A three-dimensional version of matched-field tracking (MFT), a generalization of matched-field processing (MFP), is used to locate and track a towed source using a vertical array during SWellEx-96---an experiment conducted off the San Diego coast in May 1996. Archival and in situ environmental data are used as input into a forward propagating adiabatic normal mode (ANM) model and a reciprocal propagating parabolic equation (PE) model to create the three-dimensional replica fields used to compute ambiguity volumes (the three-dimensional generalization of the ubiquitous two-dimensional ambiguity surface). Interaction with variable bathymetry caused by a downward refracting sound-speed profile and shallow water is not sufficient to provide uniqueness of the data and replica fields, thus creating many ambiguities for any given data within the fiducial volume. These ambiguities can be minimized via MFT, which uses source motion to reduce the number and relative magnitude of false ambiguities by averaging the ambiguity functions corresponding to trial source tracks defined by an initial position and velocity vector. As increasing numbers of ambiguity functions are averaged, steady movement within a fluctuating background can be detected.