Passive direction finding with a pair of acoustic vector sensors using fourth-order cumulants

In this paper, an elevation-azimuth direction finding algorithm with the use of a pair of identically oriented acoustic vector sensors, which can be arbitrarily deployed at unknown locations, is proposed. Two fourth-order cumulant (FOC) matrices, which impose the so-called translational invariance property in the coarray domain, are defined. Such invariant structure allows recovering the coarray steering vectors of the acoustic vector sensors in closed-form from the generalized eigenvectors of the matrix pencil, which is built from the two defined FOC matrices. The identifiability performance of the proposed algorithm is further investigated. It is shown that up to 9 sources can be uniquely identified. The extension of the proposed algorithm for accommodating arbitrary AVS arrays with unknown sensor locations is also addressed. Afterward, the asymptotic performance bound of the considered problem is derived. Finally, the efficacy of the proposed algorithm is verified by numerical examples.