Applying Monte Carlo Method for Straight-Line Model Sensor Calibration

Sensors are used in measurement systems to enable estimation of physical parameters. Their calibration is an essential requirement and to perform the overall system/sensor calibration, its input is changed while the output is measured. Parameters from an appropriate sensor model are then determined from these measurements. If the model is a straight-line, a first-order least squares linear regression is commonly used to estimate the slope and offset—this is often called simple linear regression. However, this method is unable to consider uncertainty in the sensor/system input measurements. This paper reviews the possible methods to estimate the optimal straight-line parameters considering uncertainties in both input and output measurements. The Monte Carlo Method can deal with all types of uncertainties in each of the measurements, whether sensor inputs or outputs, and also take into account possible covariances of these measurements. A key aspect of this work is the application to the heteroscedastic case, where measurement uncertainties vary across observations. An MCM-based strategy is proposed to optimize the selection of new measurement input values to minimize the estimated slope uncertainty. This strategy is shown to significantly reduce, in the presented case, the number of required measurement values.