Biquaternion Evolution in Attitude Estimation Using a Generalized Vector Measurement

This letter investigates attitude estimation based on biquaternions (complex quaternions) for robotic applications utilizing a single-vector observation from sensors, such as accelerometer and magnetometer. In this work, we discover the evolution of novel form of quaternion, termed the biquaternion, where each component is a complex number instead of a real scalar, in the attitude approximation process. This biquaternion form arises from the intermediate solution of differential equations obtained from quaternion attitude dynamics. We study the evolution trajectories of biquaternions in the attitude estimation workspace, unveiling their inherent patterns and physical interpretations. Furthermore, we investigate the convergence performance of the biquaternion-based attitude estimator by tuning different parameters, demonstrating its potential superiority over traditional real quaternion estimators. The proposed biquaternion attitude estimation framework offers a unique perspective on attitude representation and opens up new avenues for enhancing estimation accuracy and robustness.