Doppler Information Geometry for Wake Turbulence Monitoring

  • Zhongxun Liu
  • Frédéric Barbaresco


Here the concept of Doppler information geometry is summarized and introduced to evaluate the richness of Doppler velocity components of radar signal and applied for wake turbulence monitoring. With the methods of information geometry, we consider all the Toeplitz Hermitian Positive Definite covariance matrices of order n as a manifold \(\Omega _{n}\). Geometries of covariance matrices based on two kinds of radar data models are presented. Finally, a radar detector based on Doppler entropy assessment is analyzed and applied for wake turbulence monitoring. This advanced Doppler processing chain is also implemented by CUDA codes for GPU parallel computation


Information geometry Wake turbulence Radar monitoring GPU computation 


  1. 1.
    Amari, S., Nagaoka, H.: Methods of Information Geometry, Translations of Mathematical monographs, vol. 191. Oxford University Press, Oxford (2000)Google Scholar
  2. 2.
    Amari, S.I.: Information geometry on hierarchy of probability distributions. IEEE Trans. Inf. Theory 47(5), 1701–1711 (2001)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Andric, M.S., Todorovic, B.M.: An application of entropy approach for moving object detection. In: 18th Telecommunications Forum TELFOR 2010, Belgrade, November 2010. pp. 705–708Google Scholar
  4. 4.
    Barbaresco, F.: Innovative tools for radar signal processing based on cartan’s geometry of spd matrices and information geometry. In: Proceedings IEEE Radar Conference RADAR’08, pp. 1–6. (2008)Google Scholar
  5. 5.
    Barbaresco, F.: Information geometry of covariance matrix: Cartan-siegel homogeneous bounded domains, mostow/berger fibration and frchet median. In: MIG Proceedings, pp. 1–6. Springer, Berlin (2012)Google Scholar
  6. 6.
    Barbaresco, F., Brovelli, P., Currier, P., Garrouste, O., Klein, M.,Juge, P., Ricci, Y., Schneider, J.Y.: Radar sensors for wind & wake-vortexmonitoring on airport: first results of SESAR P12.2.2 XP0 trials campaignat Paris CDG Airport, ERAD'12 Conference, Toulouse, June 2012Google Scholar
  7. 7.
    Barbaresco, F., Jeantet, A., Meier, U.: Wake vortex X-band radar monitoring: Paris-CDG airport 2008 campaign results and prospectives. In: Proceedings of the RADAR Radar Conference-Surveillance for a Safer World Internation, pp. 1–6 (2009)Google Scholar
  8. 8.
    Barbaresco, F., Wasselin, J.P., Jeantet, A., Meier, U.: Wake vortex profiling by Doppler X-band radar: Orly trials at initial take-off and ILS interception critical areas. In: Proceedings of the IEEE Radar Conference RADAR’08, pp. 1–6 (2008)Google Scholar
  9. 9.
    Barbaresco, F., Meier, U.: Radar monitoring of a wake vortex: electromagnetic reflection of wake turbulence in clear air. Comptes Rendus Physique 11(1), 54–67 (2010)CrossRefGoogle Scholar
  10. 10.
    Barbaresco, F.: Interactions between symmetric cone and information geometries: Bruhat-tits and siegel spaces models for high resolution autoregressive doppler imagery. In: Nielsen, F. (ed.) Emerging Trends in Visual Computing, Lecture Notes in Computer Science, vol. 5416, pp. 124–163. Springer, Berlin (2009)Google Scholar
  11. 11.
    Bash, S., Carpman, D., Holl, D.: Radar pulse compression using the nvidia cuda framework. In: IEEE High Performance Extreme Computing Conference, vol. 1, p. 1 (2008)Google Scholar
  12. 12.
