DOA Estimation for a Mixture of Uncorrelated and Coherent Sources Based on Hierarchical Sparse Bayesian Inference with a Gauss-Exp-Chi² Prior

Abstract

Direction of arrival (DOA) estimation algorithms based on sparse Bayesian inference (SBI) can effectively estimate coherent sources without recurring to extra decorrelation techniques, and their estimation performance is highly dependent on the selection of sparse prior. Specifically, the specified sparse prior is expected to concentrate its mass on the zero and distribute with heavy tails; otherwise, these algorithms may suffer from performance degradation. In this paper, we introduce a new sparse-encouraging prior, referred to as "Gauss-Exp-Chi 2 " prior, and develop an efficient DOA estimation algorithm for a mixture of uncorrelated and coherent sources under a hierarchical SBI framework. The Gauss-Exp-Chi 2 prior distribution exhibits a sharp peak at the origin and heavy tails, and this property makes it an appropriate prior to encourage sparse solutions. A three-layer hierarchical sparse Bayesian model is established. Then, by exploiting variational Bayesian approximation, the model parameters are estimated by alternately updating until Kullback-Leibler (KL) divergence between the true posterior and the variational approximation becomes zero. By constructing the source power spectra with the estimated model parameters, the number and locations of the highest peaks are extracted to obtain source number and DOA estimates. In addition, some implementation details for algorithm optimization are discussed and the Cramér-Rao bound (CRB) of DOA estimation is derived. Simulation results demonstrate the effectiveness and favorable performance of the proposed algorithm as compared with the state-of-the-art sparse Bayesian algorithms.

Three-Parallel Co-Prime Polarization Sensitive Array for 2-D DOA and Polarization Estimation via Sparse Representation

“…According to (32), 2-D DOA angles are separated into two parts of the data vector, and the dictionary (β) in (33) can be easily constructed by sampling only 1-D DOA angle. Compared with the traditional SR-based 2-D DOA estimation algorithms, the dimension of the dictionary used in the sparse recover process is reduced from two to one, and the computation amount is decreased from O((Q 1 Q 2 ) 3 ) to O(Q 1 ) 3 , where Q 1 and Q 2 are the grid number in each angle domain.…”

“…The direction-of-arrival (DOA) estimation is a vital problem in the field of array signal processing [1]- [3], especially the estimation of two-dimensional (2-D) DOA and polarization parameters based on the polarization sensitive array (PSA) [4]- [6]. The PSA composed of vector sensors can measure the direction and polarization information of the electromagnetic wave signals, which offers better estimation accuracy, target classification, recognition performance, and anti-jamming capability [7]- [9].…”

Robust Tensor-Based DOA and Polarization Estimation in Conformal Polarization Sensitive Array with Bad Data

“…Therefore, to further confront the effect of the bad data and fully utilize the multidimensional information of the array received data, the VSBL technique based on the tensor model is proposed to improve the performance of DOA estimation. First, let us reshape the estimation into a tensor of , the posterior distribution of can be calculated by the Bayesian criterion [ 33 ], which is expressed as: …”

A joint DOA and polarization estimation method based on the conformal polarization sensitive array from the sparse reconstruction perspective

“…The CPSA-VSBL method is employed to update the hidden variables and hyperparameters to approximate the posterior probability [34]. We apply a three-layer hierarchical prior [35] to S sv . A zero-mean complex Gaussian (Gauss) distribution imposed on S sv as the first layer of prior where…”