Advancing low-cost air quality monitor calibration with machine learning methods.

Advancing Low-cost Air Quality Monitor Calibration with Machine Learning Methods - PMC Skip to main content An official website of the United States government Here's how you know Here's how you know Search Log in Primary site navigation Search Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Environ Pollut . Author manuscript; available in PMC: 2026 Jun 1. Published in final edited form as: Environ Pollut. 2025 Apr 3;374:126191. doi: 10.1016/j.envpol.2025.126191 Advancing Low-cost Air Quality Monitor Calibration with Machine Learning Methods Sinan Sousan 1, 2, 3, * , Rui Wu 4 , Ciprian Popoviciu 5 , Sarah Fresquez 1 , Yoo Min Park 6 Author information Article notes Copyright and License information 1 Department of Public Health, Brody School of Medicine, East Carolina University, Greenville, NC, 27858, USA. 2 North Carolina Agromedicine Institute, Greenville, NC, 27858, USA. 3 Center for Human Health and the Environment, NC State University, Raleigh, NC, USA. 4 Department of Information Technology, College of Computing and Software Engineering, Kennesaw State University, Kennesaw, GA, USA. 5 Department of Technology Systems, East Carolina University, Greenville, NC, USA. 6 Department of Geography, University of Connecticut, Storrs, CT 06269, USA. * Correspondence: sousans18@ecu.edu ; Carol Belk Building, 300 Curry Ct Greenville, NC 27858. Issue date 2025 Jun 1. PMC Copyright notice PMCID: PMC12050198  NIHMSID: NIHMS2073211  PMID: 40187520 The publisher's version of this article is available at Environ Pollut Abstract Low-cost monitors for measuring airborne contaminants have gained popularity due to their affordability, portability, and ease of use. However, they often exhibit significant biases compared to high-cost reference instruments. For optimal accuracy, these monitors require calibration and validation in their specific environment using expensive reference instruments, which are often scarce and costly. This study proposes machine-learning calibration methods that utilize a single high-cost instrument as an active reference to improve the accuracy of large networks of low-cost monitors. Three machine learning models—linear regression, random forest, and Gradient Boosting Regression (GBR)—were employed. The proposed approach was tested in a controlled chamber under two conditions: environmental simulations with salt- and dust-based aerosols and occupational settings using three electronic cigarette (ECIG) brands. The study involved thirty low-cost GeoAir2 monitors, divided into ten groups of three. Initially, all groups were collocated with a high-cost monitor using Aerosol A to develop prediction and regression models. These models, along with intrinsic error measurements from one group, were then applied to improve data accuracy for the remaining groups using Aerosol B. The results demonstrated substantial improvements in accuracy, with r 2 values ranging from 0.91 to 1.00 and RMSE reductions of up to 88%, depending on the model and aerosol type. GBR consistently provided the highest accuracy and performance, particularly for complex, nonlinear patterns, while linear regression offered a faster, computationally efficient alternative suitable for less demanding scenarios. Random forest models performed moderately well, balancing accuracy and complexity. These methods provide a scalable and cost-effective solution for deploying networked low-cost sensors. Further research is needed to validate these findings in outdoor environments with meteorological influences and indoor occupational settings where humidity effects may play a role. Graphical Abstract 1. Introduction Particulate matter (PM), especially fine particles (PM 2.5 ), defined as particles 2.5 μm in size or smaller, are associated with increased cardiopulmonary diseases and mortality ( EPA, 2023 ; Krittanawong et al., 2023 ; Pun et al., 2017 ). Therefore, the U.S. Environmental Protection Agency (EPA) and the Code of Federal Regulations have standardized Federal Reference Method (FRM) instruments to collect 24-hour ambient air samples onto filters to determine PM 2.5 mass concentrations using gravimetric analysis, where the PM2.5 daily standard established by the EPA was 35 ug/m 3 . ( Noble et al., 2001 ). Alternatively, PM 2.5 may be measured using Federal Equivalent Methods (FEMs) that mimic FRM instruments and produce similar results without meeting the same rigor of instrument standards ( Noble et al., 2001 ). Limitations of FRM and FEM instruments include their high cost of regulation, limited portability, and FRM filter mass concentration measurements being limited to daily 24-hour mean values ( Clements and Vanderpool, 2019 ). Alternatively, for occupational environments, the Occupational Safety and Health Administration (OSHA) has established PM standards to ensure the safety and health of workers. Therefore, OSHA established an 8-hour time-weighted standard of 5,000 ug/m 3 for respirable PM 4 (Particles 4 micrometers or smaller) that are otherwise not regulated. Instruments used to monitor occupational environments are also costly, which further limits their use spatially and temporally ( OSHA, 2006 ). Other monitors can serve as reference instruments without following the EPA or OSHA regulations. However, despite addressing some of the limitations of those instruments, the nonregulated monitors can still be costly. For instance, the MiniWRAS (MiniWRAS 1371, >$30,000; Grimm Aerosol Technik, Ainring, Germany) and the personal DataRAM (pDR-1500, $7,000; Thermo Scientific, Franklin, MA, USA) are both reliable and portable as reference monitors but still have a high cost. Low-cost and portable monitors that can sample PM or other readings in real-time are a promising alternative ( Park et al., 2022 ; Sousan et al., 2021 ). However, low-cost sensors are not without limitations of their own. The accuracy of a low-cost sensor may be affected by the device’s lower-cost components, lack of certification, or reduced resilience to environmental changes such as temperature or humidity. Caseiro et al. (2024) also showed that a source of bias in some low-cost monitors could be due to flaws related to inconsistent performance across size bins, which causes particle misclassification. To address these limitations, low-cost monitors should be calibrated agains high-cost or reference instruments. Several laboratory and field studies have shown that low-cost PM monitors can reach a coefficient of determination (r 2 ) correlation value as high as 0.99 once calibrated, indicating that the calibration against reference instruments is critical to their reliable use ( Alfano et al., 2020 ). Various regression types such as linear, polynomial, exponential, and power models are commonly used for PM sensor calibration with the goal of finding the highest yield r 2 value. An outdoor study conducted by Cavaliere et al. (2018) compared several linear and nonlinear regression models and developed a calibration procedure that yielded final r 2 results of 0.91 for PM 2.5 . Meanwhile, machine learning based calibration aims to predict future readings and improve regression values. One laboratory study compared linear regression and a random forest machine-learning model for PM 2.5 and found that their machine-learning model yielded an improved r 2 value of 0.98 against 0.87 for linear regression ( Wang et al., 2019 ). Another study compared linear regression to feedforward neural network and support vector machine models and found that the feedforward neural network provides the most accurate predictions for uncalibrated PM 2.5 against a reference instrument with an r 2 value of 0.905 ± 0.013 ( Chen et al., 2018a ). Both machine learning studies validated their results, with the Wang et al. (2019) study using ten-fold cross-validation and the Chen et al. (2018a) study using a FEM-approved reference instrument. These findings demonstrate the need for using regression and machine learning models to increase the accuracy of low-cost monitors through the use of reference instruments. The calibration methodology depends on the type of the monitor. For example, aerosol optical monitor calibration depends on the type of aerosol used. The calibration performed on one aerosol type tends to overestimate