The Use of Total Linear Least Squares Techniques for Identification and Parameter Estimation

Abstract Total linear least squares (TLLS) is a method of solving over-determined sets of linear equations Ax = b where both the observation vector b and the datamatrix A are inaccurate. The technique has been introduced by Golub and Van Loan and amounts to fitting a best subspace to [A, b]. The concept and geometric interpretation of the TLLS problem is given. A more general algorithm based on one singular value decomposition is proposed. The advantages of the use of TLLS in identification and system parameter estimation with respect to noise rejection in the data is shown and compared with the ordinary linear least squares technique. The superiority of TLLS over LLS for system identification is demonstrated by analytical and experimental techniques.