The attitude calculation of unmanned aerial vehicles generally involves two types of optimization algorithms: one is IMU, and the other is AHRS, which is widely adopted by various unmanned aerial vehicles. Let's discuss them together.

　　AHRS (Attitude and Heading Reference System), also known as the attitude reference system software, consists of accelerometers, magnetometers, and gyroscopes. It can provide quadcopters with information on yaw, roll, and pitch. This system is used to provide accurate and reliable state and navigation information for quadcopters. The true reference of AHRS comes from the gravitational field on Earth and the electromagnetic field of the universe. Its static precision depends on the measurement accuracy of the electromagnetic field and the measurement accuracy of the force, while the gyroscope determines its dynamic characteristics. It indicates that AHRS cannot operate normally when it is away from the gravitational and electromagnetic environment of the Earth. Moreover, it should be noted that the more orthogonal the electromagnetic field and gravitational field are, the higher the accuracy of attitude measurement will be. In other words, if the electromagnetic field and gravitational field are parallel, such as at the magnetic poles, where the magnetic field strength is directed downward, the same as the direction of the weight field, the navigation angle cannot be measured. This is a problem with the attitude system, and in high-latitude areas, the navigation angle error can also lead to significant discrepancies.

　　IMU (Inertial Measurement Unit), also known as the inertial measurement module, tells us through materials mechanics that all motion can be transformed into uniform linear motion and rotational motion. Therefore, this inertial measurement module is used to measure these two types of motion. Uniform linear motion can be measured using accelerometers, while rotational motion is measured using gyroscopes. Generally, an IMU consists of three dual-axis accelerometers and three dual-axis gyroscopes. The accelerometers detect the instantaneous velocity signals of the object in the medium coordinate system along three axes, while the gyroscopes detect the linear velocity signals of the medium relative to the navigation coordinate system, measuring the linear velocity and instantaneous velocity of the object in three-dimensional space, and calculating the object's attitude. It has significant practical value in navigation. To enhance reliability, more sensors can be configured for each axis. Generally, the IMU should be installed at the center of mass of the object being measured.

　　If the detection of the gyroscope and accelerometer in the IMU is without any errors, it can still lead to certain discrepancies. However, the gyroscope can accurately measure the object's attitude. By integrating the accelerometer's data, displacement can be obtained, achieving a complete 6DOF. In other words, carrying such a theoretical IMU in any position in space allows us to understand its current state and relative displacement, which is not limited to any field.

　　From the internal description, it can be seen that AHRS has one more electromagnetic field sensor than IMU, but why is the level of AHRS lower than that of IMU? This depends on the gravitational field and electromagnetic field! It is determined by the sensor component structure. The sensors in AHRS are generally inexpensive MEMS sensors. The noise of these sensors' gyroscopes and accelerometers is relatively high. For example, using an ADI gyroscope for integration for one minute can drift about 2 degrees. In this case, if there is no electromagnetic field and gravitational field to correct the three-axis gyroscope, then after about 3 minutes, the actual attitude of the object and the measured output attitude will be completely different. Therefore, under the framework of these inexpensive gyroscopes and accelerometers, it is necessary to use spatial vectors for correction.

　　The same is true for IMU. Because we know that there are no absolutely accurate sensors, only relatively accurate sensors, the gyroscopes in IMU use fiber optic gyroscopes or mechanical gyroscopes. These gyroscopes are expensive, and their accuracy is relatively high compared to MEMS gyroscopes. High precision does not mean accuracy; the motion precision parameters of IMU generally drift a few degrees per hour, for example, a low-end xbow has a drift of 3 degrees per hour. If using accelerometers to integrate for position, AHRS is not accurate (it can drift several tens of meters in one minute, and the rate of drift increases quadratically). AHRS generally needs to combine GPS and barometric sensors for positioning.

　　Using three-axis magnetometers to decouple and three-axis accelerometers, the influence of external instantaneous velocity is significant. In environments with motion/vibration, the output azimuth angle can also lead to considerable discrepancies. Additionally, magnetometers have limitations; their absolute reference is the magnetic field lines of the Earth. The characteristic of magnetometers is that they use standard values but have low intensity, about a few tenths of a Gauss, and are easily affected by other magnetic fields. If combined with the instantaneous velocity angle of the Z-axis gyroscope, it can make the system data more stable. The instantaneous velocity measurement is in the direction of gravity, and in the absence of external instantaneous velocity, it can accurately output the ROLL/PITCH angles without cumulative errors, remaining accurate over longer time and frequency domains. However, the drawback of instantaneous velocity sensors is that they actually use MEMS technology to detect slight deformations caused by inertial moments, and the inertial moment is essentially the same as the force. Therefore, accelerometers cannot distinguish between gravitational acceleration and external instantaneous velocity. When the system decelerates in three-dimensional space, its output becomes incorrect.

　　The mobile gyroscope outputs angular velocity, which is an instantaneous velocity quantity. Angular velocity cannot be immediately applied in motion balance; it requires integrating linear velocity over time to obtain the angle change and summing it with the original angle to get the target angle. The smaller the integration time Dt, the more accurate the output angle. However, the working principle of the mobile gyroscope determines that its measurement standard is self-referential, without an absolute reference outside the system. Additionally, Dt cannot be infinitely small, so the accumulated data error from integration will rapidly increase over time, causing the output angle to deviate from reality. Therefore, the mobile gyroscope can only operate within relatively short time and frequency domains. Thus, in the absence of other references, to obtain a more realistic attitude angle, it is necessary to use a weighted calculation algorithm to complement each other, combining the advantages of both while discarding their respective flaws, designing an algorithm to enhance the weight of the mobile gyroscope in short time and frequency domains, and increasing the weight of instantaneous velocity in longer time and frequency domains, so that the system output angle approaches the actual value.