or underestimate the measurements for a different type of aerosol. Therefore, optical aerosol monitors are calibrated in the same environment targeted for monitoring by using filter gravimetric analysis or by creating regression models using side-by-side analysis with high-cost or reference aerosol instruments. These approaches become impractical for large scale deployments due to the high cost of equipment and labor. Several researchers have addressed this problem by proposing different calibration methods for a network of sensors. Kizel et al. (2018) proposed node-to-node field calibration by collocating the first low-cost monitor next to the reference monitor and then subsequently collocating the other monitors next to the first monitor and so on until the monitor furthest away from the reference. The authors’ method applies linear regression, relocates the sensor after calibration to a new location, and compares the furthest away monitor with the reference instrument for validation. Vajs et al. (2023) also proposed a similar approach called calibration propagation, where the sensors in the network were first located at their intended locations and at distances between 0.3 and 3 km. The researchers then used machine learning to calibrate the first and nearest to the reference monitor in the network against the reference monitor. Subsequently, the second monitor was calibrated against the first and so on until reaching the last and furthest away monitor. DeSouza et al. (2022) evaluated the feasibility of applying different calibration models, from simple linear regression to machine learning methods to different low-cost monitors in the network. The authors used a network of low-cost sensors collocated or close to five reference monitors, developed models for the collocated monitors, and then validated the models at the other locations to determine temporal and spatial effects. These referenced methods are susceptible to errors, particularly in certain scenarios, such as a hurricane. These errors might be magnified during the calibration process through node-to-node error propagation. To address these limitations, this study develops calibration models using machine learning regression when three low-cost monitors of the same type are deployed at each location and the groupings are networked. In this deployment scenario, the proposed algorithm combines two models working together, a prediction model and a calibration model. The prediction model identifies temporal connections within the current group. At a given timestamp, it predicts the correct target parameter readings using the three low-cost monitor readings from the same group. In contrast, the calibration model establishes temporal connections between the current group and the reference monitor group. It estimates errors in the current monitor group by leveraging the three low-cost monitor readings and the errors identified in the reference monitor group. The groups of monitors are then moved to different environments, maintaining the reference monitor group near a high-cost or reference monitor to calculate the errors from different environments and then applying those errors to the other groups. This study aims to identify whether the errors from one monitor group can be used to correct the regression models derived in different environments, thus eliminating the constraints of monitors being usable exclusively in the environments in which they were calibrated. The objective of the study is to calibrate the networked groups of monitors using one high-cost or reference monitor., such as Typically, federally managed reference monitors located in large urban settings, whereas this work intends to support deployments that cover smaller communities as well. 2. Material and Methods 2.2. Real-time Measurements High Cost MiniWRAS Monitor The MiniWRAS uses two combined technologies to measure number concentrations over a wide range of particle sizes between 0.25 and 35 μm in 41 sizes. The device utilizes a corona charge to measure particles smaller than 0.25 μm by applying unipolar ions to charge the aerosols, with the resulting charge detected via a Faraday Cup Electrometer. For particles 0.25 μm in size and larger, the MiniWRAS uses optical science. The MiniWRAS uses the number of concentrations and density assumption to provide mass concentrations at different particle sizes, including PM2.5. The MiniWRAS records measurements at a frequency of one minute. High Cost pDR PM 2.5 Monitor The pDR photometer measures PM 2.5 concentrations, up to 400,000 μg/m 3 , using a cyclone and operating at the recommended flow rate of 1.52 L/min. The pDR was chosen for this study over other instruments due to its high-frequency, one per second, air sampling, which matches the low-cost PM monitor sampling rate. GeoAir2 Low-Cost Monitor The GeoAir2 low-cost monitor ($350, Jaycon Systems, Palm Bay, Florida, USA) measures personal exposure for PM, along with temperature and humidity ( Park et al., 2021 ). The GeoAir2 monitor mainly contains two airborne sensors. The first is the SPS30 (Sensirion, Stäfa, Switzerland) optical particle counter monitor that captures the number concentrations of particles between 0.3 and 10 μm in 6 sizes that are used to calculate PM 2.5 concentrations up to 1000 μg/m 3 , by assuming spherical particles and a density. The minimum number of 6 bin sizes might not be sufficient to accurately calculate mass concentrations due to the limited size resolution, which could oversimplify the complexity and potentially miss critical variations in particle size. This issue is overcomed by more expensive devices, such as the MiniWRAS. However, the monitor has been extensively evaluated for different PM exposures and has demonstrated exceptional outcomes, showing results very similar to the MiniWRAS measurements ( Park et al., 2022 ; Park et al., 2021 ; Sousan et al., 2023a ; Sousan et al., 2022a ; Sousan et al., 2023b ; Streuber et al., 2022 ). Despite the limitations of the low-cost monitor, the method introduced in this work is not intended to correct for atmospheric changes. Rather, it introduces errors from one monitor group that are assumed to be similar for the same manufacturer to other groups, as explained in the next section. 2.1. Experimental Setup Chamber Description A controlled 0.8 m 3 exposure chamber was used to control and assess the PM 2.5 from different airborne sources, as shown in Figure 1 . The airtight chamber is divided in half using a honeycomb air straightening section (AS100, Rusken, Grandview, MO, USA), where one half represents the generation zone and contains two fans to mix the PM 2.5 concentrations. The other half represents the sampling zone and contains the PM 2.5 monitors for assessment after the honeycomb air straightening section achieves PM 2.5 homogeneity. The entrance to the generation zone contains two HEPA filters with 99.99% efficiency to supply particle-free air from a blower, and the exit of the sampling zone contains a vacuum with HEPA and carbon filters to remove the air from the system. The blower and vacuum devices help control the aerosol generation inside the sampling zone at desired PM 2.5 concentrations, by adjusting flowrates. The temperature and relative humidity were constant during experiments at 22±2 °C and 45±5%, respectively. Figure 1: Open in a new tab The controlled exposure chamber experimental setup Aerosol Generation The goal of this work was to improve PM 2.5 concentrations derived from calibration using linear and machine-learning methods. Due to the possible differences between environmental and occupational calibrations, both target concentrations were tested based on previously published work ( Sousan et al., 2022b ; Streuber et al., 2022 ). Therefore, this work relied on using previously acquired data generated from funded research to test new calibration methodologies. The following section describes data acquisition methods and outcomes from these papers in environmental and occupational settings. Environmental Concentration Data To test PM 2.5 monitoring accuracy in environmental settings, data were used from previously published work for two aerosols, salt and dust. Salt aerosol was generated using an Aerogen nebulizer (Aerogen, Galway, Connacht, Ireland) with a 2% (wt.) NaCl solution. Particle-free