Robust autonomous flight without GPS is key to many emerging drone applications, such as delivery, search and rescue, and warehouse inspection. These and other applications require accurate trajectory tracking through cluttered static environments, where GPS can be unreliable, while high-speed, agile, flight can increase efficiency. We describe the hardware and software of a quadrotor system that meets these requirements with onboard processing: a custom 300 mm wide quadrotor that uses two wide-field-of-view cameras for visual-inertial motion tracking and relocalization to a prior map. Collision-free trajectories are planned offline and tracked online with a custom tracking controller. This controller includes compensation for drag and variability in propeller performance, enabling accurate trajectory tracking, even at high speeds where aerodynamic effects are significant. We describe a system identification approach that identifies quadrotor-specific parameters via maximum likelihood estimation from flight data. Results from flight experiments are presented, which 1) validate the system identification method, 2) show that our controller with aerodynamic compensation reduces tracking error by more than 50% in both horizontal flights at up to 8.5 m/s and vertical flights at up to 3.1 m/s compared to the state-of-the-art, and 3) demonstrate our system tracking complex, aggressive, trajectories.