The problem of estimating constant parameters from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed. The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations.