We present a partial observable, non-linear solution for AUV aided navigation, referred as the Reverse Bearing Only Target Motion Analysis (Reverse BO-TMA). Reverse BO-TMA utilizes information about the course and speed of a passing vessel to provide a passive method for self localization of an Autonomous Underwater Vehicle (AUV). In Reverse BO-TMA, the AUV relies on radiated noise from the vessel to measure the bearing to the target vessel. Compared to traditional range-based localization methods, Reverse BO-TMA is a fully passive method that allows the AUV to remain farther from the anchor and does not require collaboration or message exchange in the form of time-synchronization between the AUV and the vessel. We formalize the Reverse BO-TMA, and solve it through least squares optimization. Numerical results show that the Reverse BO-TMA provides accurate localization performance that can greatly increase the accuracy of AUV navigation during long term deployments.