  The scope of this research is the identification of unknown piecewise
constant parameters of linear regression equation under the finite excitation
condition. Compared to the known methods, to make the computational burden
lower, only one model to identify all switching states of the regression is
used in the developed procedure with the following two-fold contribution. First
of all, we propose a new truly online estimation algorithm based on a
well-known DREM approach to detect switching time and preserve time alertness
with adjustable detection delay. Secondly, despite the fact that a switching
signal function is unknown, the adaptive law is derived that provides global
exponential convergence of the regression parameters to their true values in
case the regressor is finitely exciting somewhere inside the time interval
between two consecutive parameters switches. The robustness of the proposed
identification procedure to the influence of external disturbances is
analytically proved. Its effectiveness is demonstrated via numerical
experiments, in which both abstract regressions and a second-order plant model
are used.
