Motion tomography: Mapping flow fields using autonomous underwater vehicles

Abstract

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.

A data assimilation framework for data-driven flow models enabled by motion tomography

“…We assume that vehicle heading i (j, ) can be measured by a compass or estimated with small bounded error. The influence of the vehicle heading error on MT is analyzed in our previous work (Chang et al 2017).…”

“…Therefore, flow field mapping through MT (see Algorithm 1) is achieved through an iterative process consisting of two key steps: trajectory tracing and flow field estimation. In this section, we introduce flow field estimation and refer to Chang et al (2017) for details about trajectory tracing. between simulated and real ending positions.…”

“…To solve the underdetermined nonlinear system of equations in (19), our previous work (Wu et al 2013;Chang et al , 2017) developed a method by extending the Kaczmarz method (Kaczmarz 1937(Kaczmarz , 1993. The Kaczmarz method, also known as the algebraic reconstruction technique (Gordon et al 1970), iteratively solves an underdetermined linear system of equations for computerized tomography (Kak and Malcom 2001;Natterer 1986;Cierniak 2011) in medical imaging.…”

“…Extended from the Kaczmarz method, a nonlinear Kaczmarz method has been developed in Wu et al (2013), Chang et al ( , 2017 to solve (19) for MT. Suppose we have the following system of equations:…”

“…To facilitate assimilation of Lagrangian data collected by AUVs into the GEM, we employ the motion tomography (MT) method (Wu et al 2013;Chang et al , 2017. Along the trajectory of a vehicle, its motion is typically perturbed by ambient flow, deviating the actual trajectory of the vehicle from its predicted trajectory.…”