An Improved Toeplitz Approximation Method

Abstract

This reprint suggests a modification of the Toeplitz approximation method for estimating frequencies of multiple sinusoids from covariance measurements. The method constructs a state-feedback matrix following a low-rank approximation of the Toeplitz covariance matrix via singular value decomposition. Ideally, the eigenvalues of this state-feedback matrix will be on the unit circle in the complex plane, and the angles that they make with the real axis will be equal to the unknown sinusoid frequencies. The modification proposed here exploits this prior knowledge of the modulus of the eigenvalues, and guarantees that even the presence of noise, the eigenvalues of the estimated state-feedback matrix will lie on the unit circle. Keywords: Toeplitz approximation method; Retrieving multiple sinusoids; Signal processing applications. (JHD)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA213994

Entities

People

  • Bhaskar D. Rao
  • K. S. Arun

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Air Platforms
  • Cyber
  • Sensors

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mechanics
  • Covariance
  • Data Science
  • Decomposition
  • Eigenvalues
  • Engineering
  • Equations
  • Feedback
  • Frequency
  • Information Science
  • Measurement
  • Military Research
  • Numerical Analysis
  • Signal Processing
  • Simulations
  • White Noise

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Graph Algorithms and Convex Optimization.