The lateral line system is an important sensory organ for fish and many aquatic amphibians, allowing them to detect predators/prey, perform rheotaxis, and coordinate schooling. There is an increasing interest in developing artificial lateral line systems, consisting of arrays of flow sensors, for underwater vehicles and robots. In this paper we consider the problem of localizing a vibrating sphere, also known as a dipole source, using an artificial lateral line system. Dipole sources emulate the movement of fish fins and are often used in the study of biological lateral lines. We assume that the location, vibration amplitude, and vibration direction of the dipole sources are all unknown. A nonlinear estimation problem is formulated based on the analytical model for dipole-generated flow field. We present two recursive algorithms for source localization, the first obtained by linearizing the original nonlinear estimation problem, and the other by solving the equations corresponding to the first-order optimality condition. Simulation results are presented to illustrate the effectiveness of the proposed approaches.