Direction of arrival estimation for acoustic vector sensor coprime arrays based on quaternion theory

Employing quaternion theory, this article proposes a low-complexity super-resolution algorithm aimed at direction-of-arrival estimation of underwater targets under an acoustic vector sensor coprime array. The algorithm first combines the pressure and particle velocity components of the acoustic vector sensors to model the received signals of the coprime array as quaternion observation vectors. By analyzing the intrinsic connection between the complex-to-quaternions mapping and the corresponding quaternion covariance matrices, a dimensionality-reduced reconstruction of the covariance matrix is accomplished without information loss, thereby significantly reducing the subsequent computational cost. Meanwhile, by properly designing the dimension reduction strategy, the orthogonal constraints inherent in the quaternion model are preserved. Simulation results demonstrate that the proposed algorithm is highly compatible with the framework of the acoustic vector sensor coprime array. It provides superior spatial resolution and estimation accuracy compared to existing quaternion super-resolution algorithms while effectively reducing the computational complexity.