The DOA Estimation Based On Bayesian Compression Sensing

In recent years,with the rapid development of array signal processing technology,the application of DOA estimation in military and civil fields is more and more widely.In order to achieve high precision of signal source positioning,the performance requirements for DOA estimation in various fields are becoming more and more strict.The advantages of the traditional DOA estimation algorithms of spatial spectrum estimation possesses high accuracy and high resolution,but these algorithms need a great number of snapshots and high signal-tonoise ratio.With the development of the compression sensing(CS)theory,the application of CS theory to the array signal processing is a new research of DOA estimation algorithm.In the situation of single block and low signal-to-noise,the algorithms of DOA estimation based on Bayesian compression sensing(BCS-DOAE)will produce a low accuracy and a low probability.In view of this problem currently,the measurement matrix and the reconstruction algorithm in the BCS-DOAE are thoroughly studied in this paper.The core contents are summarized as follows:(1)This paper studies the basic principles of compressed sensing theory,and studies the mathematical model of compressed sensing.Under this model,the basic process of CS is reasonably studied,and three classical sparse reconstruction algorithms are analyzed in detail.At the same time,the basic theory of array signal processing theory is studied.In order to exclude the influence of non-ideal factors,reasonable assumptions for arrays and space signals are proposed,an array receiving signal model is studied.Combining the CS theory and array signal processing theory,a model of CS-DOAE is studied.(2)On the basis of the DOA estimation model based on compressed sensing,the method of signal sparse representation for two spatial grids,i.e.,equal angle division and equal sinusoidal partition,is deeply studied,and a sparse model of signal with sub-sampling is studied.The various design methods of the measurement matrix are mainly studied,and the influence of different measurement matrix,sampling mode and sampling number on the performance of the reconstruction algorithm is evaluated by simulation.An improved measurement matrix based on matrix decomposition is studied in this paper.The rationality of the improved measurement matrix is proved by mathematical deduction,simulation results show that the improved measurement matrix improves DOA accuracy and success rate.(3)The Bayesian estimation theory is studied and analyzed,and the mathematical derivation process of Bayesian compressive sensing theory is studied.This paper focuses on the DOA estimation algorithm based on Bayesian compressed sensing and its fast algorithm,simulation results show that both algorithms improve DOA accuracy and success rate.Besides,a deep study and analysis of variational inference is worked in this paper,then by combining the variational Bayesians theory with the CS-DOAE,the DOA estimation algorithm based on variational Bayesian compressed sensing and its fast algorithm are studied,simulation results show that the two algorithms not only improve the DOA accuracy and success rate,but also reduce the algorithm running time.