The full least-squares method

被引:10
作者
D'Antona, G [1 ]
机构
[1] Politecn Milan, Dipartimento Elettrotecn, I-20133 Milan, Italy
关键词
calibration; curve fitting; data models; least-squares; parameter estimation; parameter uncertainty; surface fitting;
D O I
10.1109/TIM.2003.809489
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
This paper deals with the problem of the regression of measured quantities when measurement uncertainty affects both the regressed quantity Find the independent variables. A new criterion is given, named the full least-squares method. A compact matrix notation is used for deriving the parameter vector of the regression model and its uncertainty variance-covariance matrix. Some examples of application of the novel method are given together with a comparison with the regression obtained by the generalized least-squares and the total least-squares methods.
引用
收藏
页码:189 / 196
页数:8
相关论文
共 13 条
[1]   THE CONSTRAINED TOTAL LEAST-SQUARES TECHNIQUE AND ITS APPLICATIONS TO HARMONIC SUPERRESOLUTION [J].
ABATZOGLOU, TJ ;
MENDEL, JM ;
HARADA, GA .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1991, 39 (05) :1070-1087
[2]  
[Anonymous], SIAM J MATRIX ANAL A
[3]  
[Anonymous], 1993, MATH OPERATIONS RES
[4]  
Beck J.V., 1977, Parameter Estimation in Engineering and Science
[5]   TOTAL LEAST-SQUARES FOR AFFINELY STRUCTURED MATRICES AND THE NOISY REALIZATION PROBLEM [J].
DEMOOR, B .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1994, 42 (11) :3104-3113
[6]  
Edwards C.H, 1973, ADV CALCULUS SEVERAL
[7]   Constrained maximum likelihood solution of linear equations [J].
Fiore, PD ;
Verghese, GC .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2000, 48 (03) :671-679
[8]  
Golub G. H., 2013, Matrix Computations
[9]   AN ANALYSIS OF THE TOTAL LEAST-SQUARES PROBLEM [J].
GOLUB, GH ;
VANLOAN, CF .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1980, 17 (06) :883-893
[10]  
*ISO IEC BIPM OIML, 1995, GUID EXPR UNC MEAS