Radar Target Detection Method of Aircraft Wake Vortices Based on Matrix Information Geometry
Liu Junkai①* Li Jianbing② Ma Liang① Chen Zhongkuan① Cai Yichao①
①(Air Force Early Warning Academy, Wuhan 430019, China) ②(School of Electronic Science and Engineering, National University of Denfense Technology, Changsha 410073, China)
Abstract：The application of matrix information geometry to radar signal processing and target detection is a new and interesting subject. Wake vortices are Doppler-spread after Fourier transform. The traditional Moving Target Detection (MTD) method cannot adequately accumulate returns power of the whole spectrum. Based on matrix information geometry, a matrix Constant False Alarm Rate (CFAR) detection method is proposed to improve the detection performance of a weak wake target. In this method, covariance matrices of the observed data can be constructed into a matrix manifold; compared with CFAR detection, the geodesic distance between the covariance matrix in the detection cell and the mean of covariance matrices in the secondary cell is regarded as the detection statistics. Using simulated wake vortices, the return data in background noise and the iterative estimation performance of Riemannian mean are analyzed; the geodesic distance of covariance matrices of target return and noise with varying signal-noise rate is analyzed; and the detection performance of the matrix CFAR and the conventional MTD method is compared.
刘俊凯, 李健兵, 马 梁, 陈忠宽, 蔡益朝. 基于矩阵信息几何的飞机尾流目标检测方法[J]. 雷达学报, 2017, 6(6): 699-708.
Liu Junkai, Li Jianbing, Ma Liang, Chen Zhongkuan, Cai Yichao. Radar Target Detection Method of Aircraft Wake Vortices Based on Matrix Information Geometry. JOURNAL OF RADARS, 2017, 6(6): 699-708.
Sun Hua-fei, Zhang Zhen-ning, Peng Lin-yu, et al.. An Elementary Introduction to Information Geometry[M]. Beijing: Science Press, 2016.
[2]
Rao C. Information and the accuracy attainable in the estimation of statistical parameters[J]. Bulletin of Calcutta Mathematical Society, 1945, 37: 81-91.
[3]
Chencov N N. Statistical Decision Rules and Optimal Inference[M]. Rhode Island, USA: American Mathematical Society, 1982.
[4]
Amari S I and Nagaoka H. Methods of Information Geometry[M]. Providence, RI: American Mathematical Society, 2000.
[5]
Lenglet C, Rousson M, Deriche R, et al.. Statistics on the manifold of multivariate normal distributions: Theory and application to diffusion tensor MRI processing[J]. Journal of Mathematical Imaging and Vision, 2006, 25(3): 423-444. DOI:10.1007/s10851-006-6897-z.
[6]
Moakher M. A differential geometric approach to the geometric mean of symmetric positive-definite matrices[J]. SIAM Journal on Matrix Analysis and Applications, 2005, 26(3): 735-747. DOI:10.1137/S0895479803436937.
[7]
Nielsen F and Bhatia R. Matrix Information Geometry[M]. Berlin Heidelberg: Springer, 2013.
[8]
Barbaresco F. Interactions between symmetric cone and information geometries: Bruhat-Tits and Siegel spaces models for high resolution autoregressive Doppler imagery[C]. Proceedings of ETVC 2008 Conference, Berlin, Heidelberg, 2009: 124-163.
[9]
Barbaresco F. Innovative tools for radar signal processing based on Cartan's geometry of SPD matrices & information geometry[C]. Proceedings of 2008 IEEE Radar Conference, Rome, 2008: 1-6.
[10]
Pennec X. Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements[J]. Journal of Mathematical Imaging and Vision, 2006, 25(1): 127-154. DOI:10.1007/s10851-006-6228-4.
[11]
Barbaresco F. Robust statistical radar processing in Fréchet metric space: OS-HDR-CFAR and OS-STAP processing in Siegel homogeneous bounded domains[C]. Proceedings of 2011 IEEE International Radar Symposium, Leipzig, Germany, 2011: 639-644.
Li Xiang, Cheng Yong-qiang, Wang Hong-qiang, et al.. Methods of Information Geometry of Radar Signal Processing[M]. Beijing: Science Press, 2014.
[13]
Broderick A J, Bevilaqua P, Crouch J, et al.. Wake Turbulence: An Obstacle to Increased Air Traffic Capacity[M]. Washington, DC: The National Academies Press, 2008: 1-59.
Liu Jun-kai, Li Wen-chen, Wang Xue-song, et al.. Extraction of aircraft wake vortices radar returns based on the Doppler characteristics[J]. Journal of System Simulation, 2011, 23(7): 1323-1328. DOI:10.16182/j.cnki.joss.2011.07.015.
[15]
Gerz T, Holzäpfel F, and Darracq D. Commercial aircraft wake vortices[J]. Progress in Aerospace Sciences, 2002, 38(3): 181-208. DOI:10.1016/S0376-0421(02)00004-0.
[16]
Shephard D J, Kyte A P, and Segura C A. Radar wake vortex measurements at F and I band[C]. Proceedings of IEE Colloquium on Radar and Microwave Imaging, London, 1994: 7/1-7/5.
Wang Shou-yong, Wan Yang, Liu Jun-kai, et al.. Modern Radar Target Detection Theory and Methods[M]. Second Edition, Beijing: Science Press, 2015.
[18]
Calvo M and Oller J M. An explicit solution of information geodesic equations for the multivariate normal model[J]. Statistics & Risk Modeling, 1991, 9(1/2): 119-138.
2017, Vol. 6 
