Adaptive Kalman filter for on-line spectroscopic sensor corrections

Abstract

Spectroscopic sensors provide online information about the composition and concentration of species in a sample by analyzing the interaction of light and matter. At the industrial scale, external variables such as temperature, pressure, and particle size distribution affect spectroscopic measurements. Thus, conventional quantitative analytical methods that do not consider these external factors provide poor estimates. Their effects have to be compensated through proper modeling and processing to improve the concentration estimation. This work presents an integrated discrete-time model considering the process dynamic and a physics-based sensor model. Then, we suggest a novel application of an adaptive Kalman filter to provide concentration estimates by correcting external factor effects. The convergence of the Kalman filter requires the fulfillment of uniform observability (persistent excitation) conditions for both inputs and external signals. Simulation results illustrate the modeling methodology and the main characteristics of the proposed Kalman filter approach for performing online correction of the spectroscopic sensor signals. The results show that the proposed adaptive Kalman filter can estimate concentrations with small error under temperature variations and measurement noise.