Acoustic tracking of a freely drifting sonobuoy field

This paper develops an acoustic inversion algorithm to track a field of freely drifting sonobuoys using travel-time measurements from a series of nonsimultaneous impulsive sources deployed around the field. In this scenario, the time interval between sources can be sufficiently long that significant independent movement of the individual sonobuoys occurs. In addition, the source transmission instants are unknown, and the source positions and initial sonobuoy positions are known only approximately. The formulation developed here solves for the track of each sonobuoy (parametrized by the sonobuoy positions at the time of each source transmission), allowing arbitrary, independent sonobuoy motion between transmissions, as well as for the source positions and transmission instants. This leads to a strongly underdetermined inverse problem. However, regularized inversion provides meaningful solutions by incorporating a priori information consisting of prior estimates (with uncertainties) for the source positions and initial sonobuoy positions, and a physical model for preferred sonobuoy motion. Several models for sonobuoy motion are evaluated, with the best results obtained by minimizing the second spatial derivative of the tracks to obtain the minimum-curvature or smoothest track, subject to fitting the acoustic data to a statistically appropriate level.