Accurate navigation is required in many Unmanned Aerial Vehicle (UAV) applications. In recent years, GNSS Precise Point Positioning (PPP) has been recognised as an efficient approach for providing precise positioning services. In contrast to the widely used Real-Time Kinematic (RTK), PPP is independent of reference stations, which greatly broadens its scope of application. However, the accuracy and reliability of PPP can be significantly decreased by poor GNSS satellite geometry and outage. In response, a real-time four-constellation GNSS PPP is applied to improve the geometry in this work, and PPP is tightly coupled with an Inertial Measurement Unit (IMU) to smooth the position and velocity output, thus improving the robustness of the navigation solution. Experimental flight tests are carried out using a UAV in an open-sky area, and GNSS-challenged environments are simulated. The results show that the four-constellation GNSS PPP/IMU integration reduces the Root-Mean-Square (RMS) Three-Dimensional (3D) positioning and velocity error by 76.4% and 67.1%, respectively, in open sky with respect to the one-GNSS PPP. Under scenarios where GNSS measurements are insufficient, the coupled system can still provide continuous solutions. Moreover, the coupled PPP/IMU system can also maintain the convergence of PPP during GNSS-challenged periods and can greatly shorten the re-convergence period of PPP when the UAV returns to the open sky.