Variational Bayesian Inference For Robust DOA Estimation

Direction of arrival(DOA)estimation is one of the core contents of array signal processing,and it has a wide range of applications in the fields of wireless communication,radar positioning and aviation navigation.Traditional DOA estimation methods are usually based on the assumption that noise obeys Gaussian distribution,but there is a lot of interference in the actual wireless propagation channel.These strong interferences will bring some impulsive values that deviate significantly from the standard deviation,which is also called impulsive noise.If the impact of impulse noise is not considered,the performance of traditional DOA estimation methods will deteriorate significantly.In order to combat strong interference,domestic and foreign researchers have proposed some robust DOA estimation methods based on subspace theory.However,when the number of snapshots is limited or the signal-to-noise ratio is low,the performance of the subspace method will be significantly degraded.The method based on Sparse Bayesian Learning has been developed rapidly because it can make up for the shortcomings of algorithms based on subspace technology.In recent years,domestic and foreign scholars have proposed a large number of robust DOA estimation methods based on SBL.However,these methods still have the following problems: 1)it needs to perform the inversion calculation of a high-dimensional matrix when solving the parameter information,which has the problem of high computational complexity;2)only consider independent and identically distributed sparsity of the impulses in the noise(i.e.,the entries of impulsive noise are assumed to be independent and identically distributed).Studies have shown that impulses in the noise often appear in bursts,resulting in structured rather than independent sparsity,which can be exploited to enhance DOA estimation performance.In view of the above two issues,the main research content of this paper are as follows: 1)the robust DOA estimation method based on SBL needs to calculate the inversion of a high-dimensional matrix when solving parameter information,and the computational complexity is generally high;2)this type of method only considers the element sparseness of the noise and ignores the structured sparseness.There are common errors in Bayesian noise modeling.Based on the above theory,the main research contents of this article are as follows:Aiming at the problem of high computational complexity in the existing robust DOA estimation method based on SBL,a real-valued DOA estimation method based on variational Bayesian estimation is proposed.The proposed method uses unitary transformation to convert a complex sparse signal recovery problem into a real-valued sparse signal recovery problem,and innovatively recombines and transforms multiple real-valued vectors,effectively avoiding the inability to estimate real-valued DOA under the background of impulsive noise,greatly simplifies the Bayesian formula reasoning process,and reduces the computational complexity.The method also uses VBI technology to estimate the relevant parameters involved in the target signal and impulse noise,reduces the influence of noise in the real number domain on the signal,and maintains better DOA estimation performance in the complex number domain.Comparative experiments with existing methods show that the proposed method can effectively reduce the computational complexity without sacrificing the performance of DOA estimation.To solve the problem of failing to make full use of the structural characteristics of impulsive noise in existing robust DOA estimation methods based on SBL,a DOA estimation method based on VBI under the background of burst noise is proposed.The proposed method introduces a novel two-dimensional block sparse prior,which makes full use of the structured characteristics of strong pulses,and greatly improves the performance of DOA estimation.In addition,in view of the poor effect of the traditional grid update method under burst noise,this paper also proposes an improved grid correction method.This correction method directly determines the grid points and avoids any matrix inversion operations,effectively reducing the off-grid error and further improving the accuracy of DOA estimation.The superior impulse-resistant DOA estimation performance and computational efficiency of our proposed method are verified by simulation results.