In this paper, we present an approach to Multi-Object Tracking (MOT) that is based on the Ensemble Kalman Filter (EnKF). The EnKF is a standard algorithm for data assimilation in high-dimensional state spaces that is mainly used in geosciences, but has so far only attracted little attention for object tracking problems. In our approach, the Optimal Subpattern Assignment (OSPA) distance is used for coping with unlabeled noisy measurements and a robust covariance estimation is done using FastMCD to deal with possible outliers due to false detections. The algorithm is evaluated and compared against a global nearest neighbour Kalman Filter (NNKF) and a recently proposed JPDA-Ensemble Kalman Filter (JPDA-EnKF) in a simulated scenario with multiple objects and false detections.