Accurate 3D multi-object tracking (MOT) is crucial for autonomous driving, as it enables robust perception, navigation, and planning in complex environments. While deep learning-based solutions have demonstrated impressive 3D MOT performance, model-based approaches remain appealing for their simplicity, interpretability, and data efficiency. Conventional model-based trackers typically rely on random vector-based Bayesian filters within the tracking-by-detection (TBD) framework but face limitations due to heuristic data association and track management schemes. In contrast, random finite set (RFS)-based Bayesian filtering handles object birth, survival, and death in a theoretically sound manner, facilitating interpretability and parameter tuning. In this paper, we present OptiPMB, a novel RFS-based 3D MOT method that employs an optimized Poisson multi-Bernoulli (PMB) filter while incorporating several key innovative designs within the TBD framework. Specifically, we propose a measurement-driven hybrid adaptive birth model for improved track initialization, employ adaptive detection probability parameters to effectively maintain tracks for occluded objects, and optimize density pruning and track extraction modules to further enhance overall tracking performance. Extensive evaluations on nuScenes and KITTI datasets show that OptiPMB achieves superior tracking accuracy compared with state-of-the-art methods, thereby establishing a new benchmark for model-based 3D MOT and offering valuable insights for future research on RFS-based trackers in autonomous driving.