Vessel-position Tracking in 3-sphere Space Using an Interacting Multiple Model Based on Lie Theory

This paper proposes a method for tracking vessel positions using an interacting multiple model approach based on Lie theory in 3-sphere space. Attitude increments and errors are evaluated and corrected using Lie algebra, as well as exponential and logarithmic operations. The covariance of attitudes is appropriately represented in Lie algebra. The proposed method is compared with two methods, i.e., the unscented Kalman filter (UKF) in which the attitude is represented by a unit quaternion (quaternion-utilizing UKF) and the UKF with a single model that uses Lie theory (Lie theory-incorporating UKF). The quaternion-utilizing UKF represents the attitude using quaternions without incorporating Lie theory, whereas the Lie theory-incorporating UKF represents the attitude as a unit quaternion and utilizes Lie theory. The comparisons indicate that the proposed method effectively reduces tracking errors. Additionally, the proposed method adapts to changes in maneuvering conditions using optimized model probabilities, ensuring timely and appropriate responses. The robustness and effectiveness of the proposed method in various maneuvering scenarios demonstrate its potential for enhancing vessel tracking accuracy in real-world applications. © ICROS 2024.