Underdetermined Gridless DoA Estimation for Uniform Circular AVS Arrays via Co-Array Manifold Transformation

Abstract

Direction-of-arrival (DoA) estimation is a fundamental problem in array signal processing. In this work, we consider a uniform circular acoustic vector sensor (AVS) array and investigate underdetermined gridless DoA estimation scenarios, where the number of sources exceeds the number of physical sensors. We first characterize the co-array structure induced by the second-order statistics of the measurements and show that it can be interpreted as a concentric multi-circular array with increased degrees of freedom, whose virtual elements exhibit both pressure-like and AVS characteristics. This expanded co-array enables the identification of more sources than the number of physical array elements. Next, we employ a co-array manifold transformation based on the Jacobi–Anger expansion to map the resulting concentric multi-circular structure onto a virtual uniform linear array (ULA). This transformation enables the application of high-resolution gridless subspace-based DoA estimation techniques, such as ESPRIT and Root-MUSIC. However, since the proposed framework operates in the correlation domain of stationary signals, only a single snapshot is available, which poses a challenge for conventional subspace methods that require multiple snapshots. To address this limitation, approaches including inverse modeling with spatial smoothing (IMSS), as well as gridless sparse recovery based on atomic norm minimization (ANM), are employed. The proposed framework is evaluated under three measurement configurations: pressure-only, particle velocity-only, and combined AVS observations.