Motion tomography performed by autonomous underwater vehicles
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Motion Tomography (MT) is a novel method to estimate an ambient flow field. Based on collective data obtained from the autonomous underwater vehicles (AUV), MT formulates a specific nonlinear system of equations as an inverse problem. In this thesis, we redesign the MT algorithm by using a local approximation of the gradient of AUV position. We establish a theoretical study of motion tomography (MT) problem, where we focus on the evolution of the AUV predicted trajectory, computed by the MT algorithm, to derive the MT error dynamics. A main result of this thesis illustrates a fundamental connection between the trajectory tracing mechanism and the flow update. This insight is not only relevant for proving the convergence of the MT algorithm, but provides a new perspective on inverse problems in general. To overcome the complexity of the underlying problem, we follow a systematic scheme: We start by analyzing one vehicle MT and then we enlarge the scope to multiple vehicle MT. Therein, we looked for an appropriate way to incorporate the collected data from AUVs and accounting for several reasons, discussed in this work, we focused on Motion Tomography Correction per Cycle (MTCC). We proved the convergence of the redesigned algorithm MTCC without imposing the Lipschitz continuity property. Furthermore, we improved the accuracy of ambient flow field estimation by extending the MT algorithm with second part. We modified the AUV predicted velocity so that the simulated final time converges to the measured travel time. Finally, the simulations are in good agreement with the theoretical study and underpin the derived conclusions.