A class of bootstrap estimators and their relationship to the generalized two stage least squares estimators

This paper deals with the identification of a process modeled by a stable, linear difference equation of known order. Its output is subject to additive observation noise that is identically and independently distributed with zero mean and a constant variance. On-line estimators in which the process parameters as well as the process outputs are estimated simultaneously in real time are considered. For improving the stability of such on-line algorithms, a simple adaptive filter for the reference model is proposed. Further, it is shown that inclusion of such a filter relates the resulting bootstrap algorithms to the more general forms of the two stage least squares estimators viz. the
k
-class,
h
-class and the double
k
-class estimators. Effectiveness of the filter in stabilizing the on-line algorithms is demonstrated by using data generated by a fourth-order model.