Research On Radar Target Detection Method Based On Matrix Information Geometry

Matrix information geometry is a developed rapidly theoretical system arose from in the application of information geometry theory,and has shown great potential in information science and other fields.Aiming at the problem of radar target detection in complex heterogeneous clutter and low signal-to-clutter ratio(SCR),in this paper,the information measurement on the matrix manifold,the matrix CFAR(constant false alarm rate)detection method,the matrix manifold filtering and the covariance matrix estimation are investigated based on the matrix information geometry theory.A series of new ideas and new methods are proposed,and it provides some new technical means for radar target detection.In the Firstly chapter,the problem of radar target detection under the condition of heterogeneous clutter and low SCR is presented,and the application status of matrix information geometry in the field of natural science is summarized.The second chapter introduces the mathematical basis of matrix information geometry,and expounds some basic mathematical concepts and methods.It provides a basis for the following research.In the third chapter,aiming at the problem of radar target detection under the condition of low SCR,the radar target detection method based on extended KL(Kullback-Leibler)divergence is studied.Firstly,the extended KL divergence on the Hermitian positive-definite matrix manifold is presented,and the extended KL divergence mean and median of a set of Hermitian positive-definite matrices are derived.Secondly,a matrix CFAR detector based on the different extended KL divergence is designed on the matrix manifold.Performance advantages of different extended KL divergence matrix CFAR when compared with the FFT(fast Fourier transform)-CFAR detection are verified by means of the simulation clutter data and the real sea clutter data.Finally,the detection principle of matrix CFAR is explained from the viewpoint of pattern analysis.Based on the anisotropy of different metrics on the matrix manifold,the concept of detection potential,reflects the similarity degree of two local geometric structures on the matrix manifolds,is proposed.Experimental analysis shows that the smaller the normalized detection potential of matrix CFAR is,the better the detection performance is.In the fourth chapter,the radar target detection based on tBD(total Bregman divergence)and tJBD(total Jensen-Bregman divergence)is investigated.The definition of tBD and tJBD between two points in the convex function space is extended upon the matrix manifold.Then,the tBD and tJBD centers of a set of Hermitian positive-definite matrices are derived,and a matrix CFAR detector based on tBD and tJBD is designed on the matrix manifold.The simulation clutter and the real sea clutter data experiments verify the performance advantage of the tBD and tJBD matrix CFAR when compared with the Riemannian distance-based matrix CFAR,and the relationship between the detection potential and the corresponding detection performance of the tBD and tJBD matrix CFAR is analyzed.The fifth chapter studies a radar target detection method based on matrix manifold filtering.As the clutter energy suppression of the Riemannian distance,Log-Euclidean distance and Bhattacharyya divergence matrix CFAR are not obvious,a manifold filtering method is proposed on the matrix manifold with the idea of bilateral filtering and non-local mean filtering in image processing.Firstly,the correlation of sample data is modeled as a covariance matrix,and each covariance matrix is replaced by a weighted average of its surrounding covariance matrices with the principle of bilateral filtering and non-local mean filtering.Then,the target detection is carried out using the matrix CFAR detector on the filtered covariance matrix.Experimental results verify the detection performance superiority of the manifold filtering matrix CFAR by means of the simulated clutter and the real sea clutter.Finally,the relationship between the detection potential and the detection performance is analyzed.The experimental analysis shows that the normalized detection potential of the manifold filtering matrix CFAR in lower than the matrix CFAR in non-target cells.In the sixth chapter,an adaptive normalized matched filter(ANMF)detection method based on information divergence is proposed for radar target detection under heterogeneous clutter background.Firstly,the covariance matrix estimation problem in heterogeneous clutter background is reformulated as computing the geometric mean and median on the matrix manifold.It can avoid the degradation in the estimation performance of the sample covariance matrix,due to the inaccuracy of statistical properties of the heterogeneous clutter;then,the influence function of the geometric mean estimator and the tBD center with a outlier is derived.The robustness of geometric mean,geometric median,tBD center and tJBD center is analyzed by simulation experiments.Finally,the performance superiority and the robustness of information divergence-based ANMF is verified by experiment results.The seventh chapter summarizes the content of this paper,and puts forward several questions worth further study.In conclusion,the results of this paper not only enrich the basic theory of matrix information geometry,but also expand the application of matrix information geometry in radar signal processing,and provides a new way for the research of signal processing.