This paper presents a technique by which a low-cost, minimally-equipped unmanned underwater vehicle (UUV) can localize itself while submerged using acoustic emissions of transiting sources of opportunity (SOOs). The technique provides a bounded estimate of the UUV position and is intended to supplement the on-board Inertial Navigation System (INS). The technique exploits two physical phenomena, the Doppler effect and the waveguide invariant, which are common to received acoustic signals from sources of opportunity, and is termed waveguide invariant / Doppler-based localization (WI-DBL). The Doppler effect is used to obtain source bearing estimates through a least squares-based technique, and the waveguide invariant is applied to the channel fading pattern to obtain range estimates. There is no requirement for the source track to exhibit the closest point of approach (CPA), nor is there a requirement of prior knowledge of source frequencies or maneuvering of the receiver. Simulated results are presented, which are based on data obtained from a cargo ship transiting a shallow water region during the Noise'09 experiment.