Michael Grabe

Generalized Gaussian error calculus

Basics of Metrology.- True Values and Traceability.- Models and Approaches.- Generalized Gaussian Error Calculus.- The New Uncertainties.- Treatment of Random Errors.- Treatment of Systematic Errors.- Error Propagation.- Means and Means of Means.- Functions of Erroneous Variables.- Method of Least Squares.- Essence of Metrology.- Dissemination of Units.- Multiples and Sub-multiples.- Founding Pillars.- Fitting of Straight Lines.- Preliminaries.- Straight Lines: Case (i).- Straight Lines: Case (ii).- Straight Lines: Case (iii).- Fitting of Planes.- Preliminaries.- Planes: Case (i).- Planes: Case (ii).- Planes: Case (iii).- Fitting of Parabolas.- Preliminaries.- Parabolas: Case (i).- Parabolas: Case (ii).- Parabolas: Case (iii).- Non-Linear Fitting.- Series Truncation.- Transformation.

Uncertainties of Least Squares Estimators

Uncertainty assignments in the sequel of least squares adjustments comply with the formalism as used in the context of functional relationships.

Least Squares Trigonometric Polynomials

Trigonometric polynomials, being linear in their parameters, come close to perfectly reproduce arbitrarily curved functions.

Essence of Metrology

The true values of measurands, veiled by the providence of nature, constitute the backbone of physics.

Fundamental Constants of Physics

The net of physical constants at large and fundamental constants in particular should be consistent and meet the demand for traceability.

Bias and Randomness

The localization of the true value is a two-step process: the first aims at the bias, the second at the random errors.

Consequences of Systematic Errors

Systematic errors suspend the statistically bound properties of the minimized sum of squared residuals.

Normal Parent Distributions

Normally distributed data spawn a set of fundamentally important theoretical distribution densities.

Error Propagation, m Variables

Error propagation covering several variables asks for a growing awareness as to linearization errors.

Method of Least Squares

The method of least squares controls the flow of errors via the elements of the design matrix. Hence, assuming linear systems with differing design matrices aiming at the same set of unknowns, the adjustment’s uncertainties would differ even if the uncertainties of the input data were the same.