Motion tomography: Mapping flow fields using autonomous underwater vehicles

Since the motion of autonomous underwater vehicles is affected by ambient flow, knowledge of an environmental flow field can be used to improve the navigation of autonomous underwater vehicles. Due to imperfect knowledge of flow, the actual trajectory of an autonomous underwater vehicle deviates from the predicted trajectory. The difference between the actual and predicted trajectories is referred to as the motion-integration error, providing information of flow along the vehicle trajectory. Inspired by computerized tomography, this paper proposes motion tomography, a tomographic method for creating a fine-grid spatial map of flow based on the motion-integration error. While typical computerized tomography is a linear problem, motion tomography is a nonlinear problem because of unknown nonlinear trajectories of autonomous underwater vehicles and the dependency of the trajectories on the flow field. Therefore, motion tomography employs an iterative process consisting of two alternating steps: Trajectory tracing and flow field estimation. Starting from an initial guess of the flow field, in the trajectory tracing step, unknown nonlinear vehicle trajectories are estimated. Then, using the estimated vehicle trajectories, a spatial map of flow is constructed through either the non-parametric or parametric flow field estimation. The error bound for trajectory tracing is computed and the convergence of both the non-parametric and parametric flow field estimation algorithms is proved. Simulation and experimental data are analyzed to evaluate the performance of motion tomography when subject to changing vehicle speed and flow variability.