Analysis of the Effects of Reference Sound Speed on Direction Finding Accuracy of Multi-Dimensional Underwater Array

Reference sound speed is a critical parameter for direction-of-arrival (DOA) estimation of underwater acoustic source. The horizontal-line-array (HLA) exhibits deterministic systematic error of DOA estimation when reference sound speed deviates from phase velocity at receiver. However, the existence of similar regularity in multi-dimensional array requires further research. Firstly, this work employs ray theory and normal-mode theory to derive phase forms of received signals in horizontally invariant or horizontally varying waveguides, clarifying intrinsic relationship between reference sound speed and estimated azimuth and elevation angle of stereo-array (SA). Then simplified models of horizontal-plane-array (HPA) and vertical-plane-array (VPA) are further investigated. Moreover, the beam bending caused by angles coupling is analyzed to design optimal array shape. Finally, through simulations and experiments on DOA estimation, the following conclusions can be concluded. For azimuth, SA can achieve unbiased estimation when reference sound speed is close to sound speed at receiver; When reference sound speed satisfies the constraint condition, HPA can achieve unbiased estimation; When reference sound speed is equal to sound speed at receiver, VPA can achieve unbiased estimation. For elevation angle, the above three arrays can achieve unbiased estimation only when reference sound speed is equal to sound speed at receiver.