## 1 Introduction
[19], the relationship between sensor data and reference values is not always linear or confined to a single dimension. In cases involving nonlinear and multidimensional dependencies, machine learning (ML) algorithms present a promising alternative for sensor calibration [20]. This paper focuses on calibrating low-cost air quality sensors, particularly for PM\({}_{2.5}\) measurements. Factors such as cross-interference from varying gas concentrations and weather conditions [21], as well as zero and span drift in optical particle counters over time [22], can significantly affect the accuracy of sensor measurement data. Specifically, the presence of certain gases can lead to erroneous readings by altering the sensor's baseline or response to particulate matter, resulting in inaccurate PM\({}_{2.5}\) measurements. This phenomenon, known as cross-sensitivity, is a critical challenge for the reliable operation of low-cost sensors in dynamic environments. Traditional software compensation methods struggle to capture complex relationships, leading to poor fitting accuracy [23]. Therefore, developing an appropriate calibration model is crucial. Calibration of air pollution monitoring data primarily occurs at the data level, where calibration models are employed to correct the measurements. The proposed MCRTF-CM model calibrates low-cost air quality sensor data using a feature extractor and a calibration module. The feature extractor employs multi-scaleconvolution with residual connections to capture and preserve temporal features, which are fused and processed by the calibration module. Utilizing a GRU, the calibration module captures temporal dependencies and dynamic changes, while the FECAM (Frequency-domain Enhanced Channel Attention Mechanism) improves feature representation. A fully connected layer generates the final output, enabling the model to achieve accurate calibration by effectively leveraging sensor data features. To address these challenges, this paper proposes the MCRTF-CM model. The main contributions are as follows:  
* The feature extractor in the MCRTF-CM model utilizes a multi-scale convolutional structure to capture features across different temporal scales from sensor data. Through residual connections, the model effectively preserves critical information while reducing cross-interference from other features, enhancing feature richness and calibration accuracy. * The GRU (Gated Recurrent Unit) in the calibration module leverages gating mechanisms to control information flow and updates, effectively capturing temporal dependencies and dynamic changes in sensor data. This enhances the model's ability to utilize historical data, improving calibration accuracy in dynamic environments. * Time-domain calibration is commonly used due to its directness and broad applicability, but it may struggle with noise. To enhance calibration performance, the MCRTF-CM model incorporates a FECAM (Frequency-domain Enhanced Channel Attention Mechanism). This module uses frequency-domain analysis to improve feature representation, effectively suppressing noise and irrelevant frequency components, enabling more accurate capture and utilization of key information for high-precision calibration.