Passive source depth estimation in shallow water using two horizontally separated hydrophones.

• Source depths are estimated based on the smooth-averaged cross-correlation function. • The proposed methods can provide more accurate source depth estimates than the MFP. • The simulations show the applicable conditions of the proposed methods. A solution to the problem of acoustic source depth estimation in shallow water is presented for the case of two horizontally separated hydrophones or arrays. The solution is based on that the smooth-averaged cross-correlation function (SCF) of signals changes regularly with the source depth and is approximately independent of the source range, allowing that the source depth can be estimated independently without knowing the source range. Using different cost functions, three methods are proposed to estimate source depth by matching the normalized cross-spectral density, temporal envelope and time delay of the SCF. Then, the performance of the proposed methods are evaluated with simulations and two experiments conducted off the coast of China at water depths not exceeding 100 m. The mean absolute errors in source depth of the proposed methods are in 2.8–12.8 m. Finally, the effect of noise, frequency band, range span, horizontal spacing, sound speed profile, and parameter mismatch are numerically studied. The results show that the methods are more suitable for the case of a low-frequency band and an environment with large negative sound speed gradient. [ABSTRACT FROM AUTHOR]