The Vehicle Dynamic Model (VDM) based navigation of fixed-wing drones determines the airborne trajectory in conjunction with Inertial Measurement Unit (IMU) sensors. Without Global Navigation Satellite Systems (GNSS) signals, this method estimates navigation quantities with substantially better quality than the conventional kinematic inertial-based approach. The research focuses on the following key aspects: i) determination/calibration of aerodynamic model parameters using flight data only, ii) real-time implementation of the estimation/navigation scheme during different flight phases, and iii) experimental evaluation of two types of drones. After the introduction related to aerodynamic modeling and estimation aspects, a novel calibration of aerodynamic coefficients from flight data is proposed for their coarse and fine estimation. The first methodology is proposed as an original consecutive application of three linear estimators for the wind, aerodynamic moments, and force parameters, respectively. The information conveyed with each measurement is used within a Schmidt-Kalman filter according to a heuristic approach to observability (Grammian). The most observable parameters are thus updated, mostly in relation to dynamic maneuvers, to obtain a sufficiently good estimate, which is further improved in the second stage. There, the parameters are refined either via VDM-based filtering or with an optimal smoother. An off-line estimation is preferred for a not-yet-calibrated drone, as it can benefit from precise GNSS observations and attitude updates obtained either by a conventional combination of Inertial Navigation System (INS) and GNSS and/or via photogrammetry. The real-time model-based navigation is then implemented within a companion computer embedded in the payload of a prototype drone. The information flow between sensors, autopilot, and computer is handled via nodes of the Robotic Operation System (ROS). Following a sensitivity analysis on the quality of time-tagging between the sensors and the control commands, the open-source autopilot is modified so that the required information on the actuators is expressed in GNSS time to within less than 1 ms. The Schmidt-Kalman implementation is proposed to manage the different phases of flight, from initialization, to nominal, and interrupted reception of GNSS signals. The implementation and its navigation performance are validated in several flights using MEMS-inertial sensors of different quality for the prototype drone with a conventional shape, and for a commercial delta-wing profiled drone. After a few minutes of navigation with GNSS accounting for the possible re-estimation of parameters, autonomous VDM/IMU-based navigation outperforms that based solely on IMU and pressure sensors by up to five times in terms of absolute accuracy. These investigations and findings raise new directions for further development and the use of model-based navigation for downstream applications, such as wind estimation and operations in unstable GNSS-signal environments.