Total least squares

S. Van Huffel and J. Vandewalle, The Total Least Squares Problem Computational Aspects and Analysis. SIAM, Philadelphia, PA, 1991. 

Linear prediction singular value decomposition Linear prediction total least-squares Least-squares... 

Total least-squares has been applied to the HSVD method (HTLS),117118129 and, as in LPSVD, has been found to improve its performance slightly. Van Huffel117 found that the TLS-based LP method had better resolution and was more robust than LPSVD. 

HTLS T Y N N N AT3 Linear predication and Vandermonde decomposition (uses total least-squares) Good... 

The techniques discussed under this heading often have very little in common and this explains the absence of specific literature on this topic. Note the following two papers which discuss the theoretical aspects of linear predictions and a variant used in some linear prediction methods called total least square . 

Much attention has also been devoted to modal identification without measuring the input time history. In particular, a lot of effort has been dedicated to the case of free vibration (or impulse response) and to the case of ambient vibration. In the former case, often time-domain methods based on auto-regressive moving average (ARMA) models are employed, using least squares as the core ingredient in their formulations. However, it was found that the least-squares method yields biased estimates [76], A number of methods have been developed to eliminate this bias, including the instrumental matrix with delayed observations method [76], the correlation fit method [275], the double least-squares method [114,202] and the total least-squares method [92]. A detailed comparison of these methods can be found in Cooper [61],... 

Golub, G. H. and Van Loan, C. F. An analysis of total least squares problem. SIAM Journal of Numerical Analysis 17(6) (1980), 883-893. 

Schoukens, J., Pintelon, R. Rolain, Y. (1997). Recent Advances in Total Least Squares Techniques and Errors-In-Variables Modeling, SIAM, chapter Maximum Likelihood Estimation of Errors-In-Variables Models Using a Sample Covariance Matrix Obtained from Small Data Sets, pp. 59-68. 

Golub G, Van Loan C. An analysis of the total least squares problem. SIAM J Num Anal... 

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