Object tracking is an important and central aspect of autonomous driving, as it underlies the obstacle detection and avoidance systems of any type of autonomous vehicles. A widely used method for tracking is based on Kalman filters, both for linear and non-linear cases, with different computational burden. Unfortunately, object tracking algorithms are computationally intensive, and they may not easily meet the efficiency and responsiveness requirements of real-time applications such as autonomous driving. This issue motivates ad-hoc investigations to speed up the computation and make Kalman filtering available even within limited computational power. This paper carry out a performance evaluation of a Kalman filter based object tracking system taken from a real tramway use-case, and aims at improving its performance efficiency by leveraging parallelization. In particular, this work analyzes the possibilities of execution parallelization on multi-core processors, proposing a target-specific optimization approach and comparing the obtained results, then summing them in general lessons learned. Our technique achieves up to 80% reduction of single frame processing time in the most crowded cases.