## 1 Introduction  
For the real-time control, navigation and post-flight data analysis of aircraft flying in the atmosphere, it is necessary to accurately measure the flight parameters [1, 2]. The flush air data sensing (FADS) system has no components outside the surface of the aircraft and can be used for modern advanced aircraft such as hypersonic and stealth aircraft. In addition, the whole system has no mechanical moving parts, which reduces the maintenance time and cost, and it is considered to be one of the most promising air data measurement systems for measurements such as angle of attack and sideslip angle [3, 4, 5]. FADS relies on an array of pressure sensors distributed at the front of the aircraft to measure the pressure on the aircraft surface and indirectly obtain flight parameters from the pressure distribution. However, when the aircraft is flying at a high angle of attack, the sensitivity of the air pressure on the leeward side to the angle of attack will be seriously reduced. In addition, when the aircraft is in high dynamic maneuvering, the maneuvering of the flight itself will disrupt the original flow field, which in effect will increase the measurement error of the aircraft pressure. The above two points lead to the accuracy of FADS to be drastically reduced when the aircraft is in a high angle of attack or high dynamic maneuvering flight conditions [6]. Unlike FADS, according to the measured acceleration and angular velocity of the aircraft, the inertial navigation system (INS) calculates the velocity, position and attitude of the aircraft through the navigation algorithm and then obtains the atmospheric data according to the atmospheric model [7]. Because the information source of INS is the acceleration and angular velocity of the aircraft, it will not be affected by external interference when using inertial navigation information and an atmospheric model to solve flight parameters. However, the outstanding disadvantage of INS is that the accuracy decreases with the increase of time due to the influence of drift error; when the navigation time is long, the accuracy of the inertial navigation will be greatly reduced. It is also very difficult to accurately estimate the flight parameters of the aircraft by relying solely on an inertial navigation system [8]. Therefore, it is necessary to fuse the flight parameters estimated by INS and FADS and that the two complement each other to meet the accurate estimation of flight parameters in various flight states. At present, there are two main fusion algorithms for FADS and INS [9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. One is a data fusion algorithm based on complementary filtering, the other is a data fusion algorithm based on Kalman filtering. In reference [19], a FADS/INS fusion algorithm based on complementary filtering is designed and verified on the X-34 aircraft, the experiment proves the effectiveness of the algorithm. The essence of the algorithm is a simple complementary filter, the unbiased estimation of the state value of the atmospheric parameters is obtained by combining the parameters of the FADS and the INS parameters along the trajectory. In Reference [20], a complementary filtering algorithm based on FADS measurement results and modified by inertial navigation system is designed to calculate the angle of attack and sideslip angle, and the effectiveness of the algorithm is proved by simulation. Reference [21] proposes to use the angle of attack calculated by INS to correct the angle of attack solved by FADS and fuse the parameters solved by the two through complementary filtering. The simulation results show that the method can finitely improve the measurement accuracy of the aircraft in stable flight and high maneuvering flight. References [19; 20; 21] introduce the fusion algorithm based on complementary filtering. In addition, there is a fusion algorithm based on Kalman filtering.