air from a five-stage desiccant system was supplied via a mass flow controller (Cole-Parmer 32907–73, Antylia Scientific, Vernon Hills, Illinois, USA) into a silica column to remove moisture. The resulting dry salt particles were introduced into the mixing zone of the exposure chamber, where additional particle-free air ensured steady-state concentrations. Arizona Road Dust (ARD; PTI ID: 13328B, Powder Technology Inc, MN, USA), hereby moving forward called ‘dust’, is a reliable and reproducible standard for generating dust aerosols in controlled laboratory and industrial settings. Dust was aerosolized using the Vilnius Aerosol Generator (VAG, CH Technologies, Westwood, New Jersey, USA), which dispenses dry powder to achieve a wide range of aerosol concentrations. Particle-free air was supplied and regulated by the same mass flow controller. The ARD aerosol was then introduced into the chamber’s mixing zone, where steady-state concentrations were established. Both aerosols achieved 5-minute steady-state concentrations of 10, 20, 30, 40, and 50 μg/m 3 . The GeoAir2 monitors were located inside the chamber and recorded real-time measurements at one-second intervals, while the MiniWRAS was outside the chamber, sampling air directly from the chamber and recording data every minute. Gravimetric analysis was performed using the pDR-1500, which operated at a flow rate of 1.52 LPM and employed 37 mm filters pre- and post-weighed on a Mettler Toledo microbalance (Model: XPR26DR, Columbus, Ohio, USA) with an anti-static kit (Model: 63052302, Mettler Toledo). The MiniWRAS data were filter-corrected using gravimetric analysis and real-time measurements. The GeoAir2 data were averaged to one-minute to match the MiniWRAS sampling frequency. The one-minute air sampling of the monitors resulted in 36 data points for each instrument and aerosol type, including zero concentrations. The one-minute data were input into linear regression and machine learning models. Occupational Concentration Data To test PM 2.5 data in occupational settings, data were used from previously published work for different brands of electronic cigarette (ECIG) devices ( Sousan et al., 2022b ). ECIGs are devices with battery-powered heating elements that aerosolize and deliver chemical mixtures of stimulants, flavorants, and other solvents to a user’s lungs when inhaled ( Wu et al., 2019a ). Ingredients such as propylene glycol (PG) and vegetable glycerin (VG) contribute to the chemical mixture’s aerosolization when heated by the device, generating particles and vapors simultaneously ( Close et al., 2023 ; Havanko et al., 2019 ). Since secondhand ECIG exposure generates different PM 2.5 exposures based on the brand, it was chosen as the exposure to test the methods for this study. At the time of this study, three off the shelf ECIG devices were chosen, which include the pod mod (JUUL, Menthol flavorant ( JUUL, 2021 ), disposable (NJOY Daily, Menthol flavorant ( NJOY, 2021 ), and box mod (VOOPOO DRAG 2, Hawaiian POG flavorant, UFLORCE U4 (0.23 Ω) coil, default 70 W power Sousan et al. (2022a) . The devices were all new and purchased before the experiments. The ECIG aerosols were generated by using a diaphragm pump (Thomas 1420–0504, Gardner Denver, Davidson, NC) and a clock generator (TFIS 12–240VUC 1CO CG, Weidmüller Interface GmbH & Co. KG, Detmold, Germany) inside the mixing zone of the chamber. The generation time and flow rate for these ECIG devices have been tested in previous studies ( Sousan et al., 2022a ; Sousan et al., 2023b ). The ECIG devices simulated human vaping by using the clock generator to turn the diaphragm pump on/off and adjust the pump voltage to achieve the desired flow rate. For the JUUL, the on/off time in seconds was 5/30 with a flow rate of 1.5 L/m, compared to 4/30 and 1.0 L/m for the NJOY Daily, and 4/30 and 8.5 L/m for the VOOPOO DRAG 2, respectively. The GeoAir2 and pDR monitors were located inside the sampling zone of the chamber. The calibration of low-cost PM sensors has previously been achieved by Sousan et al. (2016) and used extensively in multiple studies ( Sousan et al., 2018 ; Sousan et al., 2021 ; Sousan et al., 2022b ; Streuber et al., 2022 ). The calibration method consisted of achieving five steady-state PM 2.5 concentrations inside the sampling zone of the chamber by controlling the particle-free airflow inside the mixing zone. The five steady-state concentrations were measured by the high-cost PM reference monitor described below, where different ECIG devices achieved different PM 2.5 concentrations due to various manufacturing specifications that are affected by device wicking ability, wattage, temperature control, PG/VG content, and device flow rate ( Chen et al., 2018b ; Close et al., 2023 ; David et al., 2020 ; Floyd et al., 2019 ; Kosmider et al., 2014 ; Li et al., 2020 ; Sousan et al., 2023b ). The steady-state PM 2.5 concentrations achieved for the three ECIG devices were 56, 97, 129, 156, 202 μg/m 3 for the JUUL, 81, 109, 142, 252, 342 μg/m 3 for the NJOY Daily and 254, 352, 525, 704, 1040 μg/m 3 for the VOOPOO DRAG 2. The one-second air sampling of the monitors resulted in 1,317 data points for each monitor and each ECIG brand, including zero concentrations, that were used as input for the machine learning models. Furthermore, the pDR was filter-corrected using values adopted from Sousan et al. (2022a) , for JUUL, NJOY, and BoxMod PM 2.5 aerosol exposure. 2.3. Calibration of Low-Cost Monitors by Constructing Prediction Models Different calibration models were used to improve low-cost monitor data accuracy, relying on the temporal information provided by clusters of 3 monitors manufactured by the same company and possibly generating similar error patterns. Two sets of machine learning models, prediction and calibration models were used. The prediction model estimates parameter values based on low-cost monitor readings from each group. The calibration model estimates possible errors in the prediction model, and the estimated errors will be used to enhance target parameter value predictions. In this work, three machine learning methods were employed to construct prediction and calibration models: linear regression, random forest, and gradient boosting regression ( Friedman, 2001 , 2002 ; Tin Kam, 1995 ). The linear regression model estimates the linear relationship between features (i.e., model inputs) and targets (i.e., model outputs). The random forest (RF) model ensembles multiple decision trees (i.e., simple tree structure machine learning models) used to produce a more accurate estimation. The Gradient boosting regression (GBR) also combines multiple decision trees, similar to RF, but this model sequentially ensembles trees to reduce bias and enhance accuracy. These three model types are commonly used in regression problems. Deep learning models were not used in this project because they typically require more data to train effectively. Deep learning models may encounter underfitting issues without sufficient data, where the model cannot adequately learn the data patterns and produce accurate results ( Wu et al., 2022 ; Wu et al., 2019b ). The salt, dust, and three ECIG brands are representative of the conceptual model described above since PM 2.5 from these sources has provided different accuracy values for the low-cost monitors, as described by Sousan et al. (2022b) and Streuber et al. (2022) . For ECIGs, despite each brand containing the same PG and VG liquids, their ratios and different commercial liquids and additives by different manufacturers show that the low-cost monitors provide different slope and intercept responses for different brands. Therefore, the JUUL, NJOY and BoxMod brands can be used for the development and testing of the calibration model proposed in this work. The calibration model derived for a specific ECIG brand can be validated in the environments simulated by the other two ECIG brands. Preprocessing Preprocessing is an optional step in analyzing raw, low-cost monitor data and it can significantly enhance data quality and enable the proposed machine learning models to produce more accurate PM 2.5 estimations. In this work, two preprocessing steps were applied: data imputation and data normalization. Data imputation estimates missing values in the dataset. Low-cost monitors are often