Increasing reliance on digital twin technology for managing indoor environments necessitates the development of spatial expansion virtual sensors (SEVS). However, in practical applications, SEVS performance often deteriorates due to shifts in data distribution and environmental conditions, presenting challenges for consistent reliability. Most existing SEVS research has primarily focused on initial model development, with limited consideration to in-situ calibration strategies. This study introduces an autoencoder reconstruction residualWasserstein distance (AR-WD)-based error estimation model, designed for spatial expansion virtual sensors with the primary objective of enhancing their performance in practical applications. The proposed model utilizes residuals from autoencoders and Wasserstein features, which can be derived without additional sensor installations, for real-time calibration. A comprehensive evaluation was conducted using temperature data from a pigsty, where the AR-WD model demonstrated robust performance across various machine learning algorithms, particularly with random forest and XGBoost, showing high predictive accuracy with a mean absolute error as low as 0.086. These findings suggest that the integration of AR-WD features significantly enhances the reliability and accuracy of virtual sensors. In addition, the AR-WD model leverages the unique characteristics of SEVS to enable real-time error estimation based solely on input data variations, thereby addressing common limitations of non-intrusive calibration methods. This research not only advances the field of virtual sensor development but also provides critical insights for optimizing sensor systems in complex indoor settings.
