Covariance methods in nonlinear model identification
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] In many practical engineering and machine learning applications, it is necessary to identify an unknown transformation that maps a known or measured set of input states to a known or measured set of output states. Examples include the construction of weather prediction models from satellite measurements or creating models for predicting the future state of the stock market. Because the general problem is so difficult, most methods described in the current literature rely on simplifying assumptions such as a given parameterized model for the unknown transformation. They usually have application specific parameters to tune and do not have a systematic way to evaluate uncertainty. The goal of this thesis is to apply the mathematical framework used for Kalman Filtering (KF) and Covariance Intersection (CI) to explore new approaches to this problem that is general and mathematically rigorous, with the advantages of quick performance assessment, optimized data usage, very few tuning parameters, and computational parallelism. Results demonstrate the effectiveness of this new model in small scale problems. Future research could experiment on real life examples to unleash its full potential.
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