Journal ArticleDOI
Note on the Application of the Method of Least Squares
TLDR
The efficiency of the method of least squares depends substantially upon the choice of the design matrix, since the latter is responsible for the transfer of the uncertainties, inherent in the initial observations, to the unknown parameters as discussed by the authors.Abstract:
The efficiency of the method of least squares depends substantially upon the choice of the design matrix, since the latter is responsible for the transfer of the uncertainties, inherent in the initial observations, to the unknown parameters. The present paper suggests that the transfer is best if, given the diagonal elements AiAi of the product matrix A A, the columns of the design matrix A are mutually orthogonal.read more
Citations
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Journal ArticleDOI
Variances, Covariances and Restraints in Mass Metrology
TL;DR: In this article, a Gauss-Markov approach is proposed and its effects on the estimates and on their covariance matrix are discussed, as well as a practical application is presented.
Journal ArticleDOI
Uncertainty modelling in mass comparisons.
TL;DR: In this paper, a general model was developed to evaluate uncertainty in mass measurements with accuracy and in accordance with recent international documents, which took account of the various contributing quantities in a multivariate context, and constructed the variance-covariance matrix of the in-vacuo mass differences.
Journal ArticleDOI
Optimum choice of measurement points for sensor calibration
Giovanni Betta,Marco Dell'Isola +1 more
TL;DR: In this paper, a sensor calibration plan with the aim of reducing the calibration curve uncertainty is proposed, which is achieved by minimizing either the standard deviations of the regression curve coefficients or the standard deviation of the whole estimated calibration curve.
Journal ArticleDOI
An Extended Error Model for Comparison Calibration
TL;DR: In this paper, the usual error model for calibration experiments is extended to situations where there are both short-term and long-term random errors of measurement, and the concept of a check standard is advanced for estimating variability and maintaining statistical control of the measurement process.
Journal ArticleDOI
From the SI mass unit to multiples and submultiples: an overview
TL;DR: In this paper, the techniques used for generating multiples and sub-multiples of the kilogram are reviewed and their historical evolution is outlined, with emphasis on estimation of the values of the measurands, in connection with the need for prior knowledge about them.
References
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Journal ArticleDOI
Calibration of a Set of Masses in Terms of One Mass Standard
D B Prowse,A R Anderson +1 more
TL;DR: In this article, the principles for designing a calibration scheme for a set of mass standards are discussed on these principles, a particular scheme has been chosen as being convenient and reasonably efficient; it is pointed out that although it has not been possible to decide whether the selected scheme is optimum, it can be said that it is more efficient than most.