneider, G. Beauquet, and F. Barbaresco, “Circulation retrieval of wake vortices under rainy conditions with an X band Radar,” J. Radar 6(6), 673–699 (2017).
[Crossref]

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. Oceanic Technol. 22(2), 117–130 (2005).
[Crossref]

Smalikho, I. N.

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]

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]

I. N. Smalikho and V. A. Banakh, “Estimation of aircraft wake vortex parameters from data measured with a 1.5-µm coherent Doppler Lidar,” Opt. Lett. 40(14), 3408–3411 (2015).
[Crossref]

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

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

V. Banakh and I. N. Smalikho, Coherent Doppler wind Lidars in a turbulence atmosphere (Artech House, 2013), Chap. 2.

Sobieski, P.

S. Brousmiche, L. Bricteux, G. Winckelmans, B. Macq, and P. Sobieski, Advances in Geoscience and Remote Sensing (Intech, 2009), Chap. 11.

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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

Tatnall, C. R.

D. A. Hinton and C. R. Tatnall, “A candidate wake vortex strength definition for application to the NASA aircraft vortex spacing system (AVOSS),” Technical Report, NASA Langley Technical Report Server, 1997.

Thirifay, F.

G. S. Winckelmans, F. Thirifay, and P. Ploumhans, “Effect of non-uniform wind shear onto vortex wakes: parametetric models for operational systems and comparison with CFD studies,” presented at the 4th WakeNet Workshop on “Wake Vortex Encounter”, Amsterdam, The Netherlands, 16-17 Oct. 2000.

Thobois, L.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

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

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 Sci. Days (URSI-France, 2015), pp. 81–110.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

Valla, M.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 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 Sci. Days (URSI-France, 2015), pp. 81–110.

Vanhoenacker-Janvier, D.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

D. Kovalev, D. Vanhoenacker-Janvier, R. Wilson, and F. Barbaresco, “Electromagnetic wind radar simulator validation using meteorological data and a zenith X-band radar,” in Proceedings of European Radar Conference (IEEE, 2016), pp. 121–124.

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), 660–672 (2017).
[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, 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. Li, X. S. Wang, and T. Wang, “Modeling of Aircraft Wake Vortices’ Dielectric Constant Distribution for Radar Detection,” IEEE Trans. Aerosp. Electron. Syst. 47(2), 820–831 (2011).
[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]

H. Gao, J. Li, P. W. Chan, K. K. Hon, and X. Wang, “Parameter-retrieval of dry-Air wake vortices with a scanning Doppler Lidar,” Opt. Express 26(13), 16377–16392 (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), 660–672 (2017).
[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, 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]

Wang, X. S.

J. Li, X. S. Wang, and T. Wang, “Modeling of Aircraft Wake Vortices’ Dielectric Constant Distribution for Radar Detection,” IEEE Trans. Aerosp. Electron. Syst. 47(2), 820–831 (2011).
[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.

Z. C. Zheng, X. Ying, and D. K. Wilson, “Behaviors of vortex wake in random atmospheric turbulence,” J. Aircraft. 46(6), 2139–2144 (2009).
[Crossref]

Wilson, R.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

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 Sci. Days (URSI-France, 2015), pp. 81–110.

D. Kovalev, D. Vanhoenacker-Janvier, R. Wilson, and F. Barbaresco, “Electromagnetic wind radar simulator validation using meteorological data and a zenith X-band radar,” in Proceedings of European Radar Conference (IEEE, 2016), pp. 121–124.

Winckelmans, G.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 13–17 Jun. 2016.

S. Brousmiche, L. Bricteux, G. Winckelmans, B. Macq, and P. Sobieski, Advances in Geoscience and Remote Sensing (Intech, 2009), Chap. 11.

Winckelmans, G. S.

G. S. Winckelmans, F. Thirifay, and P. Ploumhans, “Effect of non-uniform wind shear onto vortex wakes: parametetric models for operational systems and comparison with CFD studies,” presented at the 4th WakeNet Workshop on “Wake Vortex Encounter”, Amsterdam, The Netherlands, 16-17 Oct. 2000.

Yarovoy, A.

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

Ying, X.

Z. C. Zheng, X. Ying, and D. K. Wilson, “Behaviors of vortex wake in random atmospheric turbulence,” J. Aircraft. 46(6), 2139–2144 (2009).
[Crossref]

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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

Zheng, Z. C.

