Our objective is to locate and provide a unique identifier for each mouse in a cluttered home-cage environment through time, as a precursor to automated behaviour recognition for biological research. This is a very challenging problem due to (i) the lack of distinguishing visual features for each mouse, and (ii) the close confines of the scene with constant occlusion, making standard visual tracking approaches unusable. However, a coarse estimate of each mouse's location is available from a unique RFID implant, so there is the potential to optimally combine information from (weak) tracking with coarse information on identity. To achieve our objective, we make the following key contributions: (a) the formulation of the object identification problem as an assignment problem (solved using Integer Linear Programming), and (b) a novel probabilistic model of the affinity between tracklets and RFID data. The latter is a crucial part of the model, as it provides a principled probabilistic treatment of object detections given coarse localisation. Our approach achieves 77% accuracy on this animal identification problem, and is able to reject spurious detections when the animals are hidden.