A Mathematical Modeling Method for the Expression of Navigation Situations in Complex Port Environments

The unified expression of the mixed, dynamic and scattered navigation situation information in complex port area environments in a computable mathematical model is the foundation for ships to achieve intelligence and unmanned capability. Existing studies remain insufficient in terms of characterizing complex navigation situations involving multiple interacting factors, such as ship attributes, dynamic encounter relationships, spatial constraints, environmental conditions and navigation rules. To address this issue, a mathematical expression method for navigation situations is proposed. The ship interest perception area is first defined and discretized to characterize the directional anisotropy of surrounding situation constraints. Then, the ship interaction field, encounter conflict field, and navigation restriction field are constructed and integrated through normalization and weighted coupling. Environmental impacts, navigation-rule compliance, direction weights, and direction consistency are further incorporated to map the comprehensive situation constraint distribution into a virtual guidance direction, and a computable relationship between situation space and short-term behavioral preference space is established. Finally, the model is calibrated and validated using real ship data. The results demonstrate that the proposed model can effectively characterize directional multi-source constraints in typical complex port scenarios and generate directional preferences that are reasonably consistent with actual short-term ship motion, providing a structured information basis for navigation situation understanding and upper-level autonomous decision-making of unmanned ships.