Comparison of Unscented Kalman Filter Design for Agricultural Anaerobic Digestion Model
Simon Hellmann, Terrance Wilms, Stefan Streif, Sören Weinrich
TL;DR
The paper investigates reliable nonlinear state estimation for agricultural anaerobic digestion by comparing multiple UKF designs, including unconstrained, constrained, augmented, and fully augmented variants, on a simplified ADM1-R4-Core model. It finds that a constrained UKF with additive noise yields the highest state-estimation accuracy, while unconstrained UKFs offer faster runtimes; runtime can be dramatically reduced by precomputing gradients/Hessians and reformulating the constraint optimization as a quadratic program. Gradient and Hessian information further accelerates NLP/QP optimization, enabling more practical real-time performance for certain variants, especially with linear outputs. The work delivers actionable guidance on algorithmic choices, balancing estimation accuracy against computational cost, and discusses limitations and avenues for applying UKFs to real measurement data and higher-order ADM1-like models for demand-driven AD operation.
Abstract
Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear state estimation, and there exist numerous variants of UKF implementations, treating state constraints, improvements of numerical performance and different noise cases. So far, however, a unified comparison of proposed methods emphasizing the algorithmic details is lacking. The present study thus examines multiple unconstrained and constrained UKF variants, addresses aspects crucial for direct implementation and applies them to a simplified AD model. The constrained UKF considering additive noise delivered the most accurate state estimations. The long run time of the underlying optimization could be vastly reduced through pre-calculated gradients and Hessian of the associated cost function, as well as by reformulation of the cost function as a quadratic program. However, unconstrained UKF variants showed lower run times at competitive estimation accuracy. This study provides useful advice to practitioners working with nonlinear Kalman filters by paying close attention to algorithmic details and modifications crucial for successful implementation.