Three Minimum Variance Distortionless Response Algorithms Based on Quaternion Model for Single MEMS Vector Hydrophone
Shan Zhu, Yanan Geng, Keqiang Mu, Yongwei LI, Feng Li, Zhiqiang Gao, Yunyue Zhang, Zhicheng Zhao · Micromachines · 2026
To address the limitations of the traditional long-vector model, which cannot adequately preserve the inherent orthogonal structure among channels in the signal processing of a single vector hydrophone, three minimum variance distortionless response (MVDR) direction-of-arrival estimation algorithms based on the quaternion model are proposed for a single MEMS vector hydrophone. Compared with the traditional long-vector model, the quaternion can retain the structural relationship between channels in a more compact data representation form. First, based on the output characteristics of the sound pressure and dual-channel vibration velocity of the two-dimensional MEMS vector hydrophone, three quaternion signal models—namely Q-VV, Q-PVV, and Q-PV—are constructed. Subsequently, the corresponding MVDR spatial spectra are derived in the quaternion domain. To enhance the direction-of-arrival resolution performance under low-signal-to-noise-ratio (SNR) conditions, the algorithms are then improved by incorporating subspace decomposition theory. The simulation results show that the three proposed quaternion-based MVDR algorithms can all realize effective direction-of-arrival estimation for a single target. When the signal-to-noise ratio is greater than −4 dB, the direction estimation error is less than 1°. The results of dynamic bearing trajectory tests and fixed-point direction-of-arrival estimation experiments indicate that the proposed method can realize the continuous and stable tracking of the target azimuth. Among the involved algorithms, Q-PV-MVDR can effectively suppress false targets, with an average relative angle orientation error of 0.5°.