Improved Online Kalman Smoothing Method for Ship Maneuvering Motion Data Using Expectation-Maximization Algorithm

Despite the pivotal role of filtering and smoothing techniques in the preprocessing of ship maneuvering data for robust identification, persistent challenges in reconciling noise suppression with dynamic fidelity preservation have limited algorithmic advancements in recent decades. We propose an online smoothing method enhanced by the Expectation-Maximization (EM) algorithm framework that effectively extracts high-fidelity dynamic features from raw maneuvering data, thereby enhancing the fidelity of subsequent ship identification systems. Our method effectively addresses the challenges posed by heavy-tailed Student-t distributed noise and parameter uncertainty inherent in ship motion data, demonstrating robust parameter learning capabilities, even when initial ship motion system parameters deviate from real conditions. Through iterative data assimilation, the algorithm adaptively calibrates noise distribution parameters while preserving motion smoothness, achieving superior accuracy in velocity and heading estimation compared to conventional Rauch–Tung–Striebel (RTS) smoothers. By integrating parameter adaptation within the smoothing framework, the proposed method reduces motion prediction errors by 23.6% in irregular sea states, as validated using real ship motion data from autonomous navigation tests.