  In the adaptive control theory, the dynamic regressor extension and mixing
(DREM) procedure has become widespread as it allows one to describe a variety
of adaptive control problems in unified terms of the parameter estimation
problem of a regression equation with a scalar regressor. However, when the
system/parameterization is affected by perturbations, the estimation laws,
which are designed on the basis of such equation, asymptotically provides only
biased estimates. In this paper, based on the bias-eliminated least-squares
(BELS) approach, a modification of the DREM procedure is proposed that allows
one to annihilate perturbations asymptotically and, consequently,
asymptotically obtain unbiased estimates. The theoretical results are supported
with mathematical modelling and can be used to design adaptive observers and
control systems.
