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
fDate :
5/1/1990 12:00:00 AM
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;
Journal_Title :
Automatic Control, IEEE Transactions on
