Simple Linear Models Outperform Machine Learning in Urban Air Sensor Calibration

Researchers evaluating multi-sensor low-cost air quality devices in an urban winter setting have found that compact calibration periods using multiple linear regression outperform complex machine learning models over mid-term deployments. In a study conducted at Politecnico di Torino’s Department of Environment, Land and Infrastructure Engineering, scientists evaluated the MONICA multi-sensor platform against certified reference instruments during a four-month winter campaign in Turin, Italy. The investigation focused on three primary atmospheric contaminants—fine particulate matter under 2.5 micrometers, particulate matter under 10 micrometers, and nitrogen dioxide—regulated under European Union standards. While advanced non-parametric algorithms like random forests and generalized additive models achieved near-perfect agreement during initial training, their accuracy degraded substantially when exposed to concentration extremes later in the campaign. In contrast, multiple linear regression delivered stable temporal extrapolation, reliably tracking concentration shifts and matching regulatory exceedance events with only one to two weeks of initial co-location.

Urban air pollution constitutes a severe environmental health crisis, contributing to millions of premature deaths annually from respiratory and cardiovascular illnesses. Fine particulate matter poses grave physiological risks because microscopic particles penetrate deep into alveolar lung tissues, while nitrogen dioxide is strongly linked to airway inflammation. To mitigate these risks, European Union Directive 2024/2881 tightened statutory standards, introducing stricter daily limits alongside reduced annual thresholds. However, traditional municipal monitoring networks maintained by public agencies rely on sparse certified stations that cannot resolve the intense spatiotemporal variability characteristic of urban environments. While compact, low-cost sensor platforms offer a scalable solution for high-density spatial monitoring, practical deployment has long been hampered by concerns regarding sensor accuracy, environmental interference, and calibration durability over time.

The monitoring package is housed in a waterproof enclosure measuring 19 by 24 by 10 centimeters with mesh-protected inlets that facilitate air exchange while barring debris. Inside an internal chamber measuring 12.5 by 13.5 by 6 centimeters, the platform integrates a Plantower PMS7003 optical particle counter alongside Alphasense electrochemical cells: an NO2-A43F nitrogen dioxide sensor, an OX-A431 ozone sensor, and a CO-A4 carbon monoxide sensor. A DHT22 sensor records temperature and relative humidity. A paired Raspberry Pi single-board computer receives raw voltage and particle data via Bluetooth, forwarding observations across local Wi-Fi networks to a cloud storage platform while supporting remote troubleshooting and system monitoring through RealVNC software.

The field campaign took place in the Po Valley, an air pollution hotspot where high local emissions and winter meteorological stagnation trap pollutants near ground level. Between November 6, 2023, and February 25, 2024, the MONICA units were co-located with certified reference stations at Politecnico di Torino, operating at the fixed CC-Green Roof Laboratory and the mobile CC-TrAIRer Laboratory. Reference particulate concentrations were continuously recorded using an EN 16450-certified Palas Fidas 200 S optical spectrometer measuring particulate fractions between 0.18 and 18 micrometers. Reference nitrogen dioxide concentrations were monitored using two chemiluminescence analyzers: an EN 14211-certified ENVEA AC32e analyzer with a heated catalytic converter and a Serinus 40 analyzer employing alternating flow loops. Ambient meteorological conditions, including solar radiation, atmospheric pressure, wind metrics, and rainfall, were continuously documented by a certified Davis Vantage Pro 2 weather station.

The investigation evaluated three calibration models to translate raw sensor outputs into calibrated pollutant concentrations: multiple linear regression, generalized additive models with smoothing splines, and a random forest regressor configured with 200 decision trees in Python. Rather than randomly shuffling observations across the dataset, which causes artificial temporal data leakage, models were trained on continuous temporal windows to replicate realistic field deployments where calibration occurs immediately upon installation. Time-of-day predictors were excluded to prevent overfitting to site-specific emission cycles and preserve model transferability. During the baseline two-week training period, reference measurements ranged between 1 and 40 micrograms per cubic meter for fine particulates, 4 to 60 micrograms per cubic meter for coarse particulates, and 6 to 53 micrograms per cubic meter for nitrogen dioxide. These bounded training spans provided a realistic test of how well each model extrapolated beyond its calibration range.

