From relative to absolute: Tracking the three-dimensional shape of a vertical line array using a ship of opportunity

While the array invariant (AI) can estimate the target-dependent relative tilt of a vertical line array (VLA), it does not provide the array's absolute 3-D orientation. Accurately tracking this absolute tilt is essential for enabling a vertical receive array to also serve as an ocean current observation tool. This presentation introduces a method to address this challenge. Our approach uses a global optimization algorithm to find the most physically plausible 3-D trajectory. The method constrains the solution at each time step to an ambiguity arc derived from the AI-based relative tilt and the known array length, while seeking the smoothest overall path. The proposed method is validated using simulations and then applied to experimental data from the SAVEX15. The results demonstrate that the algorithm can successfully reconstruct the VLA's time-varying 3-D motion from real-world acoustic observations.