Z. C. Zheng, X. Ying, and D. K. Wilson, “Behaviors of vortex wake in random atmospheric turbulence,” J. Aircraft. 46(6), 2139–2144 (2009).
[Crossref]

Zrnic, D. S.

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. 17(4), 113–128 (1979).
[Crossref]

R. J. Doviak and D. S. Zrnic, Doppler Radar and Weather Observations (Academic Press, 1993).

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]

Bull. Am. Meteorol. Soc. (1)

A. O. Nijhuis, L. Thobois, F. Barbaresco, S. D. Haan, A. Dolfi-Bouteyre, D. Kovalev, O. Krasnov, D. Vanhoenacker-Janvier, R. Wilson, and A. Yarovoy, “Wind hazard and turbulence monitoring at airports with Lidar, Radar, and Mode-S downlinks: The UFO Project,” Bull. Am. Meteorol. Soc. 99(11), 2275–2293 (2018).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst. (5)

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. Li, X. S. Wang, and T. Wang, “Modeling of Aircraft Wake Vortices’ Dielectric Constant Distribution for Radar Detection,” IEEE Trans. Aerosp. Electron. Syst. 47(2), 820–831 (2011).
[Crossref]

IEEE Trans. Geosci. Electron. (1)

D. S. Zrnic, “Estimation of spectral moments for weather echoes,” IEEE Trans. Geosci. Electron. 17(4), 113–128 (1979).
[Crossref]

IET Radar Sonar Nav. (1)

F. Barbaresco, V. Brion, and N. Jeannin, “Radar wake-vortices cross-section/Doppler signature characterisation based on simulation and field tests trials,” IET Radar Sonar Nav. 10(1), 82–96 (2016).
[Crossref]

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[Crossref]

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

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R. E. Robins, D. P. Delisi, and G. C. Greene, “Algorithm for prediction of trailing vortex evolution,” J. Aircraft. 38(5), 911–917 (2001).
[Crossref]

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

Z. C. Zheng, X. Ying, and D. K. Wilson, “Behaviors of vortex wake in random atmospheric turbulence,” J. Aircraft. 46(6), 2139–2144 (2009).
[Crossref]

J. Atmos. Oceanic 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. Oceanic Technol. 20(8), 1183–1195 (2003).
[Crossref]

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

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J. Schneider, G. Beauquet, and F. Barbaresco, “Circulation retrieval of wake vortices under rainy conditions with an X band Radar,” J. Radar 6(6), 673–699 (2017).
[Crossref]

J. Liu, L. Ma, Z. Chen, and Y. Cai, “Radar target detection method of aircraft wake vortices based on matrix information geometry,” J. Radar 6(6), 660–672 (2017).
[Crossref]

L. Thobois, “Next generation scanning Lidar systems for optimizing wake turbulence separation minima,” J. Radar 6(6), 689–698 (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), 660–672 (2017).
[Crossref]

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

Opt. Express (2)

Opt. Lett. (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. (2)

C. Breitsamter, “Wake vortex characteristics of transport aircraft,” Prog. Aerospace Sci. 47(2), 89–134 (2011).
[Crossref]

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[Crossref]

Other (18)

D. Kovalev, “Radar signature simulator based on large eddy simulation of wake vortices in turbulent and stratified atmospheres,” PhD Report, UCL (Université Catholique de Louvain), 2019.

D. Kovalev, D. Vanhoenacker-Janvier, R. Wilson, and F. Barbaresco, “Electromagnetic wind radar simulator validation using meteorological data and a zenith X-band radar,” in Proceedings of European Radar Conference (IEEE, 2016), pp. 121–124.

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, 7–10 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.

A. Hallermeyer, A. Dolfi-Bouteyre, M. Valla, L. L. 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, United States, 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 Sci. Days (URSI-France, 2015), pp. 81–110.

V. Banakh and I. N. Smalikho, Coherent Doppler wind Lidars in a turbulence atmosphere (Artech House, 2013), Chap. 2.

S. Brousmiche, L. Bricteux, G. Winckelmans, B. Macq, and P. Sobieski, Advances in Geoscience and Remote Sensing (Intech, 2009), Chap. 11.

