Retrospective Cost Methods for Combined State and Parameter Estimation

This dissertation is principally concerned with the combined state and parameter estimation problem, where the goal is to estimate the state of a discrete-time, linear time-invariant system with structured uncertainty in the system dynamics. First, we prove necessary and sufficient conditions for the identifiability of unknown parameters within a state-space realization. Next, we evaluate the performance of classical techniques for solving the combined state and parameter estimation problem. We then formulate and test the retrospective cost parameter estimation algorithm under the assumption that the initial states are known. Two variants of the retrospective cost parameter estimation and smoothing algorithm are formulated and tested in the case where the initial states are unknown. Finally, the retrospective cost Kalman filter algorithm is formulated and tested for state estimation despite uncertain noise covariances and potentially nonzero-mean sensor and process noise.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138515/1/mingray_1.pd