Gaussian process regression model for dynamically calibrating and surveilling a wireless low-cost particulate matter sensor network in Delhi

Wireless low-cost particulate matter sensor networks (WLPMSNs) are transforming air quality monitoring by providing particulate matter (PM) information at finer spatial and temporal resolutions. However, large-scale WLPMSN calibration and maintenance remain a challenge. The manual labor involved in initial calibration by collocation and routine recalibration is intensive. The transferability of the calibration models determined from initial collocation to new deployment sites is questionable, as calibration factors typically vary with the urban heterogeneity of operating conditions and aerosol optical properties. Furthermore, the stability of low-cost sensors can drift or degrade over time. This study presents a simultaneous Gaussian process regression (GPR) and simple linear regression pipeline to calibrate and monitor dense WLPMSNs on the fly by leveraging all available reference monitors across an area without resorting to pre-deployment collocation calibration. We evaluated our method for Delhi, where the PM2:5 measurements of all 22 regulatory reference and 10 low-cost nodes were available for 59 d from 1 January to 31 March 2018 (PM2:5 averaged 138~31 μgm-3 among 22 reference stations), using a leaveone- out cross-validation (CV) over the 22 reference nodes. We showed that our approach can achieve an overall 30% prediction error (RMSE: 33 μgm-3) at a 24 h scale, and it is robust as it is underscored by the small variability in the GPR model parameters and in the model-produced calibration factors for the low-cost nodes among the 22-fold CV. Of the 22 reference stations, high-quality predictions were observed for those stations whose PM2:5 means were close to the Delhi-wide mean (i.e., 138~31 μgm-3), and relatively poor predictions were observed for those nodes whose means differed substantially from the Delhi-wide mean (particularly on the lower end). We also observed washed-out local variability in PM2:5 across the 10 low-cost sites after calibration using our approach, which stands in marked contrast to the true wide variability across the reference sites. These observations revealed that our proposed technique (and more generally the geostatistical technique) requires high spatial homogeneity in the pollutant concentrations to be fully effective. We further demonstrated that our algorithm performance is insensitive to training window size as the mean prediction error rate and the standard error of the mean (SEM) for the 22 reference stations remained consistent at ~ 30% and ~ 3 %-4 %, respectively, when an increment of 2 d of data was included in the model training. The markedly low requirement of our algorithm for training data enables the models to always be nearly the most updated in the field, thus realizing the algorithm's full potential for dynamically surveilling large-scale WLPMSNs by detecting malfunctioning low-cost nodes and tracking the drift with little latency. Our algorithm presented similarly stable 26 %-34% mean prediction errors and ~ 3 %-7% SEMs over the sampling period when pre-trained on the current week's data and predicting 1 week ahead, and therefore it is suitable for online calibration. Simulations conducted using our algorithm suggest that in addition to dynamic calibration, the algorithm can also be adapted for automated monitoring of large-scale WLPMSNs. In these simulations, the algorithm was able to differentiate malfunctioning low-cost nodes (due to either hardware failure or under the heavy influence of local sources) within a network by identifying aberrant modelgenerated calibration factors (i.e., slopes close to zero and intercepts close to the Delhi-wide mean of true PM2:5). The algorithm was also able to track the drift of low-cost nodes accurately within 4% error for all the simulation scenarios. The simulation results showed that ~ 20 reference stations are optimum for our solution in Delhi and confirmed that low-cost nodes can extend the spatial precision of a network by decreasing the extent of pure interpolation among only reference stations. Our solution has substantial implications in reducing the amount of manual labor for the calibration and surveillance of extensive WLPMSNs, improving the spatial comprehensiveness of PM evaluation, and enhancing the accuracy of WLPMSNs.