This paper describes a method of estimating hydrophone positions in a receiver array using the noise from a passing ship. Relative arrival times of the ship-noise signal between pairs of hydrophones are obtained from several time windows of data (corresponding to different ship locations) by cross-correlating the band-pass filtered time series. The relative arrival times are used as data in an array element localization inversion to estimate both the hydrophone and ship locations based on iterated linearization of the acoustic ray equations. The inversion applies the method of regularization to include prior information such as approximate location estimates and uncertainties for the source and receivers and the expectation that the array shape and or source tracks are smooth functions of position. Linearized and nonlinear (Monte Carlo) estimates of the position errors are in good agreement and indicate a high degree of confidence in the receiver positions (relative uncertainties of approximately 0.2 m in the horizontal and 0.05-0.1 m in the vertical). The ability to improve upon the initial source position estimates depends on the geometry of the problem, as investigated with simulations.