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In this paper we prove that it is possible to estimate on-line the parameters of a classical vector linear regression equation Y = Ωθ, where Y ∈ R n , Ω ∈ R n×q are bounded, measurable signals and θ ∈ R q is a constant vector of unknown parameters, even when the regressor Ω 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 timeinvariant 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 standard gradient or least-squares adaptation algorithms.

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In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it incorporates a forgetting factor allowing it to preserve alertness to time-varying parameters; (iii) thanks to the addition of a mixing step it relies on a set of scalar regression equations ensuring a superior transient performance; (iv) it is applicable to nonlinearly parameterized regressions verifying a monotonicity condition and to a class of systems with switched time-varying parameters; (v) it is shown that it is bounded-input-bounded-state stable with respect to additive disturbances; (vi) continuous and discrete-time versions of the estimator are given. The superior performance of the proposed estimator is illustrated with a series of examples reported in the literature.

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