A new on-line exponential parameter estimator without persistent excitation

Abstract

In this paper we propose a new algorithm that estimates on-line the parameters of a classical vector linear regression equation Y=Ωθ, where Y∈Rn,Ω∈Rn×q are bounded, measurable signals and θ∈Rq 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 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 standard gradient or least-squares adaptation algorithms.