LAPLACIAN REGULARIZED MOTION TOMOGRAHY
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Ouerghi, Meriam
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Abstract
An accurate flow field map is essential for different underwater applications in general and Autonomous Underwater Vehicle (AUV) navigation in particular.
Due to the lack of GPS signals underwater and unreliable underwater communications, AUV navigation is challenging compared with terrestrial applications. As the AUV motion is often affected by unknown disturbances arising from underwater flow fields, that are not captured by ocean models, the AUV actual trajectory may deviate from the predicted trajectory and leads to
large prediction errors when comparing the AUV’s expected surfacing location and the AUV’s measured surfacing location. This error, referred to as the Motion Integration Error, has been used by Motion Tomography algorithm (MT) to reconstruct a high resolution estimate of the underwater flow field.
The main contribution of this dissertation is a new formulation of the MT algorithm. A Laplacian regularization is incorporated in the MT cost function to address the limited data and improve the smoothness of the MT flow estimate.
The MT problem is revised and a discrete solution is derived to overcome the limitation of the continuous formulation. Since the flow model is piecewise discrete, a space discrete analytical expression of the MT forward step aligns better with the flow model and sets a clear connection with the MT inverse step, which is space discrete.
Due to the nonlinear relationship between the flow field and the AUV predicted trajectory, the MT algorithm is an iterative solution that executes the trajectory tracing operation at every iteration. Trajectory tracing is a key step in the MT algorithm to estimate the underwater trajectories based on a new estimate of flow field and accordingly to update the MT variables in the inverse step. This dissertation extends the MT algorithm by developing a set of analytical formulas to compute the underwater trajectories. These analytical formulas enable us to derive the MT error dynamics and prove that the estimated trajectory and measured trajectory end positions converge as the MT algorithm proceeds.
As the number of AUV trajectories is less than the number of model parameters, MT is highly underdetermined and requires some prior physical knowledge to compensate for the data sparsity. A Laplacian least square regularization is proposed in this dissertation. The MT cost function is extended with an explicit regularization term to penalize the non-smoothness of the predicted flow field. An iterative algorithm is derived to solve the Regularized Motion Tomography (RMT) problem. RMT error dynamics and the RMT hyperparamters are analysed to ensure the convergence of the RMT algorithm in the single vehicle and multi AUVs case.
Further, a linearized data analysis is established to compare the RMT algorithm with the other MT variants and dead reckoning algorithms. The data resolution accuracy of the RMT algorithm is evaluated using the Backus-Gilbert and Dirichlet spread functions. Two well-established metrics to assess the performance of tomography algorithms.
Finally, MT and RMT algorithms are validated through various simulations and data collected by an underwater glider deployed in the South Atlantic Bight. The experiment demonstrates that MT is able to reconstruct the ocean flow field using recorded glider surfacing positions and improve the spatial distribution of a dead reckoning flow field map.
Adding to that, experimental results are collected on the Georgia Tech Miniature Autonomous Blimps to demonstrate that the MT algorithm can be applied to compute a wind field in an indoor environment using nothing but sparse position measurements.
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Date
2021-07-30
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Dissertation