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In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.
The Kalman gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance. With a high gain, the filter places more weight on the most recent measurements, and thus conforms to them more responsively. With a low gain, the filter conforms to the model predictions more closely.
For this simulation, a sigma of 0.03 seconds for measurements of T was used; measurements of L and θ assumed negligible variability. In the figure the widths of one-, two-, and three-sigma are indicated by the vertical dotted lines with the arrows.
Given some experimental measurements of a system and some computer simulation results from its mathematical model, inverse uncertainty quantification estimates the discrepancy between the experiment and the mathematical model (which is called bias correction), and estimates the values of unknown parameters in the model if there are any (which ...
Measurement errors can be divided into two components: random and systematic. [2] Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Random errors create measurement uncertainty.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The measurement uncertainty budget is determined once and remains constant. With a constant measurement uncertainty budget, complete data records can now be acquired. The measurement uncertainty applies to every single measurement point. If the measurement uncertainty is constant, this simplifies the further processing based on the data records.
As regards weighting, one can either weight all of the measured ages equally, or weight them by the proportion of the sample that they represent. For example, if two thirds of the sample was used for the first measurement and one third for the second and final measurement, then one might weight the first measurement twice that of the second.