Reducing Measurement Uncertainty Using a Smoothing Spline

Abstract

When calibrating Measuring and Test Equipment (M&TE) it is often necessary to measure various points across a range. Random measurement errors can lead to noisy observations that are apparent when viewing the measurement results on a line graph. Making repeated measurements and averaging reduces the noise, but at the cost of increased measurement time. However, multiple observations are already available as a result of measuring across the range. A smoothing spline uses a spline function to fit a smoothed curve to the noisy observations producing results with less noise. The smoothing spline can be used without incurring additional measurement time. To evaluate the impact of smoothing on the uncertainty, a receiver linearity measurement was repeated fifty times, and the mean and Type A uncertainty determined. These statistics were then compared to the mean and Type A uncertainty of the smoothed data. The Type A uncertainty of the smoothed data was less than the uncertainty of the original observations by as much as fifty percent.