Deck motion compensation and relative navigation require real-time, accurate knowledge of a ship's center of rotation (CoR), which varies with floating condition, sea state, loading, and maneuvers and cannot be measured directly. We prove from rigid-body kinematics that, using only position or velocity observations of hull-mounted measurement points, the translation and the CoR cannot be separated: the inversion possesses gauge invariance, the unconstrained fitness surface is completely flat, and no optimization algorithm can converge. A polynomial-constrained translation model breaks this invariance, reducing the inversion to linear least squares with a closed-form global optimum. The framework holds in strict duality for multi-antenna GNSS (position domain) and multi-INS (velocity domain) observations, and a motion-excitation allocation theory predicts the longitudinal CoR component hardest to identify and the vertical easiest. Simulations, five-level sea-state excitation experiments, and at-sea validation show that the multi-INS scheme reduces the CoR root-mean-square error to 0.54 m, about 60% of the GNSS scheme, and the two independent systems agree to within 2.0 m (Z) and 6.5 m (Y) in strongly excited intervals. Requiring no ship dynamics model, the method provides a rigorous theoretical basis and a feasible dual-system framework for low-cost deck-relative navigation.
关键词
瞬时转动中心估计 规范不变性 多项式约束 多天线GNSS 多INS 甲板运动补偿
Key words
center of rotation estimation/ gauge invariance/ polynomial constraint/ multi-antenna GNSS/ multi-INS/ deck motion compensation
