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The perception of moving objects in urban environments poses new challenges for sensors and tracking algorithms. Tracking algorithms must estimate the movement of a great number of objects simultaneously while taking longitudinal, crossing, as well as turning traffic into account. In this process, the early recognition and stable tracking of a turning maneuver is a particular challenge. We present an efficient tracking algorithm that faces this task based on laser scanner data. We use a priori knowledge to recognize the objects' maneuvers early and to decide which of the three dynamic models is currently appropriate. Based on the objects' current positions in the intersection, we determine possible turning maneuvers and use them actively in the filtering process. Because the objects' current position is affected with unavoidable measurement errors, we have developed an algorithm to handle the uncertainties in the map matching process. This method enables an early recognition of the object movement and a stable tracking of longitudinal, crossing, and turning traffic.