Asymptotic Normality of the Contraction Mapping Estimator for Frequency Estimation

Abstract

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 AR(2) filter is discussed in detail to illustrate the performance of the CM method.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1991
Accession Number
ADA453892

Entities

People

  • Benjamin Kedem
  • Sid Yakowitz
  • Ta-hsin Li

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Asymptotic Normality
  • Computing-Related Activities
  • Data Science
  • Engineering
  • Estimators
  • Frequency
  • Industrial Engineering
  • Information Operations
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Normality
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Mathematics or Statistics