D. A. Hinton and C. R. Tatnall, “A candidate wake vortex strength definition for application to the NASA aircraft vortex spacing system (AVOSS),” Technical Report, NASA Langley Technical Report Server, 1997.

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H. Lamb, Hydrodynamics (Cambridge University Press, 1932), Chap. 11.

F. H. Proctor, “The NASA-Langley wake vortex modelling effort in support of an operational aircraft spacing system,” presented at the 36th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 12–15 Jan. 1998.

G. S. Winckelmans, F. Thirifay, and P. Ploumhans, “Effect of non-uniform wind shear onto vortex wakes: parametetric models for operational systems and comparison with CFD studies,” presented at the 4th WakeNet Workshop on “Wake Vortex Encounter”, Amsterdam, The Netherlands, 16-17 Oct. 2000.

L. Jacquin, D. Fabre, P. Geffory, and E. Coustols, “The properties of a transport aircraft wake in the extended near field: an experiment study,” presented at the 39th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 8–11 Jan. 2001.

H. Gao, “Parameter-retrieval of dry-air wake vortices with a scanning Doppler Lidar,” Master Degree Thesis, NUDT (National University of Defense technology), 2018.

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.

R. J. Doviak and D. S. Zrnic, Doppler Radar and Weather Observations (Academic Press, 1993).

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Figures (18)

Fig. 1.
Fig. 1. The impact of wake vortex to a following aircraft [15].
Fig. 2.
Fig. 2. Proposed geometry setup for Lidar detection of wake vortex. $P$ is a point inside the wake, $V_{L}$ and $V_{R}$ are the velocities deduced by the two vortices, $l_{n}$ is the length of measurement bins under consideration, $l'_{n}$ is a part of circle centering at the left vortex core $O_{c1}$, $l''_{n}$ is a part of radius connecting $A_{n}$ and $C_{n}$, and $S_{n}$ is the area surrounded by lines $l''_{n}$, $l'_{n}$ and $l_{n}$, $V_{c}$ is the cross wind, $V_{\epsilon }$ is the turbulence wind.
Fig. 3.
Fig. 3. Determination of vortex-cores’ radial distances by Doppler velocity range distribution, where the Doppler velocity range is the difference between the maximum and minimum of Doppler velocity along the elevation.
Fig. 4.
Fig. 4. Regions free of wake vortex that was used to estimate the background wind.
Fig. 5.
Fig. 5. Different velocity profile models for a vortex, where the circulation $\Gamma = 400 m^2/s$, the distance between the two vortices $b_{0}=50m$.
Fig. 6.
Fig. 6. Ground effect modeled by image vortices.
Fig. 7.
Fig. 7. Proposed integration path configuration for circulation retrieval, where the thick lines are the integration paths to be used.
Fig. 8.
Fig. 8. Simulated radial velocity distribution of wake vortices in a RHI.
Fig. 9.
Fig. 9. Comparison between the theoretical and estimated vortex core trajectories.
Fig. 10.
Fig. 10. Circulation Results obtained by PI method and TV method.
Fig. 11.
Fig. 11. Geometry setup of the detection campaign in HKIA, 2014 [29].
Fig. 12.
Fig. 12. An example of radial velocity distribution of wake vortices observed in Hong Kong in 2014.
Fig. 13.
Fig. 13. Vortex core locating results for two cases observed at Hong Kong international airport in 2014.
Fig. 14.
Fig. 14. Circulation retrieval results for two cases observed at Hong Kong international airport in 2014.
Fig. 15.
Fig. 15. Geometry setup of the observation in Tsingtao Liuting international airport, 2018.
Fig. 16.
Fig. 16. An example of radial velocity distribution of wake vortices observed in Tsingtao in 2018.
Fig. 17.
Fig. 17. Vortex core locating results for two cases observed at Tsingtao international airport in 2018.
Fig. 18.
Fig. 18. Vortex core circulation results for two cases observed at Tsingtao international airport in 2018.

Tables (2)

Tables Icon

Table 1. Lidar parameters used in the simulations.

Tables Icon

Table 2. Circulation results with PI method, Opt method and TV method under different turbulence and background wind simulation parameters.

