Camera calibration and localization, sometimes simply named camera calibration, enables many applications in the context of soccer broadcasting, for instance regarding the interpretation and analysis of the game, or the insertion of augmented reality graphics for storytelling or refereeing purposes. To contribute to such applications, the research community has typically focused on single-view calibration methods, leveraging the near-omnipresence of soccer field markings in wide-angle broadcast views, but leaving all temporal aspects, if considered at all, to general-purpose tracking or filtering techniques. Only a few contributions have been made to leverage any domain-specific knowledge for this tracking task, and, as a result, there lacks a truly performant and off-the-shelf camera tracking system tailored for soccer broadcasting, specifically for elevated tripod-mounted cameras around the stadium. In this work, we present such a system capable of addressing the task of soccer broadcast camera tracking efficiently, robustly, and accurately, outperforming by far the most precise methods of the state-of-the-art. By combining the available open-source soccer field detectors with carefully designed camera and tripod models, our tracking system, BroadTrack, halves the mean reprojection error rate and gains more than 15% in terms of Jaccard index for camera calibration on the SoccerNet dataset. Furthermore, as the SoccerNet dataset videos are relatively short (30 seconds), we also present qualitative results on a 20-minute broadcast clip to showcase the robustness and the soundness of our system.