unreliable and may miss reporting readings (i.e., NA values). Machine learning models used in the proposed method cannot process inputs with missing values. Two common approaches to address this issue consist of replacing all missing values with a default value (e.g., 0) or removing any data record with missing values. However, both approaches can degrade data quality by disrupting temporal information ( Wu et al., 2022 ). In this work, Multiple Imputation by Chained Equations (MICE) was used to estimate missing values, as it has proven effective for time-series data with missing entries ( van Buuren and Groothuis-Oudshoorn, 2011 ). Data normalization rescales low-cost monitor readings to fall within a range of 0 to 1. This step was critical because machine learning models do not inherently understand the meaning of different measurement units. For example, while 1 kg is equivalent to 1000 g, a machine learning model does not recognize this relationship. Normalizing the readings ensures that the models were not hindered by varying units, making it easier to identify data patterns regardless of the units used. Machine Learning Calibration Method The key feature of this work was to estimate mass concentrations from low-cost monitors in an environment that does not include a collocated reference instrument. Therefore, two types of environments were defined in this work: the “known environment”, where the reference monitor was collocated with the low-cost monitors and the “unknown environment”, where the reference instrument was not collocated with the low-cost monitors. The proposed method requires one reference monitor and multiple groups of three collocated low-cost monitors. The reference monitor (i.e., pDR or MiniWRAS) was always collocated with the first group, which is referred to as the “reference group.” The prediction and calibration machine learning models were trained in the known environment and tested in the unknown environment. Known Environment In the known environment, all groups of 3 monitors have access to the reference data to derive the calibration and prediction models and estimate the errors they generate. This data is collected in an environment using Aerosol A, which could be salt, or dust, or BoxMod, or JUUL, or NJOY data. The calibration and prediction models were developed in the known environement for 10 groups of 3 collocated monitors (the first group only has a prediction model without a calibration model), as shown in Figure 2 . Figure 2. Open in a new tab Deriving calibration and prediction models (Exposure A is either BoxMod, JUUL, or NJOY [Only one]). All groups are considered in the known environment and have access to the pDR data. Rectangles with bold text represent machine learning models. The prediction models were used to estimate the relationship between the PM 2.5 data from each group and the reference data, where the model predicted PM 2.5 mass concentrations were calculated using the following equation: y ^ i = prediction i S i (1) Where y ^ i denotes the predictions of PM 2.5 values of Group i . prediction i is the prediction model for Group i . S i denotes a vector that includes the 3 low-cost monitor readings of Group i . The calibration models were used to learn the relationship between the prediction model errors of Group 1 and the prediction errors of the other monitor groups (i.e., Groups 2–10). These models were trained using measurements from the three low-cost monitors within the group, as well as the prediction errors from Group 1. The resulting calibration model is described by the following equations: r e = reference − prediction 1 S 1 (2) y ^ error _ i = calibration i S i , r e (3) Where r e denotes the errors from the reference group (i.e., Group 1). y ^ error _ i denotes the estimated errors of prediction model in Group i . Group 1 does not need to have a calibration model because the reference monitor was always collocated with Group 1. Calibration Model Assumption: The calibration models were designed based on the assumption that low-cost monitors from the same manufacturer, when used to measure PM 2.5 , should exhibit similar error patterns in the same environment (i.e., Aerosol A and Aerosol B). unKnown Environment After establishing the prediction and calibration models for each group using Aerosol A, the models can be used to estimate aerosol mass concentration for Aerosol B used in the unknown environment. For example, for occupational settings, if Aerosol A was BoxMod, then Aerosol B would be JUUL or NJOY. If Aerosol A was JUUL, then Aerosol B would be BoxMod or NJOY. Finally, If Aerosol A was NJOY, then Aerosol B would be BoxMod or JUUL. All groups were moved to the unknown environment, except the reference group (i.e., Group 1), as shown in Figure 3 . The main difference between the unknown and known environment was access to the pDR data. Since the unknown environment does not have access to the pDR data, it cannot provide error corrections directly to that group. Rather, they will use the errors from the reference group to improve the readings for each group (i.e., the low-cost monitors), where only the reference group had access and used the pDR data to calculate errors. Figure 3. Open in a new tab After error correction (either BoxMod, JUUL, or NJOY [Only one]). All groups are considered in the unknown environment, except for the reference group (Group 1), which has access to the pDR data. Underlined bold text represents machine learning models. In the unknown environment, Groups 2–10 use the errors from the reference group (as shown in Eq. 4 below) to improve the low-cost monitor readings of each group. The final reading estimation was the sum of prediction and calibration models’ outputs (as shown in Eq. 5 ). r e ′ = reference − prediction 1 S 1 (4) f i S i , r e = prediction i S i + calibration i S i , r e ′ (5) where r e ′ denotes the errors from the reference group in the unknown environment. prediction i is the prediction model for the group i. calibration i is the calibration model for the Group i. reference is the sensor readings from the reference sensor. f i ( S i , r e ) is the final predicted PM 2.5 values of Group i . In an actual deployment involving a network of indoor or outdoor monitors, the objective is to collocate all the groups of three monitors, next to a reference monitor, and establish the calibration and prediction models. Then, all the groups are moved to the target locations while still networked and being able to communicate in real time. Only the reference group will remain collocated with the high-cost or reference monitor to provide error reference information to all the deployed groups in real time. In Figure 3 , the prediction model established for the reference group (i.e., Group 1) will generate target monitoring parameter predictions based on low-cost monitor readings. The prediction errors were then calculated using the difference between predictions and the data from the reference monitor (i.e., r e ′ in Eq. 4 ). These errors include important information that can be passed to monitor groups in the unknown environment. Based on the Calibration Model Assumption , similar error patterns can be found in Groups 2–10 since the same target monitoring parameter and the same type of low-cost monitors were used and the groups operate in the same unknown environment, i.e., Aerosol B. Data Sampling Methods To ensure the results of this work are reliable and can be generalized, repeated experiments were performed to confirm that the observed results were reproducible and not influenced by random variations or chance. One hundred experiments were performed by using two methods to split monitors into 10 groups in each experiment. The final results were the average of the results for these experiments. Monitor grouping for each experiment was performed using “With Data Replacement” and “No Data Replacement” as follows: With Data Replacement (R) Group 1 – 10 can have the same monitors, e.g., Monitor 29 in both Group 2 and 3 was allowed. No Data Replacement (NR) No groups should have the same monitors, e.g., Monitor 29 in both Group 2 and 3 was not allowed. This method advocates using multiple low-cost monitors in one group, which can be more resilient. If low-cost monitors malfunction and their outputs are extremely large or small, these deviations will be detected by anomaly event detection methods, such as Multivariate Anomaly Detection with Generative Adversarial Networks (MAD-GAN) ( Li et al., 2019 ), and these readings will be replaced with average values of the other monitors. In addition, the network will send a warning message to the system manager to inspect and potentially replace the damaged monitor. Additionally, multiple low-cost monitors within a group can generate more accurate overall results. This is inspired by ideas from ensemble machine learning algorithms that leverage outputs from multiple weak learners to generate more accurate predictions ( Dietterich, 2000 ). A case study that illustrates the proposed methods in this work is provided in the Supplemental Information document. An example of the machine learning calibration method is described in the Supplemental Information document. 