Direction-of-arrival estimation based on phase modal space for a circular acoustic vector-sensor array on the cylindrical baffle

A method is introduced for estimating the target azimuth in the phase mode domain using the minimum variance distortionless response (MVDR) technique. The approach relies on joint processing of sound pressure and velocity through a covariance matrix, arranged predominantly in vertical, horizontal, and diagonal configurations. Employing an acoustic field model with an elastic cylindrical baffle, this method transforms the phase mode of an acoustic vector circular array. Subsequently, mutual covariance matrices of sound pressure and velocity components from distinct points are generated. Extensive cross-covariance matrices are calculated with additive summation, arranged vertically, horizontally, and diagonally, then decomposed to achieve target azimuth estimation using MVDR. Theoretical analysis and numerical simulations indicate that the vertically arranged cross-covariance matrix delivers the most accurate azimuth estimation, while the additive covariance matrix exhibits the least background noise. Nevertheless, the horizontal and diagonal arrangements show inferior performance compared to the vertical arrangement. Pool and lake experiments further confirm the superior performance of the vertically arranged approach.