On the choice of a basis for a linear-in-the-parameters model

The unit pulse response of a linear-in-the-parameters model lies in a given finite-dimensional subspace. This paper studies the problem of selecting a good basis for this subspace, in the case where it is known that the power spectral density of the input signal of the model is bounded, below and above, by two known power spectral densities. We attempt to make the condition number of the correlation matrix of the internal signals of the model as small as possible for the worst possible power spectral density of the input signal.