Quadratic-Baseline Partitioning of Indoor PM$_{2.5}$ Using a Low-Cost Optical Sensor During a Facade Retrofit Case Study

A quadratic-baseline algorithm was developed to partition indoor PM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2.5}$</tex-math></inline-formula> sources using data from a single low-cost sensor without outdoor reference. A Temtop LKC-1000S+ (2nd gen.) optical particle counter (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R^{2} &gt; 0.90$</tex-math></inline-formula> vs. FEM GRIMM) was deployed for 48 days during a facade retrofit. The algorithm reproduced background periods with a mean absolute error of 2.3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> g m<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{-3}$</tex-math></inline-formula> and resolved daily PM<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2.5}$</tex-math></inline-formula> dose shares for facade work, cooking, and passive accumulation (31%, 24%, 45%). During the plastic barrier stage, the PM<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2.5}$</tex-math></inline-formula> baseline doubled, highlighting the trade-off between dust shielding and background elevation. This framework enables affordable, real-time indoor air quality diagnostics in occupied retrofits. Robust baseline fitting made it possible to account for sensor limitations at low concentrations. However, the generalizability of the findings is limited by the study design (single subject, only internal measurements), which necessitates further validation with external monitoring.