Kalman Filter Fusion With Smoothing for a Process With Continuous-Time Integrated Sensor

Abstract

Integrated Sensor is a well-known methodology of slow sampling rates in chemical processes, which gradually collects material samples within a finite period. This type of infrequent measurement specified for quality variables is a function of states over sampling time. Our objective is to solve the problem of estimating states in fast sampling rates for a continuous-time system in the presence of a slow-rate integrated sensor. For this purpose, two reformulated models are suggested for describing the system, while they do not explicitly include the integral term. Integrated Measurement Kalman Filter (IMKF) for these two models are presented by the extension of the classical Continuous-Discrete (CD) Kalman filter to the integrated systems. Then, a novel sliding window smoothing algorithm is proposed for integrated systems using pseudo-estimations of the output, past time information of the fast-rate estimates and the last available slow-rate measurement. Also, the optimal fusion algorithm employing the estimation results of two reformulated models is extended for the integrated system. Eventually, the observability condition and exponential convergence of observation error are proved for the proposed algorithm. Simulation and experimental implementations are employed to demonstrate the effectiveness of the proposed method through a drum boiler model and a laboratory-scale pressure control process, respectively.