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. 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 theurban 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 simultaneousGaussian process regression (GPR) and simple linear regression pipeline tocalibrate and monitor dense WLPMSNs on the fly by leveraging all availablereference monitors across an area without resorting to pre-deploymentcollocation calibration. We evaluated our method for Delhi, where thePM 2.5 measurements of all 22 regulatory reference and 10 low-costnodes were available for 59 d from 1 January to 31 March 2018(PM 2.5 averaged 138±31 µ g m −3 among 22 referencestations), using a leave-one-out cross-validation (CV) over the 22 referencenodes. We showed that our approach can achieve an overall 30 % predictionerror (RMSE: 33  µ g m −3 ) at a 24 h scale, and it is robust as it isunderscored by the small variability in the GPR model parameters and in themodel-produced calibration factors for the low-cost nodes among the 22-foldCV. Of the 22 reference stations, high-quality predictions were observed forthose stations whose PM 2.5 means were close to the Delhi-wide mean(i.e., 138±31 µ g m −3 ), and relatively poor predictions were observed forthose nodes whose means differed substantially from the Delhi-wide mean(particularly on the lower end). We also observed washed-out localvariability in PM 2.5 across the 10 low-cost sites after calibrationusing our approach, which stands in marked contrast to the true widevariability across the reference sites. These observations revealed that ourproposed technique (and more generally the geostatistical technique)requires high spatial homogeneity in the pollutant concentrations to befully effective. We further demonstrated that our algorithm performance isinsensitive to training window size as the mean prediction error rate andthe standard error of the mean (SEM) for the 22 reference stations remainedconsistent at ∼30  % and ∼3  %–4 %, respectively, when anincrement of 2 d of data was included in the model training. The markedlylow requirement of our algorithm for training data enables the models toalways be nearly the most updated in the field, thus realizing the algorithm'sfull potential for dynamically surveilling large-scale WLPMSNs by detectingmalfunctioning low-cost nodes and tracking the drift with little latency.Our algorithm presented similarly stable 26 %–34 % mean prediction errorsand ∼3  %–7 % SEMs over the sampling period when pre-trainedon the current week's data and predicting 1 week ahead, and therefore it is suitablefor online calibration. Simulations conducted using our algorithm suggestthat in addition to dynamic calibration, the algorithm can also be adaptedfor automated monitoring of large-scale WLPMSNs. In these simulations, thealgorithm was able to differentiate malfunctioning low-cost nodes (due toeither hardware failure or under the heavy influence of local sources)within a network by identifying aberrant model-generated calibrationfactors (i.e., slopes close to zero and intercepts close to the Delhi-widemean of true PM 2.5 ). The algorithm was also able to track the drift oflow-cost nodes accurately within 4 % error for all the simulationscenarios. The simulation results showed that ∼20 referencestations are optimum for our solution in Delhi and confirmed that low-costnodes can extend the spatial precision of a network by decreasing the extentof pure interpolation among only reference stations. Our solution hassubstantial implications in reducing the amount of manual labor for thecalibration and surveillance of extensive WLPMSNs, improving the spatialcomprehensiveness of PM evaluation, and enhancing the accuracy of WLPMSNs.

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