• DocumentCode
    1354191
  • Title

    A unifying theorem for linear and total linear least squares

  • Author

    De Moor, Bart ; Vandewalle, Joos

  • Author_Institution
    Dept. of Electr. Eng., Katholieke Univ. Leuven, Heverlee, Belgium
  • Volume
    35
  • Issue
    5
  • fYear
    1990
  • fDate
    5/1/1990 12:00:00 AM
  • Firstpage
    563
  • Lastpage
    566
  • Abstract
    It is shown how both linear least-squares and total linear least-squares estimation schemes are special cases of a rank one modification of the data matrix or the sample covariance matrix. For a problem with n unknowns, there exist n linear least-squares solutions while the total linear least-squares solution is (generically) unique. When the signal-to-noise ratio is sufficiently high, the total least-squares solution is a nonnegative combination of the least-squares solutions
  • Keywords
    estimation theory; least squares approximations; matrix algebra; signal processing; S/N ratio; data matrix; least-squares estimation; sample covariance matrix; unifying theorem; Covariance matrix; Ear; Feedback; Interpolation; Least squares approximation; Least squares methods; Poles and zeros; Robustness; Signal to noise ratio; Uncertainty;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/9.53523
  • Filename
    53523