2.4. Data Analysis For occupational settings, this study compared data collected every second by the GeoAir2 and the pDR monitors, where the 1,317 data points showed a high correlation (r 2 > 0.9) between the low-cost monitors and reference instrument for all the ECIG brands ( Sousan et al., 2021 ). The 1-minute, time-paired, mean values were used to calculate the coefficient of determination (r 2 ), RMSE, and coefficient of variation (CV, or precision) for each regression model before and after applying the machine learning methods. The CV represents the inter-monitor variability between the low-cost monitors. The RMSE and CV calculations were conducted using equations 1 and 2 ( EPA, 2021 ): RMSE = 1 NxM ∑ j = 1 M ∑ d = 1 N y d j − x d 2 (6) where N is the number of 1-minute mean values, M is the number of low-cost monitors (32), y is the estimated mass concentration of the low-cost PM 2.5 monitors, x is the estimated mass concentration of the pDR data, and n is the number of data pairs. CV = σ / μ (7) where σ is the standard deviation, and μ is the mean of the concentrations reported by the low-cost monitors for PM 2.5 . The r 2 , RMSE, and CV values were then compared to EPA standards for PM 2.5 low-cost monitors of r 2 ≥ 0.70, RMSE ≤ 7 μg/m 3 , and CV (precision) among sensors ≤ 30% standards. ( Sousan et al., 2021 ; Streuber et al., 2022 ). No OSHA acceptance criteria are available for low-cost aerosol instruments; therefore, the same EPA criteria were used. For this paper, each experiment was repeated 200 times to minimize the influence of random variations or chance. In each iteration, the low-cost monitors were first split into 10 groups using both the “With Data Replacement” (100 times) and “No Data Replacement” (100 times) sampling methods. Next, the prediction models and calibration models were built in the known environment and tested in the unknown environment, as described in Section 2.3 . The r 2 , RMSE, and CV values were then calculated for the prediction and calibration models for Groups 2–10 in the unknown environment. To illustrate the method, Group 2 is used as an example. As shown in Figure 3 , Prediction Model 2 outputs predicted PM 2.5 values using Eq. 1 . By comparing these predicted values with the reference monitor values, the r 2 and RMSE values were calculated. This process was repeated for Groups 3–10, resulting in a total of nine r 2 and RMSE values. The nine values were then averaged to determine the accuracy measures (i.e., three averaged r 2 and RMSE) before calibration for the current iteration. The CV value was calculated using the predicted PM 2.5 values from Groups 2–10. According to Eq. (7) , both the standard deviation and mean values are required. These values are calculated using the outputs of Prediction Models 2–10 at the same timestamp, resulting in one CV value per timestamp. All CV values are then averaged to obtain the overall CV value before calibration for the current iteration. For calibration, Group 2 is used as an example. Calibration Model 2 estimated the possible errors of Prediction Model 2. Using Eq. 5 , these estimated errors were combined with the predictions to generate the final estimated PM 2.5 readings. The outputs of Eq. 5 for Group 2 were compared with the reference monitor to calculate the r 2 and RMSE values. This process was repeated for Groups 3–10, resulting in nine r 2 and RMSE values. These nine values were averaged to determine the accuracy measures (i.e., three averaged r 2 and RMSE values) after calibration for the current iteration. The CV value was calculated with the enhanced Groups 2–10 predicted PM 2.5 values using Eq. (5) . According to Eq. (7) , both the standard deviation and mean values are required. These values at each timestamp can be calculated with Eq. (5) output of Group 2–10, resulting in one CV value per timestamp. All CV values are then averaged to obtain the overall CV value after calibration for the current iteration. An iteration or experiment was completed once the average r 2 , RMSE, and CV values were calculated. This process was repeated for 100 iterations using the “ With Data Replacement ” sampling method, generating 100 sets of averaged r 2 , RMSE, and CV values both before and after calibration. Finally, these 100 sets of values were averaged to obtain the final results (i.e., three averages of the mean r 2 , RMSE, and CV values before calibration and three averages of the mean r 2 , RMSE, and CV values after calibration), as shown in Section 3 . This process was also repeated for 100 iterations using the “ No Data Replacement ” sampling method. Similarly, 100 sets were averaged for r 2 , RMSE, and CV values both before and after calibration and have three averages of the mean r 2 , RMSE, and CV values before calibration and three averages of the mean r 2 , RMSE, and CV values for after calibration, as shown in Section 3 . In this paper, low-cost monitors were divided into 10 groups, with each group containing 3 monitors. If the proposed method is applied to similar problems, the number of groups and the number of monitors per group could vary. It is important to note that if only 2 groups are defined, the precision value will be 0. This occurs because, as described in the algorithm above, at any given timestamp, the standard deviation becomes 0 (since there is only one group per timestamp, and the standard deviation of a single value is 0). Figures that represent the values before and after error corrections for both with and without replacements were plotted. The before values were calculated from the regression model derived using the known environment (e.g. salt or JUUL) and applied to the unknown environment (e.g. dust or NJOY). For example, the regression model was derived from collocating the monitors next to the high-cost monitor in the BoxMod experiment and then using that model to calculate the corrected values in the JUUL or NJOY experiments. In other words, it used the BoxMod regression model on the JUUL or NJOY experiments. The after values were calculated by adding the before values to the errors calculated by the reference group (Group 1) for the JUUL and NJOY experiments, respectively. 3. Results The results presented in this section are based on the environmental data, salt and dust aerosols, and occupational data, ECIG aerosols. The scatter plots and tables show the r 2 , RMSE, and precision for the literature reviewed in this paper along with the results of this work. The literature data compares low-cost monitor measurements against reference monitors. The new data generated by the prediction models calculated from equation 1 (highlighted in blue in Figure 3 ) are represented as Before calibration and the data from the final readings calculated from equation 5 (highlighted in green in Figure 3 ) are represented as After calibration. 