Embrace the imperfection: how intrinsic variability of roll-to-roll manufactured environmental sensors enable self-calibrating, high-precision quorum sensing

Roll-to-Roll (R2R) process is well suited for manufacturing low cost, miniaturized, solid contact Ion-selective electrodes (ISEs) of potentiometric sensors to be used for continuous monitoring of various analytes in environmental, industrial, and health-care applications. It is presumed that the intrinsic thickness variability of the R2R process would limit the accuracy of the ISE-based sensors and would make them inferior to sensors fabricated by higher precision manufacturing processes. Instead, in this paper we propose to use the intrinsic variability of R2R process as a "resource" to achieve high-accuracy sensing even when the sensors are operated in uncontrolled field conditions. This is achieved by applying a fundamentally new physics-guided statistical approach involving: (i) 'Self calibration' where we calculate temperature from differential measurement of the ISEs induced by R2R variability to calibrate the sensors in uncontrolled temperature condition, and (ii) 'Quorum sensing' where we use a collection of R2R manufactured sensors to estimate the true concentration considering credibility of each sensor calculated by Bayesian Maximum Likelihood Estimation method. With these two new techniques, we demonstrate the use of "low-precision" R2R sensors to measure nitrate concentration of an agricultural field continuously over a period of 15 days within 10% of the ground-truth measured by the traditional high-precision commercial nitrate sensor.