Robust State Estimation and Deep Learning for Time Series Analysis

Weiss, Matthew L.

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Robust State Estimation and Deep Learning for Time Series Analysis

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In this dissertation, we leverage the power of deep learning and mathematics in the service of developing a generalized time series state estimation system. Specifically, we combine a deep autoencoder and Kalman Filter to develop a novel hybrid filtering algorithm called the Autoencoder-Kalman Filter (AEKF). Traditionally, the Kalman Filter utilizes a single measurement noise covariance matrix to represent the noise present in a time series. In contrast, the AEKF utilizes a neural network to learn a point-wise sequence of measurement noise covariance matrices, one for each measurement in the time series. This allows the AEKF to weight the quality of each measurement individually, a feature that is especially important in the case of outlier measurements. The training of the AEKF relies on a technique known as domain randomization, which is a method to train deep learning models in simulation. Working towards the goal of a generalized time series state estimation system, we train a single AEKF to filter progressively larger families of functions, each of which contains the previous family as a subset. After presenting results showing that the AEKF attains superior state estimation over a standard Kalman Filter and a Long Short-Term Memory Recurrent Neural Network, we present a mathematical proof which explains the AEKF's outlier mitigation behavior in terms of matrix eigenvalues learned by the neural network. As a result, in this dissertation we demonstrate how well-understood mathematical models can inform neural network design.

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