Approaches for instantaneous passive source localization using a towed horizontal receiver array in a random range-dependent ocean waveguide are examined. They include: (1) Moving array triangulation, (2) array invariant, (3) bearings-only target motion analysis in modified polar coordinates via the extended Kalman filter, and (4) bearings-migration minimum mean-square error. These methods are applied to localize and track a vertical source array deployed in the far-field of a towed horizontal receiver array during the Gulf of Maine 2006 Experiment. The source transmitted intermittent broadband pulses in the 300 to 1200 Hz frequency range. A nonlinear matched-filter kernel designed to replicate the acoustic signal measured by the receiver array is applied to enhance the signal-to-noise ratio. The source localization accuracy is found to be highly dependent on source-receiver geometry and the localization approach. For a relatively stationary source drifting at speeds much slower than the receiver array tow-speed, the mean source position can be estimated by moving array triangulation with less than 3% error near broadside direction. For a moving source, the Kalman filter method gives the best performance with 5.5% error. The array invariant is the best approach for localizing sources within the endfire beam of the receiver array with 7% error.