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On the computation and statistical properties of the MLE for the frequency response of NCFs

This paper deals with computations and statistical properties, as well as transfer function selections involved in frequency response estimation for normalized coprime factors (NCF). A simple expression and the probability density function (PDF) are derived for the maximum likelihood estimate (MLE). It is shown that the statistical characteristics of the MLE are independent of the auxiliary plant. Based on this observation, all the coprime factors of the auxiliary transfer function have been derived which lead to an almost unbiased estimate when the noise level is low. Moreover, an analytic expression has been established for the involved free transfer functions which minimize both the bias and the variance of the estimate. The theoretical conclusions have been verified through numerical simulations.