On time and frequency characteristics of weighted least squares estimators applied to nonstationary system identification

After reviewing the already known "static" characteristics of weighted least squares (WLS) estimators such as the effective and equivalent numbers of observations, their tracking properties are investigated. Several new "dynamic" characteristics of WLSE\´s are proposed, like the associate impulse response, associate frequency characteristics, estimation bandwidth and estimation delay. It is shown that the associate frequency characteristics may serve as a convenient basis for comparison of WLS estimators corresponding to different weighting sequences, and allow the seldom raised question of how fast parameter variations can be tracked successfully by estimators of this type (i.e. what is the estimation bandwidth of WLSE\´s)to be answered precisely.