Modus+: A Probabilistic Machine Learning Framework for Calibration of Low-Cost Air Quality Sensor Networks

Low-cost air quality sensors (LCS) are increasingly used to complement regulatory monitoring, but their wider adoption is constrained by challenges in data quality and calibration. To address this, we developed Modus+, a novel probabilistic machine learning framework for network calibration and quality assurance. Modus+ maintains indicative-class measurements suitable for public health communication and policy applications while eliminating the need for resource-intensive co-location with a reference.

Modus+ integrates diverse inputs – including satellite data, nearby reference monitors, and local meteorology – to generate probabilistic pollution predictions at each sensor location that serve as a proxy for a co-located reference. Where inputs lack predictive power, prediction intervals widen, providing an explicit quantification of uncertainty in space and time. Comparing predictions with LCS measurements, the system derives simple linear calibrations with confidence intervals on the slope, intercept and bias at the relevant limit value. This enables an evidence-based decision on whether and how to correct individual sensors, while preserving traceability to the underlying measurements. The framework is pollutant and sensor-agnostic and can be applied across diverse networks and operating conditions.

We validated Modus+ through a three-year co-location study and a case study of its operational deployment within the Transport for Greater Manchester (TfGM) sensor network. Twelve low-cost PM sensors were co-located at four reference sites between 2022 and 2025, and for rolling 12-week periods we compared relative expanded uncertainty from (i) uncorrected data, (ii) calibration using short-term co-location (10 days), (iii) calibration using full co-location data, and (iv) Modus+ network calibration. Modus+ significantly improves performance compared to uncorrected data and short-term co-location and achieves the 50% relative expanded uncertainty criterion for indicative measurements. Through our ongoing deployment across the TfGM network, stakeholders have gained a robust understanding of how pollution levels change across the region. This information is being used to explore the impact of local pollution sources, such as domestic wood burning, and aid public engagement.