Passive source depth estimation without prior sound speed profile in reliable acoustic path environments

In a deep-water reliable acoustic path environment, the sound field is dominated by the direct (D) and surface-reflected (SR) paths. Utilizing the time delay between these two paths (D-SR time delay), we can estimate the source depth, exploiting the relationship between the time delay and the source depth based on the knowledge of the channel sound speed profile (SSP). However, mismatches in SSP can significantly degrade estimation performance. In this work, we theoretically demonstrate that the D-SR time delay exhibits a linear relationship with both the source depth and an SSP-related nuisance term. Utilizing multiple observations of the D-SR time delay, we then reformulate the source depth estimation as a problem of estimating a linear coefficient vector within a linear model. We propose solving for the source depth using least squares methods, which yields a closed-form solution. This approach, termed the joint sound-speed and source depth estimator, enables accurate source depth estimation without SSP knowledge and facilitates rapid computation. Simulation results confirm the method's robustness against SSP mismatches compared to existing techniques. The real data collected from experiments in the Western Pacific also demonstrate its effectiveness.