Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
12-2025
Committee Chair or Co-Chairs
Jeff Randall Knisley
Committee Members
Maryam Skafyan, Mostafa Zahed
Abstract
This thesis presents an extension of the Kalman filter to handle nonlinear and non-Gaussian systems. The standard Kalman filter is optimal under Gaussian assumptions but struggles with more complex noise models. This work introduces a novel loss function based on the Mahalanobis distance, which incorporates the covariance structure of measurement errors, enabling the filter to adapt to non-Gaussian scenarios. The neural network framework is applied to predict the system’s process model, while retaining the classical Kalman measurement update. The proposed methodology is demonstrated through examples of car position and rocket altitude tracking. The results show that the new approach performs as well as the classical Kalman filter in Gaussian settings and offers superior performance when dealing with non-Gaussian noise. This hybrid method combines the strengths of both the Kalman filter and neural networks, ensuring efficient estimation in diverse environments.
Document Type
Thesis - unrestricted
Recommended Citation
Quaye, Rexford Julius, "Deep Learning with Kalman Filter" (2025). Electronic Theses and Dissertations. Paper 4614. https://dc.etsu.edu/etd/4614
Copyright
Copyright by the authors.
Included in
Applied Mathematics Commons, Computer Sciences Commons, Statistics and Probability Commons