    Bobylev, A.V., Vyshinsky, V.V., Soudakov, G.G., Yaroshevsky, V.A.: Aircraft vortex wake and flight safety problems. J. Aircr. 47, 663–674 (2010)CrossRefGoogle Scholar
  13. 13.
    De Donno, D., Esposito, A., Tarricone, L., Catarinucci, L.: Introduction to GPU computing and CUDA programming: A case study on FDTD [em programmer’s notebook]. IEEE Antennas Propag. Mag. 52(3), 116–122 (2010)CrossRefGoogle Scholar
  14. 14.
    Gerz, T., Holzpfel, F., Darracq, D.: Commercial aircraft wake vortices. Prog. Aerosp. Sci. 38(3), 181–208 (2002)CrossRefGoogle Scholar
  15. 15.
    Ginevsky, A., Zhelannikov, A.: Vortex Wakes of Aircrafts, Foundations of Engineering Mechanics. Springer, Berlin (2009)CrossRefGoogle Scholar
  16. 16.
    Liu, Z., Jeannin, N., Vincent, F., Wang, X.: Development of a radarsimulator for monitoring wake vortices in rainy weather. Radar (Radar),2011 IEEE CIE International Conference on vol.1, pp. 284--287, 24--27Oct 2011. doi:  10.1109/CIE-Radar.2011.6159533
  17. 17.
    Lu, Y., Wang, K., Liu, X., Yu, W.: A GPU based real-time SAR simulation for complex scenes. In: International Radar Conference, Bordeaux, October 2009Google Scholar
  18. 18.
    NVIDIA: NVIDIA CUDA Programming Guide Version 1.0. NVIDIA (2007)Google Scholar
  19. 19.
    Pettersson, J.: Radar Signal Processing with Graphics Processors (GPUs). Master’s thesis, Uppsala Universitet (2010)Google Scholar
  20. 20.
    Shariff, K., Wray, A.: Analysis of the radar reflectivity of aircraft vortex wakes. J. Fluid Mech 463, 121–161 (2002)Google Scholar
  21. 21.
    Srivastava, S., Gupta, M.: Bayesian estimation of the entropy of the multivariate gaussian. In: IEEE International Symposium on Information Theory ISIT 2008. pp. 1103–1107 (2008)Google Scholar
  22. 22.
    Trench, W.F.: An algorithm for the inversion of finite toeplitz matrices. J. Soc. Ind. App. Math. 12(3), 515–522 (1964).
  23. 23.
    Vanhoenacker-Janvier, D., Djafri, K., della Faille de Leverghem, R., van Swieten, B., Barbaresco, F.: Simulation of the Radar cross-sectionof wake vortices in clear air, ERAD'12 Conference, Toulouse, June 2012Google Scholar
  24. 24.
    Weber, R., Gothandaraman, A., Hinde, R., Peterson, G.: Comparing hardware accelerators in scientific applications: A case study. IEEE Trans. Parallel Distributed Syst. 22(1), 58–68 (2011)CrossRefGoogle Scholar
  25. 25.
    Yang, L.: Riemannian median and its estimation. LMS J. Comput. Math. 13, 461–479 (2010)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Yang, L., Arnaudon, M., Barbaresco, F.: Riemannian median, geometry of covariance matrices and radar target detection. In: European Radar Conference (EuRAD) 2010, pp. 415–418 (2010)Google Scholar
  27. 27.
    Yang, L., Arnaudon, M., Barbaresco, F.: Geometry of covariance matrices and computation of median. In: Proceedings of the 30th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and, Engineering (2010)Google Scholar
  28. 28.
    Zhang B., Liu G.-b., Liu D., Fan Z.-L.: Real-time software gnss signal simulator accelerated by cuda. In: 2nd International Conference on Future Computer and Communication [Volume 1] (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of Toulouse, ISAEToulouseFrance
  2. 2.College of Electronic Science and EngineeringNational University of Defense TechnologyChangshaPeople’s Republic of China
  3. 3.Advanced Developments DepartmentThales Air Systems, Surface Radar Domain, Technical DirectorateLimoursFrance

Personalised recommendations