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Akihiro Takigawa| Applied Mathematics, University of Waterloo
A comparison of the Kalman filter and recurrent neural networks for state estimation of dynamical systems
The study of dynamical systems is of great interest in many fields, with a wide range of applications. In some cases, these dynamical systems may be affected by noise and the availability of measurements may be limited. State estimations methods which can account for these challenges are valuable tools in analyzing these systems. While for linear systems the standard method is by using an algorithm called the Kalman filter, data-driven methods employing the versatility of artificial neural networks have also been proposed. In this thesis, we first introduce state estimation using the Kalman filter. Next, we provide an overview of a type of artificial neural network called recurrent neural networks (RNNs), which are particularly suited for tasks on time series data. We finally present the results of implementing RNN-based estimators for a number of dynamical systems with comparisons to Kalman filtering.