The problem of determining accurate locations for arrays of underwater instruments is similar to the problem of locating local earthquakes by utilizing a limited number of receivers but is complicated by the fact that estimated errors in longitude and latitude of a given receiver (ship) position are nonzero and are typically correlated. Estimates of ship positions at sea are commonly determined by fixes from the Navy Transit nagivation satellite system. This system calculates position error ellipses which vary in size and orientation from fix to fix. Deviations in the orientations of the principal axes of the error ellipses from north-south and east-west result in the introduction of off-diagonal elements in the ship position variance matrix. Tying each ship fix to a stationary array of ocean bottom seismometers (OBS's) using acoustic ranging allows averaging of fixes, thus solving simultaneously for ship and OBS positions, puts tight constraints on the system as a whole and especially on the relative positions of the OBS's. In addition to ship positions, the data required to locate the instruments are two-way travel times between the ship and transponders on the instruments, and initial depth estimates of OBS's read from the bathymetry. The parameters which we solve for are the locations of the instruments (including depth) and of the ship at each fix. The forward problem, calculating acoustic travel times from distances between ship fixes and OBS's, is solved by a ray shooting algorithm. This system of equations is linearized and transformed to diagonalize the covariances; it is then solved iteratively by inverting the data jointly using singular value decomposition and step-length damping. The solution includes the covariances of the parameters. We show calculations of positions of four OBS's for deployments during three experiments including the Rivera oceanic seismic experiment (ROSE). Typical fix error ellipses (1 &sgr;) are 300 m by 200 m and resulting instrument position uncertainties are approximately 100 m. Relative instrument positions are accurate to about 50 m. Relative errors can be decreased to 10 to 20 m by using simultaneous rather than sequential ranging.