To ensure parsimony and avoid computational over-parameterization, the authors conducted feature selection using an all-subset regression procedure in R, discarding variables that failed to improve predictive skill. For fine particulate matter, the selected model incorporated adjusted mass concentrations, particle number counts above 2.5 micrometers, and relative humidity. The coarse particulate model retained adjusted and standard mass concentrations alongside relative humidity, while excluding coarse particle counts. The nitrogen dioxide calibration incorporated primary sensor working electrode voltage, relative humidity, and working electrode voltage from the ozone sensor to correct for ozone cross-interference. Ambient temperature was excluded from all final equations. Because winter temperatures occupied a narrow range from 0.6 to 20.9 degrees Celsius and correlated moderately with humidity, relative humidity captured thermal variance without requiring an explicit temperature term, especially given that MONICA already features hardware-level thermal baseline compensation.

Model comparisons across subsequent testing intervals highlighted major differences between parametric regression and non-parametric machine learning. During the two-week calibration period, the random forest achieved the highest accuracy, with coefficients of determination exceeding 0.95 across all pollutants. Generalized additive models performed slightly lower, yielding a coefficient of 0.66 for nitrogen dioxide, while linear regression showed comparable training performance. However, during Week 7—five weeks after calibration—this hierarchy reversed. Because decision tree ensembles cannot predict values outside the boundaries of their training leaf nodes, the random forest saturated when particulate concentrations reached 80 and 110 micrograms per cubic meter. Generalized additive models also diverged noticeably at elevated particulate concentrations, increasing root mean square errors. Conversely, multiple linear regression successfully extrapolated beyond the training ceiling, maintaining tight alignment with reference observations during acute winter pollution episodes.

Analyzing calibration duration revealed that required co-location periods differ substantially depending on the target pollutant and initial concentration coverage. Extending particulate matter calibration from one to two weeks significantly improved measurement accuracy, lowering root mean square errors and narrowing fractional biases. This improvement occurred because two weeks of co-location expanded dynamic range coverage from 23 to 31 percent for fine particulates and from 35 to 46 percent for coarse particulates relative to the campaign maxima. For nitrogen dioxide, however, a single week of calibration proved entirely sufficient, with longer training durations yielding negligible performance gains. This rapid model convergence stemmed directly from urban atmospheric dynamics: during the initial week alone, ambient nitrogen dioxide ranged between 6 and 48 micrograms per cubic meter, already encompassing 57 percent of the 85 microgram maximum concentration recorded across the entire four-month monitoring effort.

Assessing sensor longevity across the winter campaign revealed distinct drift characteristics between optical counters and electrochemical gas sensors. Nevertheless, root mean square errors and fractional biases gradually increased after Week 6, with pronounced deterioration following a one-month instrument hiatus between Weeks 8 and 9. While sensors accurately tracked relative fluctuations, absolute concentration accuracy drifted toward negative bias. For nitrogen dioxide, performance degraded more sharply, exhibiting localized errors during Week 7 and a steep decline across all metrics after the operational interruption. This vulnerability underscores the susceptibility of electrochemical cells to baseline drift and shifting chemical dynamics, indicating that gaseous sensors demand more frequent recalibration than optical particulate monitors.

Evaluating sensor outputs against the regulatory thresholds of Directive 2024/2881 demonstrated the practical efficacy of low-cost systems for urban compliance monitoring. Reference instruments documented widespread limit exceedances throughout the winter, with daily fine particulate thresholds of 25 micrograms per cubic meter exceeded on more than 60 percent of days, and daily coarse particulate caps of 45 micrograms per cubic meter exceeded on roughly 40 percent of days. Nitrogen dioxide exceeded its 50 microgram threshold on only two percent of days. The MONICA system calibrated via two-week linear regression identified an almost identical frequency of exceedance events, despite systematic underestimations of 18 percent for fine particulates, 13 percent for coarse particulates, and 1 percent for nitrogen dioxide. These empirical findings demonstrate that well-calibrated multi-sensor systems offer a reliable, cost-effective tool for expanding municipal air monitoring networks and identifying regulatory non-compliance.

Subject of Research: Field calibration and mid-term performance evaluation of multi-sensor low-cost air quality monitors in an urban environment

Article Title: Mid-term Performance and Calibration of Multi-sensor Low-Cost Systems for Air Quality Monitoring in Urban Environments

Article References: Fellini, S., Gallione, D., Vaccaro, V., Mastromatteo, N., Fattoruso, G., Clerico, M., & Salizzoni, P. (2026). Mid-term Performance and Calibration of Multi-sensor Low-Cost Systems for Air Quality Monitoring in Urban Environments. Aerosol and Air Quality Research, 26(9), Article 73. https://doi.org/10.1007/s44408-026-00150-1

Image Credits: AI Generated

DOI: 10.1007/s44408-026-00150-1

Keywords: air quality monitoring, low-cost sensors, sensor calibration, multiple linear regression, particulate matter, nitrogen dioxide, urban air pollution, Directive 2024/2881, Mid-term, Performance, Calibration, Multi-sensor