AI-Based Koopman Distributed Kalman Filter for Air Quality Monitoring Through Integrated Particulate Sensors

This study presents an enhanced Kalman filtering (KF) approach for real-time air quality monitoring, with a particular focus on estimating inhalable particulate matter (PM2.5 and PM10) concentrations across a distributed sensor network. The classical Kalman Filter (KF) is initially employed to provide state estimation based on environmental inputs such as wind speed and humidity. While KF demonstrates effectiveness in linear systems, its accuracy degrades significantly in the presence of nonlinear pollutant behaviors, sensor noise, and dynamic disturbances that characterize real-world conditions. To address these limitations, we propose an AI-augmented Kalman Filter (AI-KF) that integrates a lightweight neural network (NN) to model and compensate for the residual errors produced by the KF. This neural module operates as a data-driven corrector that enhances the filter’s adaptability to nonlinear dynamics and environmental variability. Unlike the standard KF, the AI-KF can learn complex relationships between state variables and measurements, offering improved accuracy in scenarios with unmodeled nonlinearities. It demonstrates strong robustness to sensor drift and measurement noise by continuously adapting to shifting data patterns. Moreover, the AI-KF maintains the interpretability of the traditional KF framework while introducing an intelligent layer capable of real-time correction and adaptation. Experimental results on synthetic pollution data confirm that the proposed AI-KF consistently outperforms the standard KF, achieving lower root-mean-square error (RMSE) and enhanced state reconstruction. These findings highlight the potential of combining model-based estimation with neural residual learning for scalable, accurate, and robust environmental monitoring applications.