Uncertainty-aware temperature interpolation for measurement rooms using ordinary Kriging

Abstract

Accurate measurements in dimensional metrology necessitate strict controls on spatial and temporal variations in the measurement room temperature. Due to limitations in the number of sensors that can be placed in a given room, interpolation methods that leverage information from multiple sensors are necessary to assess conditions at unsampled locations. In this contribution, Kriging is used to spatially interpolate room temperatures from a limited number of sensors with different measurement uncertainties in a temperature controlled room housing two coordinate measurement machines. A novel method to propagate sensor uncertainties to the interpolated values using a Monte Carlo simulation is also demonstrated. The uncertainty propagation is considered for the explicitly heteroskedastic, i.e. a constituent network of sensors with different measurement uncertainties. The influence of a localized disturbance in the form of a movable heating element in the room is also investigated.