Data filtering, reparametrization, and the numerical accuracy of parameter estimators

It is established that a reparametrization of a discrete transfer function in terms of polynomials other than the classical powers of the shift operator z is equivalent to a filtering of the data. In adaptive parameter estimation problems, such reparametrization can yield significantly better accuracy for the estimate and convergence speed for the parameter estimator. One such generalized parametrization is presented. It yields good numerical results independently of the spectral properties of the data that enter into the unknown system