This paper proposes a fast and online method for jointly performing 3D multi-object tracking and pose estimation using multiple monocular cameras. Our algorithm requires only 2D bounding box and pose detections, eliminating the need for costly 3D training data or computationally expensive deep learning models. Our solution is an efficient implementation of a Bayes-optimal multi-object tracking filter, enhancing computational efficiency while maintaining accuracy. We demonstrate that our algorithm is significantly faster than state-of-the-art methods without compromising accuracy, using only publicly available pre-trained 2D detection models. We also illustrate the robust performance of our algorithm in scenarios where multiple cameras are intermittently disconnected or reconnected during operation.