Xu, Hua.

This thesis focuses on the performance of the Kalman filters for scalar time-invariant systems when modeling errors are present. A complete classification of errors according to their effect on the filter performance is carried. Certain errors may drive the Kalman filter into instability. Other errors affect only certain statistical properties of the innovations process. Some of the results have been extended to the scalar time-varying and vector time invariant filtering problems.

The dissertation focuses on robot manipulator dynamic modeling, and inertial
and kinematic parameters identification problem. An automatic dynamic parameters
derivation symbolic algorithm is presented. This algorithm provides the linearly
independent dynamic parameters set. It is shown that all the dynamic parameters are
identifiable when the trajectory is persistently exciting. The parameters set satisfies
the necessary condition of finding a persistently exciting trajectory. Since in practice the system data matrix is corrupted with noise, conventional
estimation methods do not converge to the true values. An error bound is given for
Kalman filters. Total least squares method is introduced to obtain unbiased
estimates.
Simulations studies are presented for five particular identification methods.
The simulations are performed under different noise levels.
Observability problems for the inertial and kinematic parameters are
investigated. U%wer certain conditions all L%wearly Independent Parameters
derived from are observable.
The inertial and kinematic parameters can be categorized into three parts
according to their influences on the system dynamics. The dissertation gives an
algorithm to classify these parameters.