Airspeed measurement is crucial for UAV control. To achieve accurate airspeed measurements for UAV, this paper calculates airspeed data by measuring changes in air pressure and temperature. Based on this, a data processing method based on mechanical filtering and improved AR-SHAKF algorithm is proposed to indirectly measure airspeed with high precision. In particular, a mathematical model for an airspeed measurement system is established, and an installation method for the pressure sensor is designed to measure the total pressure, static pressure and temperature. Secondly, the measurement principle of the sensor are analyzed, and a metal tube is installed to act as a mechanical filter, particularly in cases where the aircraft has a significant impact on the gas flow field. Furthermore, a time-series model is used to establish the sensor state equation and the initial noise values. It also enhances the Sage-Husa adaptive filter to analyze the unavoidable error impact of initial noise values. By constraining the range of measurement noise, it achieves adaptive noise estimation. To validate the superiority of the proposed method, a low-complexity airspeed measurement device based on MEMS pressure sensors is designed. The results demonstrate that the airspeed measurement device and the designed velocity measurement method can effectively calculate airspeed with high measurement accuracy and strong interference resistance.