Realization of Covariance Sequences

Abstract

This paper examines the problem of positivity in relation to the partial realization of scalar power series. An exact criterion of positivity is proved for second-order realizations. The general case is currently unsolved. Even the special results contained here show that the so-called maximum entropy principle cannot be applied to the realization problem in the naive sense in which it is employed by physicists. It would be better to call this principle a prejudice because it does not fully utilize the information inherent in the data and does not provide a realization with natural (minimal) mathematical properties.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1981
Accession Number
ADA145082

Entities

People

  • R. E. Kalman

Organizations

  • University of Florida

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Covariance
  • Mathematics
  • Military Research
  • Polynomials
  • Power Series
  • Prejudice
  • Probability
  • Scientific Research
  • Sequences
  • Universities

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Joint Military Operations and Doctrine.