This work demonstrates an airflow inertial based odometry system with multi-sensor data fusion, including thermal anemometer, IMU, ESC, and barometer. This goal is challenging because low-cost IMUs and barometers have significant bias, and anemometer measurements are very susceptible to interference from spinning propellers and ground effects. We employ a GRU-based deep neural network to estimate relative air speed from noisy and disturbed anemometer measurements, and an observer with bias model to fuse the sensor data and thus estimate the state of aerial vehicle. A complete flight data, including takeoff and landing on the ground, shows that the approach is able to decouple the downwash induced wind speed caused by propellers and the ground effect, and accurately estimate the flight speed in a wind-free indoor environment. IMU, and barometer bias are effectively estimated, which significantly reduces the position integration drift, which is only 5.7m for 203s manual random flight. The open source is available on https://github.com/SyRoCo-ISIR/Flight-Speed-Estimation-Airflow.