Calculating Navigation Angles Using Quaternions

In this article, we briefly introduce a method for calculating navigation angles that combines quaternion mathematics with gyroscope and accelerometer signals. Quaternions serve as a mathematical tool for representing rotation orientation and angles, effectively resolving the gimbal lock problem associated with Euler angles. By fusing gyroscope and accelerometer data—where the gyroscope measures angular velocity and the accelerometer detects gravitational acceleration—we achieve more accurate and stable navigation angles, thereby enhancing the precision and reliability of navigation systems. From a code implementation perspective, this typically involves initializing a quaternion, then continuously updating it using gyroscope data via numerical integration (e.g., the Runge-Kutta method or a simpler first-order approximation). The accelerometer data is used for drift correction, often through complementary filtering or Kalman filtering algorithms to compensate for gyroscope bias. Key functions may include `quaternion_update()` for propagating the quaternion state and `accel_correction()` for normalizing and fusing accelerometer measurements. This approach has been widely adopted in applications such as aircraft navigation and attitude control systems. Consequently, the quaternion-based method for calculating navigation angles offers a robust and efficient solution for the design and implementation of advanced navigation systems.