  In this paper, we prove that it is possible to estimate online the parameters
of a classical vector linear regression equation $ Y=\Omega \theta$, where $ Y
\in \mathbb{R}^n,\;\Omega \in \mathbb{R}^{n \times q}$ are bounded, measurable
signals and $\theta \in \mathbb{R}^q$ is a constant vector of unknown
parameters, even when the regressor $\Omega$ is not persistently exciting.
Moreover, the convergence of the new parameter estimator is global and
exponential and is given for both continuous-time and discrete-time
implementations. As an illustration example, we consider the problem of
parameter estimation of a linear time-invariant system, when the input signal
is not sufficiently exciting, which is known to be a necessary and sufficient
condition for the solution of the problem with the standard gradient or
least-squares adaptation algorithms.
