Attitude Resolution for Strapdown Inertial Systems Using Quaternion Methods

Quaternion methods serve as an efficient and stable mathematical tool for attitude resolution in strapdown inertial systems, particularly suitable for applications requiring precise attitude control such as aircraft and spacecraft. Quaternions represent three-dimensional rotations using four parameters (one real component and three imaginary components), offering advantages over traditional Euler angle methods by eliminating gimbal lock issues and providing higher computational efficiency.

In strapdown inertial systems, gyroscopes provide angular velocity data for real-time attitude updates. The quaternion differential equation transforms gyroscope measurements into attitude changes. The key implementation involves quaternion update algorithms, typically employing numerical integration methods like Runge-Kutta to solve differential equations while maintaining computational accuracy during high-speed maneuvers or large-angle rotations. Code implementation often includes normalizing quaternions after each update to prevent numerical drift.

Accelerometer data primarily supports attitude correction through auxiliary measurements. Since the gravity vector's direction in the navigation coordinate system is known, comparing accelerometer-measured specific force direction with gravity direction enables attitude error calculation. This error is fed back into the quaternion update process using complementary filtering or Kalman filtering algorithms, effectively suppressing cumulative errors caused by gyroscope drift. Implementation typically involves sensor fusion algorithms that weight accelerometer data more heavily during low-acceleration periods.

For navigation parameter computation, the resolved quaternion is converted into a direction cosine matrix to transform coordinates from the body frame to the navigation frame. Combined with other sensor data, this enables calculation of velocity, position, and other navigation parameters. The implementation requires consistent coordinate system definitions and careful time synchronization of multisensor data. Code typically includes coordinate transformation functions and timestamp management routines.

Practical engineering implementations must address computational efficiency optimization and singularity handling. Modern strapdown inertial navigation systems often integrate GPS and other navigation aids through data fusion techniques, further enhancing attitude resolution accuracy and reliability. Implementation considerations include real-time processing optimization, memory management for embedded systems, and fault-tolerant algorithm design.