Eigenstructure methods for DOA estimation of circular acoustic vector sensor array with axial angle bias in nonuniform noise

Abstract

To improve the performance of direction of arrival (DOA) estimation under the coexistence of nonuniform noise and axial angle bias, we propose new DOA estimation methods based on the eigendecomposition of a covariance matrix constructed by the analytic velocity and acoustic pressure. The analytical velocity model can convert axial angle bias into phase error to facilitate its estimation. Meanwhile, the diagonal unloading (DU) technique equalizes the noise power to minimize the effect of noise non-uniformity, and the minimum diagonal element of this covariance matrix can precisely determine the amount of DU. Next, two eigenstructure-based estimation algorithms are developed from the objective function formulated by the orthogonality of the true steering vector and the noise subspace. The first method is to get a quadratic matrix from this objective function and estimate the DOAs by judging its singularity at different spatial angles. In the second method, an optimization problem is formulated to deduce a closed-form solution of the bias weight vector corresponding to the preset spatial angle, and a joint iterative approach further improves the estimation accuracy of the DOAs and axial angle bias parameters. Simulation results are provided to show the superiority of the proposed methods.