Experiences implementing the extended Kalman filter on an industrial batch reactor

The unscented filter as an alternative to the EKF for nonlinear state estimation: a simulation case study

“…These concerns are especially acute in complex industrial set-ups (Wilson, Agarwal, & Rippin, 1998). Although higher order Kalman filters exist, they are more difficult to implement and prone to instability.…”

Practical implementation of extended Kalman filtering in chemical systems with sparse measurements

“…They elaborate at least two approaches for constructing EKF schemes, which can lead to a great variety of practical filtering algorithms based on ordinary or stochastic differential equation numerical methods. Thus, some criticism published on performance of the EKF in chemical systems for o ine models and industrial applications [6,12,33,35,36,39,40] does not mean that all other implementations of this method will also fail, as shown below.…”

High-order accurate continuous-discrete extended Kalman filter for chemical engineering

“…Also, all realizations of w(t), v k and x 0 are assumed to be taken from mutually independent Gaussian distributions. Thus, the continuousdiscrete stochastic state-space model (1), (2) is best suited for state estimation in chemical systems and widely used in chemistry research and industrial applications (see, for instance, Wilson et al (1998); Soroush (1998); Dochain (2003); Rawlings (2002, 2005); Jørgensen (2007); Rawlings and Bakshi (2006); Romanenko and Castro (2004); ). Concerning state estimation algorithms, we have to remark that, at present, there exist a great variety of different methods starting from a rigorous probabilistic approach solving Kolmogorov's (Fokker-Planck's) forward equation (as discussed, for instance, in Jazwinski (1970); Maybeck (1982)) till approximate approaches including various nonlinear modifications and implementations of the well-known Kalman filter (see Lewis (1986); Singer (2002Singer ( , 2006; Julier et al (2000); Julier and Uhlmann (2004); Ito and Xiong (2000); Nørgaard et al (2000); Haykin (2008, 2009); Arasaratnam et al (2010); Frogerais et al (2012); Jørgensen et al (2007); Kulikov and Kulikova (2014); Rawlings and Bakshi (2006); Romanenko and Castro (2004); ; Schneider and Georgakis (2013)) as well as optimization based approaches usually referred to as the moving horizon estimation (studied by Jang et al (1986); Rao et al (2001); Rawlings (2002, 2005); Rawlings and Bakshi (2006) and so on).…”

“…Despite EKF's popularity, this method has been criticized on its performance for offline models and industrial applications in chemical research by Wilson et al (1998); Soroush (1998); Dochain (2003); Rawlings (2002, 2005); Jørgensen (2007); Rawlings and Bakshi (2006); Romanenko and Castro (2004); . For example, Rawlings (2002, 2005) report that their EKF fails for two types of chemical reactors meaning that wrong steady-states are calculated and negative concentrations are observed after convergence, which are of no physical sense.…”