Asymptotic Normality of the Contraction Mapping Estimator for Frequency Estimation
MARYLAND UNIV COLLEGE PARK SYSTEMS RESEARCH CENTER
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This paper investigates the asymptotic distribution of the recently-proposed contraction mapping CM method for frequency estimation. Given a finite sample composed of a sinusoidal signal in additive noise, the CM method applies to the data a parametric filter that matches its parameter with the first-order autocorrelation of the filtered noise. The CM estimator is defined as the fixed-point of the parametrized first-order sample autocorrelation of the filtered data. In this paper, it is proved that under appropriate conditions, the CM estimator is asymptotically normal with a variance inversely related to the signal-to-noise ratio. A useful example of the AR2 filter is discussed in detail to illustrate the performance of the CM method.
- Numerical Mathematics
- Statistics and Probability
- Atomic and Molecular Physics and Spectroscopy