  Sheaf theory, which is a complex but powerful tool supported by topological
theory, offers more flexibility and precision than traditional graph theory
when it comes to modeling relationships between multiple features. In the realm
of air quality monitoring, this can be incredibly useful in detecting sudden
changes in local dust particle density, which can be difficult to accurately
measure using commercial instruments. Traditional methods for air quality
measurement often rely on calibrating the measurement with public standard
instruments or calculating the measurements moving average over a constant
period. However, this can lead to an incorrect index at the measurement
location, as well as an oversmoothing effect on the signal. In this study, we
propose a compact device that uses sheaf theory to detect and count vehicles as
a local air quality change-causing factor. By inferring the number of vehicles
into the PM2.5 index and propagating it into the recorded PM2.5 index from
low-cost air monitoring sensors such as PMS7003 and BME280, we can achieve
self-correction in real-time. Plus, the sheaf-theoretic method allows for easy
scaling to multiple nodes for further filtering effects. By implementing sheaf
theory in air quality monitoring, we can overcome the limitations of
traditional methods and provide more accurate and reliable results.
