This paper presents a coupled, joint probabilistic data association (JPDA) algorithm for multi-target tracking using a modified version of the standard measurement-to-track assignment model. The mutually exclusive nature of standard JPDA association events precludes any measurement being associated with more than one target in a given event. This constraint is relaxed here to allow a measurement to be assigned to multiple targets. All other JPDA assumptions are retained (i.e., no measurement can be simultaneously associated with target and clutter, and each track can claim at most one measurement). The computational requirements of the resulting algorithm grow linearly with the number of tracks. The recursive estimators for the coupled track means and covariance are derived and presented.