Ankit Goel

Presentation Info:
Date: April 26, 2019
Time: 9:00 AM
Location: Francois-Xavier Bagnoud Building, 1044 McDivitt Conference Room

Dissertation Committee:
Chair:
Professor Dennis S. Bernstein
Cognate Member:
Professor Aaron Ridley

Members:
Professor Karthik Duraisamy
Assistant Professor Alex Gorodetsky

In many applications, models of physical systems have known structure but unknown parameters. By viewing the unknown parameters as constant states, nonlinear estimation methods such as the extended Kalman filter, unscented Kalman filter, and ensemble Kalman filter can be used to estimate the states of the augmented system, thereby providing estimates of the parameters along with the dynamic states. These methods tend to be computationally expensive due to the need for Jacobians, ensembles, or adjoint, especially when the models are high-dimensional.

This dissertation presents the retrospective cost parameter estimation (RCPE) algorithm, which does not require gradients, ensembles, or adjoints. Rather, RCPE estimates unknown parameters from a single trajectory, and requires updating only as many adaptive integrator gains as the number of unknown parameters. RCPE is applicable to parameter estimation in linear and nonlinear models, where the parameterization may be either affine or nonaffine.

The main contribution of this work is to show that the parameter estimates may be permuted in an arbitrary way, and thus a permutation is needed to correctly associate each parameter estimate with the corresponding unknown parameter. RCPE is illustrated through several numerical examples including the Burgers equation and the Global Ionosphere Thermosphere Model (GITM).