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

Abstract

Autonomous underwater vehicles (AUVs) have become central to data collection for scientific and monitoring missions in the coastal and global oceans. To provide immediate navigational support for AUVs, computational data-driven flow models described as generic environmental models (GEMs) construct a map of the environment around AUVs. This paper proposes a data assimilation framework for the GEM to update the map using data collected by the AUVs. Unlike Eulerian data, Lagrangian data along the AUV trajectory carry time-integrated flow information. To facilitate assimilation of Lagrangian data into the GEM, the motion tomography method is employed to convert Lagrangian data of AUVs into an Eulerian spatial map of a flow field. This process allows assimilation of both Eulerian and Lagrangian data into the GEM to be incorporated in a unified framework, which introduces a nonlinear filtering problem. Considering potential complementarity of Eulerian and Lagrangian data in estimating spatial and temporal characteristics of flow, we develop a filtering method for estimation of the spatial and temporal parameters in the GEM. The observability is analyzed to verify the convergence of our filtering method. The proposed data assimilation framework for the GEM is demonstrated through simulations using two flow fields with different characteristics: (i) a double-gyre flow field and (ii) a flow field constructed by using real ocean surface flow observations from high-frequency radar.

Laplacian regularized motion tomography for underwater vehicle flow mapping with sporadic localization measurements

“…Later, [19] extends MT for distributed flow estimation of multi-agent systems. In addition, the MT method is applied to facilitate assimilation of the Lagrangian data stream collected by the underwater vehicles to Eulerian flow prediction model [20]. [21] generalizes the MT algorithm by parameterizing the flow field using the occupation kernels.…”

“…RMT leverages the spatial correlation of the flow field distribution and enforce some smoothness in the computed solution without under-fitting the data. Comparing to implicit regularization used in [17,20], Laplacian regularization offers a practical trade off between capturing the spatial structure and reducing the noise in the computed flow field.…”

Feature-Informed Data Assimilation -- Definitions and Illustrative Examples

“…In numerical weather prediction, some widely used algorithms are four-dimensional variational data assimilation (4D-Var) [3,4,6,7], ensemble Kalman filters (EnKF) [2,8,9], and their varieties. There are also many engineering applications of DA such as [10] on robotics and [11] on multi-fidelity modeling.…”