A method for monitoring the permanganate index (COD_Mn) by integrating the Gaussian hidden Markov model and inversion of hyperspectral remote sensing data under sparse sample conditions

This study aims to address the challenges in monitoring the permanganate index (COD_Mn) under conditions of sparsely distributed samples across a wide area. Hence, an integrated analytical method combining remote sensing images and time-series data was proposed, in which the inversion technique of remote sensing data and the Gaussian hidden Markov model (GHMM) are used for data analysis. Specifically, based on the high-accuracy GHMM prediction results, the current fluctuation trends of COD_Mn values are captured using the inversion technique, enabling the correction of the basic prediction results, thereby enhancing the overall accuracy. The experimental results show that compared to existing methods, the proposed method delivered higher accuracy and a higher coefficient of determination (R²). The COD_Mn inversion results exhibited a mean relative error of 0.177 mg·L^-1, a root mean square error of 0.272 mg·L^-1, a mean absolute percentage error of 7.276%, and a R² value of 0.954. Therefore, the proposed method can achieve large-scale, multi-point, and high-accuracy monitoring of COD_Mn under the sparse distribution of initial water quality samples, providing scientific support and technical guidance for inland water body monitoring and pollution warning.