This paper describes a general method to localize multiple broadband sources in a range- and azimuth-dependent environment when properties of the environment are not well known. Both the source locations and the unknown environmental parameters are included as variables in a simulated annealing inversion that searches for the best match between the measured and modeled fields. The example used to illustrate the method involves localizing an unknown number of ice-ridge building events in an Arctic environment where the bathymetry is poorly known. A number of aspects of this problem are examined in a synthetic study, including the effect of errors in the bathymetry on localization, the importance of simultaneous localization, and determining the number of sources present. The inversion accurately localizes multiple synthetic sources, particularly in cases where the sources are spatially separated and the spectral shape is known. The inversion is also applied to a set of ambient noise measurements recorded in the Lincoln Sea. The results indicate that a small number of ice-ridging sources is sufficient to accurately model the measured fields. Estimates of the number of sources and the source bearings are unambiguous and are reasonably consistent between samples; however, source ranges could not be estimated unambiguously.