Strong consistency of the contraction mapping method for frequency estimation

Some statistical properties in regard to the contraction mapping (CM) method are discussed. One of the requirements in this method is that the filter be parameterized to satisfy a certain fundamental property. The parameterization clearly depends on the normalized noise spectrum which theoretically has to be known or estimated a priori. If this information is available, one can first whiten the noise with a linear filter and then apply the CM method to the filtered data. In this way, the parameterization only needs to be done under the white noise assumption and filters like the AR(2) can be used by the CM method. In applications, however, prewhitening may not always be necessary