Equations (30)

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Δ V ( R ) = max α V d ( R , α ) min α V d ( R , α ) , α [ α min , α max ] ,
α ^ c i = argmax α V d ( R c i , α ) + argmin α V d ( R c i , α ) 2 , α [ α min , α max ] ,
V = V L + V R + V c + V ϵ ,
V c = V c x x + V c y y .
V c x = V c 0 + β y ,
V r = V c 0 cos α + β y cos α + V c y sin α .
V ~ = V V c = V L + V R + V ϵ .
l n + l n + l n V L d l = S n × V L d S .
V t ( r ) = { Γ 2 π r c r r c , r r c , Γ 2 π r , r > r c ,
× V = { Γ π r c 2 , r r c 0 , r > r c .
S n × V L d S = 0.
l n V L d l = 0.
l n V L d l = θ c 1 2 π Γ c 1 ,
θ c 1 = arg ( O c 1 A n ) x + i ( O c 1 A n ) y ( O c 1 B n ) x + i ( O c 1 B n ) y ,
l n V L d l = θ c 1 2 π Γ c 1 .
l n V R d l = θ c 2 2 π Γ c 2 .
l n V ϵ d l 0.
l n V ~ d l = l n ( V V c ) d l = l n ( V L + V R + V ϵ ) d l = 1 2 π ( θ c 1 Γ c 1 + θ c 2 Γ c 2 ) .
l n V ~ d l m = 1 M n V ~ ( α n , m ) δ ,
[ m = 1 M 1 V ~ ( α 1 , m ) m = 1 M 2 V ~ ( α 2 , m ) m = 1 M N V ~ ( α N , m ) ] 1 2 π δ [ θ c 1 ( 1 ) θ c 2 ( 1 ) θ c 1 ( 2 ) θ c 2 ( 2 ) θ c 1 ( N ) θ c 2 ( N ) ] [ Γ c 1 Γ c 2 ] Θ [ Γ c 1 Γ c 2 ] ,
[ Γ ^ c 1 Γ ^ c 2 ] [ Θ H Θ ] 1 Θ H [ m = 1 M 1 V ~ ( α 1 , m ) m = 1 M 2 V ~ ( α 2 , m ) m = 1 M N V ~ ( α N , m ) ] .
V c 1 , descent = | Γ c 2 | 2 π b 0 , V c 2 , descent = | Γ c 1 | 2 π b 0 .
O ^ c 1 ( t n ) = O c 1 ( t c 1 ) + [ V c x V c y | Γ c 2 | 2 π b ^ 0 ] ( t n t c 1 ) , O ^ c 2 ( t n ) = O c 2 ( t c 2 ) + [ V c x V c y | Γ c 1 | 2 π b ^ 0 ] ( t n t c 2 ) ,
[ m = 1 M 1 V ~ ( α 1 , m ) m = 1 M 2 V ~ ( α 2 , m ) m = 1 M N V ~ ( α N , m ) ] = Θ ( Γ ^ c 1 , Γ ^ c 2 ) [ Γ ^ c 1 Γ ^ c 2 ] ,
[ Γ ^ c 1 Γ ^ c 2 ] [ Θ ( Γ ^ c 1 , Γ ^ c 2 ) H Θ ( Γ ^ c 1 , Γ ^ c 2 ) ] 1 Θ ( Γ ^ c 1 , Γ ^ c 2 ) H [ m = 1 M 1 V ~ ( α 1 , m ) m = 1 M 2 V ~ ( α 2 , m ) m = 1 M N V ~ ( α N , m ) ] .
O ^ c 1 ( t ~ ) = O c 1 ( t c 1 ) + [ V c x V c y | Γ c 2 | 2 π b ^ 0 ] ( t ~ t c 1 ) , O ^ c 2 ( t ~ ) = O c 2 ( t c 2 ) + [ V c x V c y | Γ c 1 | 2 π b ^ 0 ] ( t ~ t c 2 ) .
l n V ~ d l = 1 2 π [ ( θ c 1 θ img , c 1 ) Γ c 1 + ( θ c 2 θ img , c 2 ) Γ c 2 ] .
z ( t s ) = k = 1 N ( ρ k S 0 exp [ ( t s 2 r k / c ) 2 2 σ w 2 ] × exp ( 4 π j t s v k / λ ) + n k ) ,
E s = 1 N j = 1 N | P c i ( j ) P c i j b 0 | × 100 % , i = 1 , 2 ,
E r = 1 N j = 1 N | Γ c i ( j ) Γ c i j Γ c i j | × 100 % , i = 1 , 2 ,

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