In 1996, an acoustic research array with both horizontal and vertical components was deployed through the polar ice pack north of Ellesmere Island. The horizontal components consist of a 2.4-km horizontal line array (HLA) of 80 hydrophones on the seafloor and a 240-m secondary HLA of 8 hydrophones perpendicular to the main HLA. To accurately localize these hydrophones, a series of recordings were made immediately after deployment. Glass light bulbs were imploded at 50-m depth at eight locations surrounding the array. Source locations were known to within approximately 2 m; however, to invert the travel time data to within their estimated uncertainties, it was necessary to include corrections to the source locations as unknowns. Source instants were not measured, and were also included as unknowns. An iterative inversion algorithm was formulated by expanding the ray-tracing equations and neglecting second-order terms to yield a linear system of equations. The system was solved by minimizing the HLA curvature and source-location corrections subject to fitting the data to a statistically meaningful level. Minimizing HLA curvature produces a minimum-structure solution in which any deviations from a straight array are absolutely required by the data, and are not artifacts of the starting model.