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 It o ^ -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.