Moore-Penrose-pseudo-inverse-based Kalman-like filtering methods for estimation of stiff continuous-discrete stochastic systems with ill-conditioned measurements

This study aims at exploring numerical stability properties of software sensors used in chemical and other engineering. These are utilised for evaluation of variables and/or parameters of plants, which are not measurable by technical devices. Software sensors are often grounded in the extended Kalman filtering (EKF) technique. A conventional continuous-discrete stochastic system consists of an Ito-type stochastic differential equation representing the plant's dynamics and a discrete-time equation linking the model's state to measurements. Here, the authors focus on the numerical stability of EKF-type methods, which are applicable to ill-conditioned stiff stochastic models arisen in applied science and engineering. They explore filters' accuracies when the inverse matrices are replaced with the Moore-Penrose pseudo-inverse ones in their measurement updates. This investigation is fulfilled within the authors' ill-conditioned stochastic Oregonator scenario and evidences that the pseudo-inversion indeed resolves many performance problems in some non-square-root methods when the stochastic system is sufficiently ill-conditioned. However, it fails to improve the accuracy in the mildly ill-conditioned case. Eventually, only the square-root nested implicit Runge-Kutta-based filters are found out to be accurate and robust in their examination and, hence, to be the methods of choice.

CEMAT - Center for Computational and Stochastic Mathematics