## 4 Conclusions  
This paper conducts calibration research on the low performance of low-cost air quality sensors in monitoring air pollutants, using high-precision government monitoring station data as reference features to learn the time-series characteristics of air pollutant data collected by low-cost sensors. The study focuses on calibrating a specific low-cost PM\({}_{2.5}\) sensor. A calibration method based on the MCRTF-CM network is proposed, which takes various air pollutant gases and meteorological features as inputs and utilizes a multi-scale convolutional residual network to extract diverse features from the sensor data, ensuring that more original information is retained and leveraged at deeper network layers. The extracted features are then fed into a GRU network to capture long-term dependencies in the temporal dimension. Additionally, a FECAM is employed to detect periodicity and trends in the time-series data through frequency-domain transformation, which are challenging to capture directly in the time domain. By integrating both time-domain and frequency-domain learning, the MCRTF-CM model effectively maps the measurements from low-cost sensors and additional features to national standard air quality data, thereby enhancing calibration accuracy. Test results show that the MCRTF-CM model outperforms other models in calibrating low-cost air quality data, demonstrating superior performance and robustness across various evaluation metrics. Despite the significant findings of this study, some limitations must be considered. First, the calibration model was primarily validated in specific regions and specific pollutants, limiting its generalizability to other regions and pollutants. Future research should focus on testing the model in more diverse environmental conditions, with a broader range of sensor types and pollutants, to assess its adaptability and robustness. Additionally, the issue of sensor drift over long-term use remains a critical challenge, as the performance of low-cost sensors may degrade over time. Addressing this issue will require the develop \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MAE** & **RMSE** & **MSE** & **MAPE (\%)** \\ \hline Model 1 & 6.200 & 8.197 & 67.188 & 21.213 \\ Model 2 & 6.131 & 8.204 & 67.312 & 21.240 \\ Model 3 & 5.664 & 7.320 & 53.586 & 21.527 \\ Model 4 & 5.707 & 7.477 & 55.900 & 21.068 \\ Model 5 & 6.021 & 7.928 & 62.853 & 23.148 \\ Model 6 & 5.834 & 7.676 & 58.927 & 19.763 \\ Model 7 & 5.832 & 7.600 & 57.761 & 21.488 \\ Model 8 & 6.256 & 8.197 & 67.198 & 21.522 \\ MCRTF-CM & 5.450 & 7.206 & 51.926 & 19.216 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ablation study of different modules. ment of more effective calibration techniques to account for sensor aging and environmental factors. Furthermore, while the current model performs well under the conditions tested, exploring potential improvements in model scalability and computational efficiency is an important direction for future work. These efforts will help extend the applicability of the MCRTF-CM model to real-world air quality monitoring systems on a larger scale. Conceptualization, J.L. and F.S. ; methodology, J.L. ; software, J.L. ; validation, J.L. and Z.J. ; formal analysis, J.L., Z.J. and J.Q. ; investigation, J.L., Z.J. and J.Q. ; resources, J.Q. ; data curation, J.L. ; writing--original draft preparation, J.L. ; writing--review and editing, J.L., F.S., Z.J. and J.Q. ; visualization, J.L. ; supervision, F.S. ; project administration, J.L. ; funding acquisition, F.S. All authors have read and agreed to the published version of the manuscript. This work was supported by the Key Research and Development Program of Xinjiang Uygur Autonomous Region: Research and Development of Key Technologies for Calculation, Measurement, and Digitized Management of Carbon Emission and Carbon Sink Indicators in the Energy Sector (No. 2022B01010), the National Natural Science Foundation of China (No.