Three Minimum Variance Distortionless Response Algorithms Based on Quaternion Model for Single MEMS Vector Hydrophone

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°.