In multi-target tracking, the maintaining of the correct identity of targets is challenging. In the presented tracking method, accurate target identification is achieved by incorporating the appearance information of the spatial and temporal context of each target. The spatial context of a target involves local background and nearby targets. The first contribution of the paper is to provide a new discriminative model for multi-target tracking with the embedded classification of each target against its context. As a result, the tracker not only searches for the image region similar to the target but also avoids latching on nearby targets or on a background region. The temporal context of a target includes its appearances seen during tracking in the past. The past appearances are used to train a probabilistic PCA that is used as the measurement model of the target at the present. As the second contribution, we develop a new incremental scheme for probabilistic PCA. It can update accurately the full set of parameters including a noise parameter still ignored in related literature. The experiments show robust tracking performance under the condition of severe clutter, occlusions and pose changes.