A Laplacian Regularized Least Square Algorithm for Motion Tomography

摘要

The motion of an Autonomous Underwater Vehicle (AUV) is often affected by unknown disturbances arising from underwater flow fields. These disturbances may result in large prediction errors when comparing the AUV's expected surfacing location (for example from dead reckoning) and the AUV's measured surfacing location. This error, referred to as the Motion Integration Error, has been used by Motion Tomography algorithm (MT) to reconstruct an estimate of the underwater flow field. In this paper, we extend the MT algorithm to solve the MT problem by introducing Laplacian regularization that penalizes the non-smoothness of the predicted flow field. We propose an iterative algorithm to solve the Regularized MT (RMT) problem. The convergence of the RMT algorithm in the single vehicle case is theoretically justified. The effectiveness of the algorithm for multiple vehicle applications is validated through simulations with cyclonic flow field models. We show that the RMT algorithm outperforms the parametric MT in terms of estimation accuracy and convergence rate.