Some manufacturers of low-cost particle sensors use proprietary algorithms to estimate particle mass concentrations such as PM2.5. Often little or no information is given regarding the calibration aerosol, how the algorithm was created or tested, or how the mass was estimated from the particle number counts. If the algorithm is faulty in some way, researchers have little ability to correct it in a fundamental way, although they can multiply the output by some calibration factor to match the particular aerosol combination they are studying. However, the adjustment still requires the use of the proprietary algorithm, which may have quirks that make it impossible to fix completely using a single calibration factor. It might be possible in some cases to avoid using the proprietary algorithm at all. That is the approach of this study. The low-cost sensor studied is the Plantower PMS 5003, and the algorithm is the CF_1 algorithm offered by the manufacturer. Data from a six-month study of four collocated PurpleAir PA-II monitors, each containing two independent Plantower PMS 5003 sensors, were collected. Two of these monitors had previously been calibrated against research-grade monitors. The best-fitting model for PM1 was found to be of the form PM1 = a*(N1 + N2) + d, where N1 and N2 are the particle numbers in the size categories 0.3-0.5 μm and 0.5-1 μm, and d is an additive constant. The best-fitting model for PM2.5 was of the form a*(N1 + N2) + b*N3 + d, where N3 is the number of particles in the third size fraction (1-2.5 μm). The individual models for all 8 sensors matched the reported CF_1 values for both PM1 and PM2.5 with R2 values exceeding 0.99, intercepts near zero, and slopes in the 0.99-1.01 range. The proposed models may also explain why the CF_1 algorithm reports values of zero for a substantial portion of PM1 and PM2.5 estimates. General models capable of being applied to other datasets were developed and estimated to have mean absolute errors (MAEs) <1 μg/m3.
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