Direction-of-Arrival Estimation for Nested Acoustic Vector-Sensor Arrays Using Quaternions

There is an increasing interest in direction-of-arrival (DOA) estimation using nested arrays composed of vector sensors. Considering acoustic vector sensors (AVSs) commonly used in underwater applications, this article proposes a novel algorithm, called augmented nested quaternion-multiple signal classification (ANQ-MUSIC), to perform DOA estimation. By judiciously arranging the multicomponent outputs of AVSs, we model the received signals from the entire nested AVS array (NAA) as a quaternion observation vector in a compact way to reduce computational complexity. Next, we formulate a quaternion-based difference co-array (QDCA) model via vectorizing the quaternion covariance matrix (QCM). Based on the obtained insights from the QDCA model, we derive a suitable QCM, which is constructed by applying the spatial smoothing (SS) technique. Finally, classical quaternion-MUSIC (Q-MUSIC) is logically introduced to estimate the DOA parameters. In simulations, we take into account nonuniform received noise and intercomponent correlated (ICC) noise, which may occur in practical underwater environments. The results demonstrate that the proposed method shows superiority in angular resolution and achieves a desirable tradeoff between estimate accuracy and computational burden, besides showing robust performance in the above test scenarios.