Orthogonal subspace approach for underwater acoustic wave-vector direction estimation based on acousto-optic sensing

High-precision wave-vector direction estimation is critical for underwater acoustic positioning, target detection, and tracking. Traditional array-based methods typically require large apertures, whereas a single acoustic vector sensor depends on inter-channel phase consistency and remains underexplored at mid-to-high frequencies. To overcome these limitations, we replace piezoelectric or electromagnetic principles with the acousto-optic effect for acoustic vector sensing, which provides multidimensional, high-order, non-contact sensing and is well suited to wave-vector sensing in the mid- to high- frequency range. Building on the classical MUSIC method and the acousto-optic sensing principle, we develop an orthogonal-subspace wave-vector direction estimation algorithm (named MUSIC-L) tailored to acousto-optic wave-vector sensing and validate it through simulations and experiments. Simulation results show that the proposed method is robust and that the theoretical error is almost independent of angle; at a signal-to-noise ratio of 10 dB with 80 snapshots (2 MHz sampling rate, 75 kHz source), the root mean square error is 1.4°. Finally, we design and fabricate an acousto-optic vector hydrophone prototype (0.5 m × 0.5 m × 0.185 m) and measure the wave-vector direction in an anechoic tank. The results show that, with 80 snapshots, the estimation error remains below 1°, with a standard deviation of approximately 0.23°.