Research On Signal Detection Theory And Methods Based On Krylov Subspace

Signal detection is an extremely important part in signal processing field.In complex and changeable environments full of various disturbances,how to improve the detection performance has always been one of the important research topics in radar systems and sonar systems.In most of cases,environments are heterogeneous,which leads to the rareness of the number of training samples that can be used for target signal detection.Furthermore,the detection performances of many detection methods decline due to the reduction of training samples.In addition,many detection methods include matrix inversion,and direct matrix inversion usually requires a lot of computation resources,which brings a large computational burden for the detection system.As efficient iterative methods in solving linear system problems,Krylov subspace methods can usually achieve convergence using only a few iterations to reduce the computational cost.In recent years,Krylov subspace methods have been frequently utilized in signal processing field.Currently,the research of the signal detection based on Krylov subspace is still in the initial stage at home and abroad.The signal detection in heterogeneous environment has always been a hot topic in signal detection.Therefore,in this dissertation,signal detection based on Krylov subspace is studied in heterogeneous environment.It should be noted that the conjugate gradient algorithm in Krylov subspace methods mainly plays the part of the bridge by which Krylov subspace is embedded into signal detection in this dissertation.The main contributions and innovations of this dissertation are summarized as follows:(1)An adaptive matched detection method based on conjugate gradient and Clean method is proposed in the heterogeneous environment including point interferences or point Gaussian clutters,and the approximate expression of the expected value corresponding to the output signal-to-noise ratio of the proposed method is briefly analyzed.The detection environment is often sparse,which results in a low-rank correction structure of the covariance matrix of the environment.Conjugate gradient algorithm has efficient convergence for the covariance matrix with a low-rank correction structure,and thus can reduce the computational cost.The Clean method can efficiently estimate the point interferences and point Gaussian clutters by utilizing the multi-level uniform interpolation scan.Compared with the conventional adaptive matched filter,the proposed method has better detection performance when the training size is small.(2)In order to further improve the detection performance of the conventional parameterized adaptive matched filter in the heterogeneous environment,a conjugate gradient parameterized adaptive matched detection method based on the covariance reconstruction is proposed in the dissertation.The proposed method is mainly suitable for the heterogeneous environment which contains point interferences or point Gaussian clutters.The proposed method obviously improves the detection performance of the conventional parameterized adaptive matched filter in the heterogeneous environment.(3)In the heterogeneous environment of Gaussian distributed clutter,a parameterized adaptive matched detection method based on conjugate gradient and space-time uniform scan is proposed in the dissertation.In the heterogeneous environment containing Gaussian distributed clutter,the proposed method significantly improves the detection performance of the conventional parametric adaptive matched filter.Then,the detection stability of this method is briefly and qualitatively analyzed.(4)Based on persymmetric adaptive matched filter,a conjugate gradient persymmetric adaptive matched detection method is proposed in the dissertation.In heterogeneous environment,compared with persymmetric adaptive matched filter and conjugate gradient adaptive matched filter,the proposed method has better detection performance and lower computational cost.Meanwhile,the approximate mathematical analysis of the output signal-to-interference-and-noise ratio of the proposed method is also carried out,and the approximate expression of the expected value corresponding to the output signal to interference noise ratio of the proposed method is obtained.(5)In the signal detection scene of airborne bistatic radars,in order to make better use of clutter rank and Krylov subspace to improve the detection performance of the parametric adaptive matched filter,combined with look-up table method,a conjugate gradient parametric adaptive matched detection method based on clutter rank and space-time scan is proposed in this dissertation.In the heterogeneous environment of bistatic radar signal detection scene,the proposed method shows better detection performance than the parametric adaptive matched filter and other conventional detection methods.