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This paper describes a regularized acoustic inversion algorithm for tracking individual elements of a freely drifting sonobuoy field using measured acoustic arrival times from a series of impulsive sources. The acoustic experiment involved 11 sonobuoys distributed over an 8×6-km field, with a total of six sources deployed over 72 min. The inversion solves for an independent track for each sonobuoy (parameterized by the sonobuoy positions at the time of each source transmission), as well as for the source positions and transmission instants. Although this is a strongly under-determined problem, meaningful solutions are obtained by incorporating a priori information consisting of prior estimates (with uncertainties) for the source positions and initial sonobuoy positions and a physical model for sonobuoy motion along preferentially smooth tracks. The inversion results indicate that the sonobuoys move approximately 260-700 m during the source-deployment period. Closely spaced sonobuoys move along similar tracks; however, there is considerable variability in track directions over the entire field. Positioning uncertainties in horizontal coordinates are estimated using a Monte Carlo appraisal procedure to be approximately 100 m in an absolute sense and 65 m in a relative sense. A sensitivity study indicates that the uncertainties of the a priori position estimates are the limiting factor for track accuracy, rather than data uncertainties or source configuration.