This paper presents a study on object tracking in surveillance systems using Gaussian-Sum Filter and Aggregate Channel Features (ACF) detection to address the challenges of accurately tracking multiple objects in dynamic environments. Object tracking is crucial in computer vision, with applications from surveillance and security to autonomous navigation and robotics. This study employs the Gaussian-Sum Filter, a proven Bayesian filtering algorithm known for its predominance in non-linear scenarios, which keeps object tracking more consistent over time. However, since the ACF detection method can detect objects over multiple frames with higher accuracy than our initial detections, we combine it with initial ones. Performance testing is conducted across four datasets, using key metrics such as precision, Multiple Object Tracking Precision (MOTP), and Multiple Object Tracking Accuracy (MOTA) to evaluate effectiveness. The results show that while Gaussian Sum Filter combined with ACF detection achieves different precision with specific datasets (7%-98%) and MOTP rates (10%-73%), challenges arise in maintaining uninterrupted tracking accuracy, as evidenced by very low MOTA (-6%-10%) and a significant rate of false negatives, especially in complex scenarios with occlusions. These findings suggest that although Gaussian-Sum Filter and ACF detection are effective for initial detection and data handling, enhancements or hybrid methods may be required for applications demanding high accuracy in continuous multi-object tracking.