Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

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The thesis explores the optimal Bayesian filtering problem by focusing on Gaussian distributions, enabling the development of computationally efficient algorithms. It addresses three specific scenarios: filtering using only Gaussian distributions, employing Gaussian mixture filtering for handling strong nonlinearities, and utilizing Gaussian process filtering in data-driven contexts. For each scenario, the author derives effective algorithms and demonstrates their application to real-world challenges, highlighting the practical implications of these methods in various domains.