Uncertainty-Based Calibration Method for Environmental Sensors—Application to Chlorine and pH Monitoring With Carbon Nanotube Sensor Array

Societal demands in the field of air and water pollution monitoring require the ability to simultaneously detect a wide variety of chemical elements at very low concentrations in complex environments using compact and low-cost sensor devices. Although nanomaterial-based sensors have long been proposed as a solution to these exacting requirements, their detection accuracy is generally degraded in real-world conditions compared to laboratory conditions due to the effects of various interferents. To manage the related uncertainties and to associate confidence to the estimations, it seems natural to formulate the calibration-estimation problem in a probabilistic framework. This probabilistic formulation and its successful application to the monitoring of pH and active chlorine in drinking water are the main contributions of this work. While other tested calibration methods only allowed the monitoring of active chlorine, our solution enables the monitoring of both active chlorine and pH with quantified and reasonable uncertainties. Its success relies mainly on two adaptations of standard calibration methods: the consideration of the sensor inputs measurement errors (and not only the errors associated with the sensor outputs as it is generally done), and the introduction of two sources of model error (ME), one accounting for the approximate character of the calibration model, the other for unmeasured—and possibly unknown—interferents in the calibration environment.