Motion tomography performed by underwater mobile sensor networks
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Knowledge of the flow field is crucial to guide underwater mobile sensing agents (UMSAs). However, existing flow data sources provide insufficient spatio-temporal resolutions for precise guidance of UMSAs. Because of the imperfect knowledge of flow, the actual trajectory of the UMSA deviates from its predicted trajectory, providing Lagrangian flow information. This thesis develops a method referred to as motion tomography (MT) for creating a high-resolution flow map in the region traversed by UMSAs. The MT method constructs a nonlinear system of equations based on the influence of the underlying flow field on the motion of the UMSA that accumulates along its trajectory. Then, MT formulates estimation of the underlying flow field as an inverse problem. To solve this inverse problem, iterative sub-optimization methods referred to as Kaczmarz-type methods are developed. For easy analysis of the theory, MT first focuses on time-invariant flow with non-parametric and parametric flow models. While non-parametric MT estimates flow for individual grid cells in a discretized domain, parametric MT, which incorporates a data-driven flow model that approximates the flow using basis functions with corresponding parameters, estimates parameters of the flow model. To resolve the coupling between temporal variations and spatial variations in flow modeling, two approaches are proposed. The first approach discretizes the MT mapping domain in both space and time. Because of this spatio-temporal discretization, the solution variables may have a high dimension and may be sparse. To resolve this issue, a data-driven flow model is employed and spatial and temporal parameters are estimated through MT to construct a time-varying flow field. Another approach employs a generic environmental model (GEM) that is a data-driven flow model combined with real-time data streams from UMSAs. The constructed GEM assimilates Lagrangian data, collected from UMSAs and processed through MT for spatial variability, and Eulerian data, collected from stationary sensors such for temporal variability. Due to the coupling between temporal and spatial components of flow, parameter estimation for the GEM becomes a nonlinear filtering problem. By decomposing this nonlinear filtering problem into two linear sub-filtering problems, this approach estimates temporal and spatial parameters. UMSAs often form a data network referred to as an underwater mobile sensor network, but data cannot be always obtained collectively. To address this problem, iterative sub-optimization methods for MT (i.e., Kaczmarz-type methods) are extended to a distributed version. Then, distributed Kaczmarz-type methods are implemented in distributed MT, which solves an inverse problem for MT in a distributed fashion. The performance of MT with the proposed approaches is demonstrated through simulations and experiments.