## 3 Experimental Results and Analysis
### Data Source and Preprocessing  
This study uses air quality data from 14 November 2018 to 11 June 2019 as the dataset [38]. This paper proposes a method for calibrating low-cost sensors for PM\({}_{2.5}\) measurements. A low-cost sensor developed by a certain company is used as an example in this study. To calibrate the PM\({}_{2.5}\) sensor, a low-cost station equipped with air quality and meteorological sensors was developed. This station enables real-time grid-based air quality monitoring in a specific region and simultaneously measures meteorological parameters such as temperature, humidity, wind speed, pressure, and precipitation. The dataset used for calibration consists of hourly measurements collected by the self-developed low-cost station during the period from 14 November 2018 to 11 June 2019 (Table 2). The low-cost station was located near a national control point (reference station), and the PM\({}_{2.5}\) data measured by the reference station during the same period were used to validate the PM\({}_{2.5}\) measurements obtained from the low-cost sensor calibrated with the proposed method. Data were collected at 1-h intervals based on national control points, resulting in 5022 data entries. The dataset consists of 11 features, including PM\({}_{2.5}\), PM\({}_{10}\), CO, NO\({}_{2}\), SO\({}_{2}\), O\({}_{3}\), and meteorological parameters such as temperature, wind speed, humidity, pressure, and precipitation. Since various pollutants and meteorological factors can affect PM\({}_{2.5}\) measurements, these features were input into the calibration model to enhance PM\({}_{2.5}\) accuracy.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Value** \\ \hline Feature extractor & Kernel size/convolution filter (\(C_{1}\))/stride of \(Conv_{1}\) & 1/26/1 \\  & Kernel size/convolution filter (\(C_{2}\))/stride/padding & 3/26/1/1 \\  & \multicolumn{2}{c}{Feature channels after fusion (\(C_{3}\))} & 26 \\ Calibration module & Hidden neurons in GRU and FECAM & 64 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the MCRTF-CM model.  
To improve the model's convergence speed and calibration accuracy, the raw data were preprocessed. This involved removing missing values, normalization and denormalization, and splitting the data into training and test sets. During data collection, environmental factors like temperature, wind speed, humidity, pressure, and precipitation affected the monitoring equipment, leading to missing or anomalous data. For example, while the reference station (national control point) was supposed to record data hourly for 5021 h, only 4200 h of data were available, leaving 821 h missing. Assuming no sudden weather changes, missing values were imputed using the average of neighboring data points. The low-cost air quality sensors (self-built stations) recorded data every 5 min. To match the reference station's hourly data, the self-built station data were resampled to hourly intervals by averaging. The resulting hourly data were then compared to the reference station data to analyze their differences.  
Due to the varying scales of features in the air quality data, differences in magnitude can reduce the model's accuracy and convergence speed. Therefore, the sample data were normalized using the Min-Max method, mapping values between 0 and 1, as shown in the following formula:  
\[x^{\prime}=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{11}\]  
where \(x^{\prime}\) represents the normalized data, \(x\) is the original sample data, and \(x_{max}\) and \(x_{min}\) are the maximum and minimum values of the sample data, respectively.  
To ensure the predicted results are meaningful, the calibration results were denormalized using the following formula:  
\[x=(x_{max}-x_{min})x^{\prime}+x_{min} \tag{12}\]  
After these processes, the input time series for model training was constructed by selecting data from 15 November 2018 to 1 May 2019 as the training set and from 1 May 2019 to 11 June 2019 as the test set, with an 8:2 training-to-testing ratio.