Beamforming for an array typically requires array-element localization (AEL) to within one-tenth of a wavelength. Often it is impractical to install dedicated, large-bandwidth AEL transponders with an array. This paper presents an approach to AEL for fixed, bottom-mounted arrays without transponders. High-SNR signals from multiple near-field imploding lightbulbs and interpolated correlations allow a statistical reduction in the inherent uncertainty in arrival-time measurements imposed by the bandwidth of the sensors. The method is illustrated with an application to the SWSS (shallow-water sensor string) array offshore of San Diego, at depths from 180 to 200 m.