3.1. Environmental Calibration Results The data was collected in simulated environments involving concentration levels between 0 and 50 μg/m 3 , as described in the methods section. Scatter plots for the dust to salt and salt to dust tests for all the models, with and without replacement, before and after calibration are shown in Figure 4 and the accompanying r 2 , RMSE and precision data are shown in Table 1 . Figure 4: Open in a new tab The PM 2.5 mass concentrations (μg/m 3 ) of (A) dust To salt and (B) salt To dust, reported by the low-cost monitors against the reference device for the Linear Regression (LR), RF, and GBR models, Before calibration (BC) and After calibration (AC), using the no replacement (NR) and replacement (R) methods. Table 1: The r 2 , RMSE, and precision of Dust To Salt and Salt to Dust reported by the low-cost monitors against the reference device for the Linear Regression (LR), RF, and GBR models, Before calibration (BC) and After calibration (AC), using the no replacement (NR) and replacement (R) methods. In addition to the original previously published data for comparison. r 2 RMSE Precision Salt Dust Salt Dust Salt Dust Previous Work 0.93 0.99 12.02 3.42 20.58 37.63 Dust To Salt Salt To Dust Dust To Salt Salt To Dust Dust To Salt Salt To Dust LR_NR_BC 0.97 0.94 3.95 4.10 5.55 12.50 LR_NR_AC 0.99 0.96 2.06 3.13 12.46 11.54 LR_R_BC 0.97 0.95 3.48 3.37 13.95 9.56 LR_R_AC 0.99 0.96 2.48 2.47 16.97 10.29 RF_NR_BC 0.98 0.97 3.87 3.58 12.28 10.45 RF_NR_AC 0.99 0.98 3.74 3.51 16.50 11.49 RF_R_BC 0.98 0.97 3.96 3.92 5.13 11.37 RF_R_AC 0.99 0.98 2.00 3.11 15.17 11.49 GBR_NR_BC 0.97 0.96 3.56 3.36 14.72 9.74 GBR_NR_AC 0.97 0.96 2.51 2.47 18.13 10.22 GBR_R_BC 0.97 0.96 3.75 3.60 11.74 10.45 GBR_R_AC 0.98 0.96 3.60 3.53 16.19 11.53 Open in a new tab A ‘salt to dust’ methodology involves the derivation of calibration and prediction models using salt aerosol measurement data, followed by their validation against, or application to, dust aerosol measurement data. The inverse process, where models derived from dust aerosol measurements are applied to salt aerosol data, is designated ‘dust to salt’. For dust to salt ( Figure 4a , Table 1 ), both the Before and After calibration data greatly improved compared to the original data. The r 2 values for all the data ranged between 0.93 and 0.99, meeting the EPA standard of r 2 = 0.7. The r 2 Before and After values improved by 4–6% compared to the original data across all regression models. Additionally, the r 2 After values showed a 1–2% improvement over the Before data for all regression models. For RMSE values, the Before and After data improved by 67–83% compared to the original data across all regression models. Notably, the original data had an RMSE value of 12.02 μg/m 3 , which was above the required EPA RMSE standard of 7 μg/m 3 . In contrast, the Before and After RMSE values ranged between 2.00 and 3.00 μg/m 3 . While the r 2 After values improved by 1–2% compared to the Before data across all models, the GBR no-replacement method remained unchanged. Similarly, the RMSE After values showed a 10–15% improvement over the Before data for all models, except for the RF no-replacement method, which exhibited only a slight 3% improvement. Regarding precision, all data were within the EPA CV standard of ≤30%, with precision values ranging between 5–20%. The Before and After data improved over the original by 11–75%. However, the After values decreased by 11–40% compared to the Before data. Aside from this inconsistency, the no-replacement and replacement methods yielded similar or identical results. For salt to dust ( Figure 4b , Table 1 ), the original data closely followed the 100% accuracy (graph diagonal) line, and both the Before and After data visually remained on the line as well. The r 2 values for all data ranged between 0.94 and 0.99, meeting the EPA r 2 = 0.7 standard. However, the r 2 Before and After values decreased from the original value (0.90) to 0.94 and 0.98 across all regression models. The After values showed improvements over the Before values but remained below the r 2 = 0.90 threshold. For RMSE, all data met the EPA RMSE standard of ≤7 μg/m 3 , with values between 2.00 and 4.00 μg/m 3 . Improvements were noted in 50% of the Before and After data across all models, particularly with linear regression, especially for the After data. For precision, the original data exceeded the EPA CV standard (≤30%) with a value of 37.63%. However, the Before and After data showed marked improvements, with values ranging between 9–12%. Despite this, the After values decreased by ~70% compared to the Before values. The no-replacement and replacement methods provided similar results. 3.2. Occupational Calibration Results When simulating the occupational exposure environment, the concentration levels were different for each ECIG brand, with the maximum values measured by the pDR for the JUUL, NJOY, and BoxMod up to 1415, 2119, and 9,871 μg/m 3 . BoxMod generated much higher mass concentrations compared to the JUUL and NJOY, which were similar to Sousan et al. (2022b) . Scatter plots for BoxMod to JUUL and BoxMod to NJOY across all models, with and without replacement, Before and After calibration, are shown in Figure 5 , with corresponding r 2 , RMSE, and precision data detailed in Table 2 . For BoxMod to JUUL, reference concentrations reached ~1,400 μg/m 3 , while for BoxMod to NJOY, reference concentrations reached ~2,000 μg/m 3 . The Before and After data improved and aligned more closely with the reference monitor line compared to the original data. For BoxMod to JUUL, the linear regression and GBR models demonstrated greater improvements than the RF model. Similarly, for BoxMod to NJOY, linear regression and GBR showed better performance compared to the RF model and the linear regression with replacement. Regarding r 2 , for BoxMod to JUUL and BoxMod to NJOY, values ranged from 0.93–1.00 and 0.95–1.00, respectively, meeting the EPA r 2 = 0.7 standard. Although r 2 slightly decreased in the Before data, it increased to r 2 = 1.00 in the After data across all regression models. For RMSE, all values exceeded the EPA standard of ≤7 μg/m 3 , with ranges of 21–120 μg/m 3 for BoxMod to JUUL and 31–168 μg/m 3 for BoxMod to NJOY in both the Before and After datasets. However, both datasets showed significant reductions from their original RMSE values of 201 μg/m 3 (JUUL) and 349 μg/m 3 (NJOY). For precision, the original CV values were 35% for JUUL and 33% for NJOY. The Before and After precision values decreased to 35–113% for JUUL and 31–95% for NJOY, with the RF model showing smaller decreases in CV compared to linear regression and GBR. The no-replacement and replacement methods yielded similar results across all metrics. Figure 5: Open in a new tab The PM2.5 mass concentrations (μg/m 3 ) of (A) BoxMod To JUUL and (B) BoxMod To NJOY, reported by the low-cost monitors against the reference device for the Linear Regression (LR), RF, and GBR models, Before calibration (BC) and After calibration (AC), using the no replacement (NR) and replacement (R) methods. Table 2: The r 2 , RMSE, and precision of BoxMod To JUUL, BoxMod To NJOY, JUUL To BoxMod, JUUL To NJOY, NJOY To BoxMod, NJOY To JUUL reported by the low-cost monitors against the reference device for the Linear Regression (LR), RF, and GBR models, Before calibration (BC) and After calibration (AC), using the no replacement (NR) and replacement (R) methods. In addition to the original previously published data for comparison. r 2 BoxMod JUUL NJOY Previous Work 0.96 0.94 0.98 BoxMod_JU UL BoxMod_NJ OY JUUL_to_Bo xMod JUUL_to_NJ OY NJOY_to_Bo xMod NJOY_to_JU UL LR_NR_BC 0.93 0.95 0.91 0.95 0.91 0.93 LR_NR_AC 1.00 1.00 0.99 1.00 0.99 1.00 LR_R_BC 0.93 0.96 0.92 0.95 0.91 0.93 LR_R_AC 1.00 0.99 0.97 0.99 0.97 0.99 RF_NR_BC 0.93 0.96 0.92 0.95 0.92 0.93 RF_NR_AC 0.99 0.99 0.99 1.00 0.97 0.98 RF_R_BC 0.93 0.96 0.92 0.95 0.92 0.93 RF_R_AC 0.99 0.99 0.98 1.00 0.97 0.98 GBR_NR_BC 0.93 0.95 0.91 0.95 0.92 0.93 GBR_NR_AC 1.00 1.00 0.99 1.00 0.99 1.00 GBR_R_BC 0.93 0.95 0.91 0.95 0.92 0.93 GBR_R_AC 1.00 1.00 0.94 1.00 0.99 0.99 RMSE BoxMod JUUL NJOY Previous Work 1722 201 349 BoxMod_JU UL BoxMod_NJ OY JUUL_to_Bo xMod JUUL_to_NJ OY NJOY_to_Bo xMod NJOY_to_JU UL LR_NR_BC 115 165 795 134 760 96 LR_NR_AC 22 35 237 41 238 25 LR_R_BC 114 168 728 133 761 89 LR_R_AC 23 97 412 69 429 26 RF_NR_BC 115 162 714 128 680 92 RF_NR_AC 53 79 252 42 416 52 RF_R_BC 120 166 707 130 692 92 RF_R_AC 51 81 397 35 405 57 GBR_NR_BC 110 164 793 129 670 87 GBR_NR_AC 21 31 203 45 236 24 GBR_R_BC 114 166 773 130 676 88 GBR_R_AC 27 36 234 42 216 28 Precision BoxMod JUUL NJOY Previous Work 32 35 33 BoxMod_JU UL BoxMod_NJ OY JUUL_to_Bo xMod JUUL_to_NJ OY NJOY_to_Bo xMod NJOY_to_JU UL LR_NR_BC 87 69 29 39 24 25 LR_NR_AC 55 51 43 47 53 45 LR_R_BC 113 36 23 37 55 25 LR_R_AC 53 46 32 38 54 32 RF_NR_BC 35 33 22 45 25 16 RF_NR_AC 39 38 40 47 31 28 RF_R_BC 