Journal
IET CONTROL THEORY AND APPLICATIONS
Volume 12, Issue 16, Pages 2205-2212Publisher
WILEY
DOI: 10.1049/iet-cta.2018.5404
Keywords
Kalman filters; Runge-Kutta methods; filtering theory; matrix algebra; differential equations; stochastic systems; nonlinear filters; continuous-discrete stochastic system; ill-conditioned measurements; numerical stability properties; software sensors; extended Kalman filtering technique; discrete-time equation; EKF-type methods; stiff stochastic models; inverse matrices; nonsquare-root methods; square-root nested implicit Runge-Kutta-based filters; stochastic differential equation; Moore-Penrose-pseudoinverse-based Kalman-like filtering method
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Funding
- Portuguese National Funds through the Fundacao para a Ciencia e a Tecnologia (FCT) [UID/Multi/04621/2013]
- Investigador FCT 2013 programme
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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 continuousdiscrete 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.
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