Target Angle Estimation With Sparse Bayesian Learning

Target angle estimation is one of the most important topics in the field of array signal processing area,which mainly includes the estimation of Direction of Departure(DOD)and Direction of Arrival(DOA).Traditional target angle estimation algorithms are usually based on subspace theory(e.g.,MUSIC,ESPRIT).In order to obtain better estimation precision,subspace-based algorithms require accurate information for covariance matrix,noise subspace and signal subspace of the received data.In the presence of limited snapshots or low signal-to-noise ratios,the estimation performance of the subspace algorithms may degrade significantly.The sparse Bayesian learning(SBL)method overcome the main shortcomings of the subspace algorithms because it does not need to estimate the covariance matrix,and has low sensitivity to noise and snapshots.A large number of target angle estimation algorithms based on sparse Bayesian learning have been proposed in recent years.However,the extensions to nested arrays and two-dimensional angle estimate have not been well addressed yet: 1)The existing sparse Bayesian learning DOA estimation method for nested arrays suffers from two major drawbacks: reduced array aperture and inevitable modeling error;2)the original sparse Bayesian method cannot be directly applied to two-dimensional angle estimate because of dense grid and heavy computing cost.To solve these problems,the main research contents of this paper are as follows:A novel nested array DOA estimation algorithm based on off-grid sparse Bayesian learning is derived in this paper to deal with the problems of array aperture loss and modeling error in the existing nested array SBL algorithm.To solve these issues,a new data model formulation is first presented in this paper,in which we take the noise variance as a part of the unknown signal of interest,so as to learn its value by the Bayesian inference inherently.Then,we provide a novel grid refining procedure to eliminate the modeling error caused by off-grid gap,where we consider the locations of grid points as adjustable parameters and proceed to refine the grid point iteratively.Simulation results demonstrate that our method significantly improves the DOA estimation performance especially using a coarse grid.To the best of our knowledge,there does not exist any available SBL-based algorithm that can handle two-dimensional target angle estimation,where the main challenges are that 1)the grid used for two-dimensional target angle estimation is much denser than the one used for one-dimensional target angle estimation,which will bring a huge computational complexity;and 2)the column vectors in the dictionary matrix are highly correlated for each other,which might make the SBL algorithm fail to work.To solve these issues,we employ a coarse grid and combine it with an off-grid technology.Since the dimension of the dictionary matrix is small with the coarse grid,the computational complexity is greatly reduced and the column vectors are no longer highly correlated.To combat the off-grid gap caused by the coarse grid,we extend our previous off-grid method to two-dimensional situation.Note that the estimated DODs and DOAs are automatically matched.Simulation results show that the spatial resolution and estimation accuracy of the proposed method are much better than those of traditional algorithms.