36 31 22 38 27 16 RF_R_AC 40 36 34 48 36 29 GBR_NR_BC 87 46 29 43 46 18 GBR_NR_AC 55 55 45 48 48 40 GBR_R_BC 84 95 28 40 43 17 GBR_R_AC 55 46 40 41 51 42 Open in a new tab Scatter plots for JUUL to BoxMod and JUUL to NJOY across all models, with and without replacement, Before and After calibration, are shown in Figure 6 , with corresponding r 2 , RMSE, and precision data detailed in Table 2 . For JUUL to BoxMod, reference concentrations reached ~10,000 μg/m 3 , while for JUUL to NJOY, reference concentrations reached ~2,000 μg/m 3 . Both the Before and After data showed improvements, aligning more closely with the reference monitor line compared to the original data. Visually, all models improved, except for minor discrepancies at higher concentrations for JUUL to BoxMod using linear regression and RF with replacement, and JUUL to NJOY using linear regression with replacement. Regarding r 2 , values ranged from 0.91–0.99 for JUUL to BoxMod and 0.95–1.00 for JUUL to NJOY, meeting the EPA r 2 = 0.7 standard. While r 2 slightly decreased in the Before data, it improved up to r 2 = 1.00 in the After data for all models, except for JUUL to BoxMod using the GBR model with replacement, which showed a slight decrease. For RMSE, values exceeded the EPA standard of ≤7 μg/m 3 , ranging from 203–795 μg/m 3 for JUUL to BoxMod and 35–134 μg/m 3 for JUUL to NJOY. Both datasets showed significant reductions from their original RMSE values of 1,722 μg/m 3 (BoxMod) and 349 μg/m 3 (NJOY). For precision, the original CV values were 32% for BoxMod and 33% for NJOY. For JUUL to BoxMod, precision improved below the EPA standard for the Before data (22–29%), but the After values ranged between 32–45%. For JUUL to NJOY, both the Before and After precision values improved across all models, albeit inconsistently. Figure 6: Open in a new tab The PM2.5 mass concentrations (μg/m3) of (A) JUUL To BoxMod and (B) JUUL To NJOY, reported by the low-cost monitors against the reference device for the Linear Regression (LR), RF, and GBR models, Before calibration (BC) and After calibration (AC), using the no replacement (NR) and replacement (R) methods. Scatter plots for NJOY to BoxMod and NJOY to JUUL across all models, with and without replacement, before and after calibration, are shown in Figure 7 , with corresponding r 2 , RMSE, and precision data detailed in Table 2 . For NJOY to BoxMod, reference concentrations reached ~10,000 μg/m 3 , while for NJOY to JUUL, concentrations reached ~2,000 μg/m 3 . Both the Before and After data improved, aligning closer to the refernce monitor line compared to the original data. However, slight imperfections were observed for higher concentrations using linear regression with replacement for NJOY to BoxMod and RF for NJOY to JUUL. Regarding r 2 , values ranged from 0.91–0.99 for NJOY to BoxMod and 0.93–1.00 for NJOY to JUUL, meeting the EPA r 2 = 0.7 standard. r 2 slightly decreased in the Before data but increased up to r 2 = 1.00 in the After data for all models, especially for NJOY to JUUL. For RMSE, all values exceeded the EPA standard of ≤7 μg/m 3 , with ranges of 216–761 μg/m 3 for NJOY to BoxMod and 24–96 μg/m 3 for NJOY to JUUL. Both datasets showed reductions from their original RMSE values of 1,722 μg/m 3 (BoxMod) and 201 μg/m 3 (JUUL). For precision, the original CV values were 32% for BoxMod and 35% for JUUL. NJOY to BoxMod precision improved below the EPA standard for linear regression without replacement and RF (24–27%). However, After values ranged between 31–54%, slightly decreasing in some cases. For NJOY to JUUL, precision improved below the EPA standard for the Before data (16–25%) across all models, but the After data only showed consistent improvements for RF. Figure 7: Open in a new tab The PM2.5 mass concentrations (μg/m3) of (A) NJOY To BoxMod and (B) NJOY To JUUL, reported by the low-cost monitors against the reference device for the Linear Regression (LR), RF, and GBR models, Before calibration (BC) and After calibration (AC), using the no replacement (NR) and replacement (R) methods. 4. Discussion This work tested a new method to improve the accuracy of low-cost aerosol monitors through prediction and calibration models developed in a lab environment using one aerosol type and tested in an environment using a different type of aerosol. The method introduced an error correction model, derived based on data collected from a single group of low-cost monitors collocated with a reference monitor in both environmental and occupational settings. The model was developed using lab tests data and published data for different aerosol types. The model helped improve data accuracy in all scenarios studied. The experimental results indicate that linear regression and GBR are viable options for developing the prediction and calibration models. Linear regression requires minimal computing power and can produce enhanced low-cost monitoring readings faster than other models. While its accuracy may be slightly lower than that of RF or GBR, it remains acceptable in certain scenarios. On the other hand, GBR typically delivers the best performance (though it may perform less accurately if there is not enough data, e.g., in some dust and salt experiments), achieving the highest accuracy for our proposed method. However, this approach demands more computing power compared to the other models and requires more training data. For the Dust-to-Salt data, most methods showed improvements in r 2 or RMSE, while some methods only showed slight improvements, which could be attributed to the low number of data points that these machine learning models require. Regarding precision, higher “After” calibration precision values indicate instability or inconsistency in the model’s performance across different datasets. This means that after applying the calibration model, the overall accuracy of the enhanced low-cost monitor readings improves, but the performance varies across different subsets of the data. To achieve more consistent performance, additional training data is needed to help the model learn diverse patterns. For Salt-to-Dust, it is important to note that both the r 2 and RMSE values were already within EPA standards, so further improvements may be ineffective, which is why some results did not show improvement. Another factor could be the smaller datasets, where machine learning models used in the proposed methods require more data to effectively learn diverse data patterns. The occupational environment test results are very promising, as the machine learning models can acquire sufficient knowledge (i.e., how to predict the real target monitor parameter and how to estimate possible errors). The results generally show that the error patterns can be approximated as close to linear. Therefore, a linear regression model was well-suited for learning these patterns. However, the experimental data is sufficient for a GBR model to capture both linear and nonlinear error patterns, leading to better performance compared to linear regression models. Unlike GBR, the RF models do not assign higher weights to training data records that contribute to larger errors, which may lead to performance issues. In addition, the metrics improvement suggests that the calibration models show great potential for learning the possible errors made by prediction models within the same group. However, it is important to note that all experiments were conducted in controlled lab environments. In real-world settings, the environment can be much more complex and difficult to control, making it challenging to achieve similarly high r 2 values of 1.0. Additionally, the lower performance seen in the RF model in some instances could indicate that the method requires more data to capture the different patterns present in the entire dataset, which helps enhance consistency in the enhanced low-cost monitor readings. Furthermore, the “no replacement” and “replacement” methods yielded similar results across all metrics. This may be due to all sensors performing similarly in the controlled JUUL and NJOY environments. Moreover, the decrease in precision values could indicate that the proposed method requires more data to capture the different patterns present in the entire dataset, which helps enhance consistency in the enhanced low-cost monitor readings. For