This paper describes the application of a Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter for tracking objects in surveillance video. Clark et al. have proposed a point-based GM-PHD filter designed for track label consistency. However, this cannot be used for track consistency when using rectangles covering an object. The proposed solution modifies this filter to increase tracking performance when objects split and overlap. Results on synthetic data and real data show that the number of false detections is slightly lower using the rectangle GM-PHD, for the same error distance. The advantage is that split objects are better handled (10%-20 % lower error distance) by the rectangle GM-PHD filter. We conclude that the overall performance is slightly better of the proposed rectangle tracker, but improvements in occlusion handling are required. 1