Strapdown Inertial Navigation: Quaternion Method for Navigation Attitude Calculation

Attitude calculation in strapdown inertial navigation systems represents a core computational challenge that directly impacts navigation accuracy and system performance. The quaternion method has emerged as a popular approach for attitude resolution, offering significant advantages over Euler angles and direction cosine matrices in terms of reduced computational load and absence of singularity issues.

The fundamental principle of attitude calculation in strapdown systems involves real-time updating of the vehicle's orientation using angular velocity data measured by gyroscopes. The quaternion method employs angular velocity information to construct quaternion differential equations, which are then solved using numerical integration techniques to obtain the current attitude quaternion. In code implementation, this typically involves maintaining a quaternion state variable that gets updated at each sensor sampling interval.

In practical implementation, numerical integration methods such as the Runge-Kutta algorithm are commonly employed to solve the quaternion differential equations. Since quaternion normalization is critical for accurate attitude representation, normalization processing must be performed during calculation to ensure the quaternion maintains unit magnitude. After computation completion, the resulting quaternion can be converted to more intuitive attitude representations like Euler angles or direction cosine matrices as needed. The conversion functions typically involve mathematical operations that extract roll, pitch, and yaw angles from the quaternion components.

The quaternion method's primary advantages include avoidance of gimbal lock issues inherent in Euler angle approaches and superior computational efficiency compared to direction cosine matrix methods. However, practical applications must account for gyroscope noise and drift effects on calculation accuracy, often requiring integration with other sensor data through Kalman filtering or complementary filtering techniques to enhance system robustness and measurement reliability.