Resolving Temporal Variations in Data-Driven Flow Models Constructed by Motion Tomography**The research work is supported by ONR grants N00014-10-10712 (YIP) and N00014-14-1-0635; and NSF grants OCE-1032285, IIS-1319874, and CMMI-1436284

Modeling and predicting ocean flow are great challenges in physical oceanography. To answer such challenges, mobile sensing platforms have been an effective tool for providing Lagrangian flow information. Such information is typically incorporated into ocean models using Lagrangian data assimilation which requires significant amount of computing power and time. Motion tomography (MT) constructs generic environmental models (GEMs) that combine computational ocean models with real-time data collected from mobile platforms to provide highresolution predictions near the mobile platforms. MT employs Lagrangian data from mobile platforms to create a spatial map of flow in the region traversed by the mobile platforms. This paper extends the MT method to resolve the coupling between temporal variations and spatial variations in flow modeling. Along with Lagrangian data from a mobile sensor, Eulerian data are collected from a stationary sensor deployed in the region where the mobile sensor collects data. Assimilation of these two data sets into GEMs introduces a nonlinear filtering problem. This paper presents the formulation of such nonlinear filtering problem and derives a filtering method for estimating flow model parameters. We analyze observability for the derived filters and demonstrate that the resulting method improves navigation accuracy for mobile platforms.