Partition‐based distributed extended Kalman filter for large‐scale nonlinear processes with application to chemical and wastewater treatment processes

• Published in: AIChE journal Vol. 69; no. 12
• Main Authors: Li, Xiaojie, Law, Adrian Wing‐Keung, Yin, Xunyuan
• Format: Journal Article
• Language: English
• Published: New York American Institute of Chemical Engineers 01.12.2023
• Subjects: Algorithms; Dynamic stability; Exact solutions; Extended Kalman filter; Local optimization; Stability analysis; State estimation; Subsystems; Wastewater treatment; Water treatment
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.18229

Abstract In this article, we address a partition‐based distributed state estimation problem for large‐scale general nonlinear processes by proposing a Kalman‐based approach. First, we formulate a linear full‐information estimation design within a distributed framework as the basis for developing our approach. Second, the analytical solution to the local optimization problems associated with the formulated distributed full‐information design is established, in the form of a recursive distributed Kalman filter algorithm. Then, the linear distributed Kalman filter is extended to the nonlinear context by incorporating successive linearization of nonlinear subsystem models, and the proposed distributed extended Kalman filter approach is formulated. We conduct rigorous analysis and prove the stability of the estimation error dynamics provided by the proposed method for general nonlinear processes consisting of interconnected subsystems. A chemical process example is used to illustrate the effectiveness of the proposed method and to justify the validity of the theoretical findings. In addition, the proposed method is applied to a wastewater treatment process for estimating the full‐state of the process with 145 state variables.