Using optimal mass transport in bearing-time records for underwater target localization and tracking

This paper proposes the use of an optimal mass transport framework for the generation of bearing-time records, similar to those that are displayed on the detection screens of sonar operators. The proposed method operates by interpolating between spatial spectra estimated at sparse time steps using the information encoded in the respective estimated covariance matrices at those time steps. This interpolation is based on the formulation of transport plans between successive time steps, which minimize the transportation cost between the spatial spectra that are consistent with the estimated covariance matrices. The study was motivated by the consideration that the stationarity assumptions of the proposed framework are commonly met in passive-sonar scenarios. The evaluation was performed on simulated and real-world data of a non-uniform linear hydrophone array. The results indicate improved performance compared to traditional spectral estimation techniques, and demonstrate the potential of the proposed framework for application in contemporary passive-sonar systems.