Matrix Information Geometry Based Clutter Suppression Method For Airborne Radar

Information geometry is a fundamental and cutting-edge theory that uses modern differential geometry methods to study problems in the field of statistics and information.It takes advantage of the nonlinear geometric structure of Riemannian manifolds and shows strong theoretical advantages and great potential in dealing with nonlinear and stochastic problems.The matrix manifold is an important Riemannian manifold.Based on the matrix manifold,matrix information geometry plays a great potential in the fields of information coding,computer vision and image processing,medical signal analysis,and so forth.Aiming at clutter suppression and target detection of airborne radar,a series of new methods based on the theory of information geometry is proposed,which provides a new way for the application of information geometry in the field of radar signal processing.In complex environments,the difficult characterization of echo properties,the low accuracy of clutter covariance matrix estimation,and the poor performance of heterogeneous clutter suppression are important factors restricting the clutter suppression performance for airborne radar.Faced with this situation,this thesis aims to improve the clutter suppression performance of airborne radars in complex environments from the above three aspects.The specific research contents are listed as follows:To address the problem of difficult characterization of echo properties,the matrix manifold presentation of airborne radar echo properties is studied.Firstly,the differences between clutter and targets are analyzed based on measured data.Then,a matrix manifold is constructed based on these differences,and geometric metrics between clutter and targets on matrix manifolds are investigated.Finally,combined with the theory of information geometry,the connotation of clutter suppression and target detection on matrix manifold is pointed out,and the framework of clutter suppression and target detection on matrix manifold is established.Aiming at the problem that the estimation accuracy of the clutter covariance matrix of space-time adaptive processing(STAP)is low and the clutter suppression performance is poor due to heterogeneous samples,research is carried out from two aspects.One is to circumvent the deleterious effects of heterogeneous samples and study the estimation method of robust clutter covariance matrix under small samples.The second is to study the sample augmentation method by using the geometric structure of matrix manifold.In the aspect of reducing the influence of heterogeneous samples,the distribution properties of clutter samples on matrix manifold are analyzed,and two heterogeneous sample screening methods are proposed.Moreover,to improve the accuracy of clutter covariance matrix estimation with small sample support,a matrix-manifold-based clutter covariance matrix estimation method is proposed.In terms of sample augmentation,a clutter suppression method via affine transformation on matrix manifolds is studied.Firstly,a clutter classification method based on Kullback Leibler divergence is proposed.Then,based on this classification result,a sample augmentation method via affine transformation on matrix manifolds is proposed.It is deduced that the proposed affine transformation can effectively shorten the distance between homogeneous samples and heterogeneous samples,which reflects the difference between homogeneous samples and heterogeneous samples.Finally,the clutter covariance matrix is estimated with affine transformed samples and homogeneous samples,so as to improve the heterogeneous clutter suppression and the slowly moving target detection performance.The verification of measured data shows that the signal-to-clutter ratio(SCR)improvement of the small sample support method is 4.67 d B compared with the classical LSMI method,and 1.8d B compared with the well-performed RMI method.Similarly,the SCR improvement of the sample augmentation method is about 1.5d B compared with the well-performed Tyler’s method.Because the STAP method for clutter suppression of airborne radar has difficulty to obtain homogeneous samples and high computational complexity,a heterogeneous clutter suppression method combining matrix manifold and sparse recovery is studied.Combined with the advantages of Riemannian manifold optimization,a clutter suppression method via robust PCA over low-rank matrix variety is proposed by using the sparsity of targets and the low-rank of clutter.To this end,the heterogeneous clutter suppression problem is modeled as an optimization problem of robust PCA.Then,to solve this NP-hard problem,a proximal gradient over the low-rank matrix variety(PGLr V)algorithm is proposed.This algorithm updates low-rank components over manifold with Riemannian gradient and updates sparse components with the proximal gradient in Euclidean space.Through iterative optimization,the clutter and targets can be recovered robustly.Measured data results show that the SCR improvement is more than 3d B compared with Go Dec and STAP methods when the detection probability is0.8,and it is less affected by sparsity parameters than the Go Dec method.The clutter suppression method of joint design of transmit waveform and receive filter is studied since it is difficult to meet the requirements of clutter suppression performance when only considering the filter design at the receiver.Although the joint design based on the SCNR criterion can improve the output signal-to-noise ratio,this criterion is the optimal performance criterion under the condition that the two assumed distributions are Gaussian distributions,which may not be satisfied in practice.Stein lemma shows that the optimal detection performance of radar systems can be determined by the Kullback Leibler divergence of two hypothetical distributions.Therefore,a joint design based on Kullback Leibler divergence is proposed,in which the Riemannian gradient of Kullback Leibler divergence about filter weight w and waveform s are deduced.So the optimal filter weight w and waveform s can be obtained at the same time over Riemannian product manifolds.Simulation results show that the proposed method has better clutter suppression performance than the joint design method based on the SCNR criterion.In particular,the detection probability of the proposed method is increased by 20% under a fixed false alarm rate.Taking advantage of matrix information geometry,this thesis studies new methods of airborne radar clutter covariance matrix estimation and heterogeneous clutter suppression,which improves the detection performance of airborne radar slow-moving targets in strong clutter backgrounds.The research results of this thesis provide a new way for clutter suppression and target detection of airborne radar.