Uncertainty Evaluation for Testing and Calibrating Mobile Sensors Only Using Short Collocation Periods

Low-cost sensors are increasingly being used, and also considered for usage in regulatory contexts like air quality monitoring. Proper sensor calibration and uncertainty evaluation is necessary in such cases. With the advance of mobile sensors, for example, installed on top of a car, new test and calibration paradigms are required, in particular if the sensor and reference instrument are only compared during short collocation times, whereby the collocation time is shorter than the averaging time of the reference instrument and the underlying process is varying over time. In this paper it is shown how sensors can be tested and calibrated in such situations. A first result of this paper are analytical expressions for the variance and covariance of averages of Gaussian processes. Next, performance testing of sensors based on short collocation periods is addressed. It is shown that the process variability should be taken into account for best results in terms of either small sample sizes or preventing unnecessarily rejecting well functioning sensors. Finally, a new regression procedure, called corrected generalized distance regression (C-GDR), is developed, and its performance is evaluated and compared with established methods in a numerical study. The parameters in this study are based on a dataset containing real measurement data of an (Formula presented.) sensor together with the data from a reference instrument. The parameters are then varied to cover more difficult cases as well. It is concluded that in a situation in which the uncertainty of the reference instrument is much lower than that of the other instrument, ordinary least-squares regression performs properly. However, when uncertainties become more similar and the measured process starts varying more, the C-GDR approach outperforms the other methods.