the JUUL-to-BoxMod and JUUL-to-NJOY cases specifically, the results show that the higher concentration condition leads to lower performance in linear regression and RF models. This condition could introduce more nonlinear patterns in the data, which are harder for linear regression models to learn. These scenarios require RF models to focus more on nonlinear patterns, rather than treating all points equally (i.e., assigning the same weight to each point) during training. The R 2 value for the JUUL-to-BoxMod GBR model with replacement slightly decreased compared to the previous value. This could be due to the fact that some low-cost monitors do not perform as well as others. Repeatedly selecting these monitors can lower overall performance. Most previous studies using a network of low-cost monitors to measure airborne concentrations have utilized data from one monitor to correct for other sensors in the network ( Barcelo-Ordinas et al., 2019 ; Malings et al., 2019 ). deSouza et al. (2022) calibrated a network of aerosol sensors compared to an EPA reference monitor in outdoor settings using linear regression and multiple machine-learning models to predict aerosol concentrations using RF. neural networks, gradient boosting, and super-learner. They had one set of machine learning models for the calibrations, compared two sets used in this work. However, since the study was outdoors, the regression models used temperature and humidity for calibration and showed high r 2 values (>0.90) and low RMSE, especially for the RF model at 1.71. Vajs et al. (2023) used a network of aerosol sensors with a reference air quality station to calibrate using linear regression RF. The authors also employed two sets of machine learning models, although the first was always linear regression followed by RF. However, the authors did not use multiple units of the same monitor in the same group. In contrast, our method used three monitors of the same kind to improve the robustness of the calibration and the resiliency of the solution. The authors showed improvement in r 2 values by up to 34% and a decrease in RMSE values by up to 64% for the aerosol sensors. Limitations and Future work The major limitation of the study is that it evaluated laboratory exposure data generated in a controlled setting for different ECIG exposures. The proposed method could lead to different results in environmental settings which are affected by meteorological parameters and spatial distance. In addition, indoor occupational settings could be affected by changes in humidity or the different mix of aerosol types generated in large facilities. In addition, the current study simplified these algorithms in a controlled laboratory chamber and used only one reference monitor, as the low-cost monitor groups were all collocated in the same chamber. The use of two reference monitors, one for obtaining errors and the other for calculating the metrics, would have been more appropriate and will be implemented in future work. However, even if two reference monitors of the same brand were used, one for Group 1 error calculations and the other to calculate R 2 and RMSE, these two reference monitors would likely provide nearly identical measurements. This is because they would have been placed near each other in the chamber, used to measure the same target parameter, and sourced from the same manufacturer. Future work will focus on evaluating low-cost aerosol monitors and testing the methods derived in this work in environmental and occupational settings where spatial and meteorological effects are included. The investigation will involve two reference instruments for environmental or occupational applications, one static for calibration and one mobile for validation. In addition, the proposed method was predicated on the assumption that all low-cost monitor groups exhibit similar error patterns. This assumption holds when all low-cost monitors originate from the same companies, are not placed very far away, and are employed to measure identical data types. However, if this assumption is violated, while the proposed prediction models may still function, the calibration models may not. This method should be tested in both outdoor and indoor occupational environments to identify and address limitations in real-world applications, where adjacent microenvironments could introduce different exposures compared to the reference group location. 4. Conclusion This study introduced a calibration method using linear regression and machine learning methods that could be applied to clustered and networked low-cost monitors. The method used a calibration model obtained from one environment, the Before values, and applied it to a new target environment. Subsequently, the obtained values were improved by applying the errors calculated from a model built under the new environment, resulting in the After values. PM 2.5 exposure was targeted for analysis for environmental settings with salt and dust, and occupational settings generated through three different types of exposures represented by three different ECIG brands. The calibration process applied to the datasets, both before and after calibration, led to notable improvements in model performance. Specifically, the r 2 values for all datasets met or exceeded the EPA standards, with RMSE values decreasing significantly from the original values to meet the required thresholds. In addition, precision values were greatly improved, although slight inconsistencies remained for certain models and datasets. The findings demonstrate that dynamic calibration is a valuable tool in improving the accuracy, precision, and reliability of regression models used for environmental or occupational settings. Despite the success of the GBR machine learning method, the simple linear regression method showed similar, if not better, results, except when the calibration was performed for lower concentrations than applied for higher concentrations. Therefore, linear regression should be used in general, for its simplicity and low compute requirements, unless the calibration is out of the calibration range, in which case machine learning models are a better fit. The calibration and validation of low-cost airborne monitors are crucial for providing data with high accuracy and low errors. Environments could be affected by micro exposures or short-term events represented by forest fires or accidental spills that could release airborne hazards. Therefore, providing real-time measurements through a network of low-cost monitors that are continuously correcting their measurements could prove crucial for understanding immediate hotspots and addressing environmental and public health concerns. Supplementary Material 1 NIHMS2073211-supplement-1.docx (21.8KB, docx) Highlights. Low-cost air quality monitors require real-time calibration for improved estimates. Machine learning models can be used to improve air quality estimates. A collocated low-cost group and reference monitor can be sufficient for calibration. Results showed improved r 2 values to 0.91–1.00 across all datasets. RMSE decreased significantly, reducing up to 88% from the original values. Acknowledgment The data in this manuscript was reused from Streuber et al. (2022) and Sousan et al. (2022b) that was supported by grant numbers R15ES032138 and P30ES025128 from the National Institute on Environmental Health Sciences of the National Institutes of Health. U.S. Application 63/652997 titled “Artificial Intelligence Enabled Data Accuracy Optimization for Low-Cost Sensors” was filed for the Artificial Intelligence (AI) algorithms used in this manuscript on May 29, 2024, by the East Carolina University (ECU) Office of Licensing & Commercialization. Claims are directed towards improving data accuracy using AI with errors calculated from one monitor group for other groups with two models. In addition, the claim includes AI special error calculations that are not included in this work. Funding Part of Sinan Sousan’s efforts is also supported by the National Institute of Environmental Health Sciences of the National Institutes of Health under Award Number P30ES025128. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Footnotes Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. 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