Adaptive Kalman Filtering for Compensating External Effects in On-Line Spectroscopic Measurements

This study addresses the challenges of real-time spectroscopic sensing in industrial applications, where external factors such as temperature fluctuations, pressure variations, and particle size distribution significantly impact measurement accuracy. Conventional quantitative analytical methods often neglect these dynamic influences, leading to erroneous concentration estimates. To overcome these limitations, we propose an integrated modeling framework that combines a discrete-time process model with a physics-based spectroscopic sensor model, explicitly accounting for the dynamic properties of the system. A key innovation of this work is the development and application of an Adaptive Kalman Filter (AKF) to systematically correct for measurement distortions caused by external disturbances. Unlike conventional filtering techniques, the AKF dynamically adjusts to changing process conditions by leveraging real-time observability analysis, ensuring robustness even in the presence of sensor noise and environmental variability. Furthermore, to address cases where full observability is not achievable, we introduce a reduced-order Adaptive Kalman Filter (rAKF), which optimally estimates concentrations while minimizing computational complexity. A comprehensive series of simulations was conducted to assess the sensitivity of the estimation to variations in external signal type, noise levels, and initial values for parameters and states. The findings of this study demonstrate the superior performance of both AKF and rAKF in comparison to conventional filtering techniques, including the Extended Kalman Filter. The proposed approaches have been shown to enhance the reliability of spectroscopic sensor measurements, enabling more precise real-time estimations that can be used for monitoring and advanced process control strategies in industrial settings.