Power noise filtration in DREM

The problem of estimation in the linear regression model is studied under the hypothesis that the noise is sufficiently small comparing to the regressor. Then the estimation solution is searched for a new regression containing the powers of the unknown parameters and disturbance, where the influence of the latter is attenuated. It is shown that power transformation of a regressor can preserve the excitation under mild assumptions. Possibilities of evaluation of powers of parameters are investigated using the dynamic regression extension and mixing (DREM) method. The performance of the estimators is demonstrated in numerical experiments.