2018
DOI: 10.1002/rnc.4440
|View full text |Cite
|
Sign up to set email alerts
|

Numerical robustness of extended Kalman filtering based state estimation in ill‐conditioned continuous‐discrete nonlinear stochastic chemical systems

Abstract: This paper presents a case study investigation of numerical robustness of extended Kalman filters used for estimation of stochastic chemical systems with ill-conditioned measurements. Here, we consider both a batch reactor model and that of a continuously stirred tank reactor. Our purpose is to explore performance of extended Kalman filtering-based state estimators when the measurement model becomes increasingly ill conditioned. In this way, we determine numerically robust methods, which are suitable for accur… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1

Citation Types

1
16
0

Year Published

2019
2019
2023
2023

Publication Types

Select...
3
2

Relationship

2
3

Authors

Journals

citations
Cited by 31 publications
(17 citation statements)
references
References 71 publications
(206 reference statements)
1
16
0
Order By: Relevance
“…Also, each measurement vector pk,sk is supposed to be corrupted by a two‐dimensional normally distributed noise vk𝒩0,Rσ with the covariance matrix R σ =σ 2 I 2 depending on the ill‐conditioning parameter σ. We stress that measurements with the measurement‐noise‐covariance‐matrix R σ depending on the scalar σ are typical means in numerical stability studies of various KF algorithms including the continuous‐discrete ones . More precisely, these correspond to the third reason of ill‐conditioning in the list of Grewal and Andrews (page 209 of Reference ) because the matrix inversion fulfilled in the computation of the Kalman gain Wk will become more and more ill‐conditioned as σ→0.…”
Section: Numerical Examination and Discussionmentioning
confidence: 99%
See 2 more Smart Citations
“…Also, each measurement vector pk,sk is supposed to be corrupted by a two‐dimensional normally distributed noise vk𝒩0,Rσ with the covariance matrix R σ =σ 2 I 2 depending on the ill‐conditioning parameter σ. We stress that measurements with the measurement‐noise‐covariance‐matrix R σ depending on the scalar σ are typical means in numerical stability studies of various KF algorithms including the continuous‐discrete ones . More precisely, these correspond to the third reason of ill‐conditioning in the list of Grewal and Andrews (page 209 of Reference ) because the matrix inversion fulfilled in the computation of the Kalman gain Wk will become more and more ill‐conditioned as σ→0.…”
Section: Numerical Examination and Discussionmentioning
confidence: 99%
“…First, as samples of our new SR‐ACD‐EUKF and JSR‐ACD‐EUKF techniques depicted in Figure , we restrict ourselves to one method A.2(cu) based on the cubature parametrization and the other state estimator A.4(cl) implemented with the classical parametrization in this comparative study. Second, the additional variable‐stepsize continuous‐discrete filters under examination are abbreviated and listed as follows: M22‐EKF is the acronym of the CD‐EKF method grounded in the hybrid MDE solver M2(2) with local error control per unit step and the local error threshold ϵ loc :=10 −4 designed by Mazzoni (its implementation details and the entire state estimation algorithm are also presented in Kulikov and Kulikova (section 3.2.2 of Reference )); ESDIRK34‐EKF is the acronym of the CD‐EKF method grounded in the MDE solver ESDIRK3(4) with local error control and the local error threshold ϵ loc :=10 −4 designed by Jørgensen et al (its implementation details and the entire state estimation algorithm are also presented in Kulikov and Kulikova (section 3.2.3 of Reference )); ODE45‐EKF is the acronym of the CD‐EKF method grounded in the MATLAB code ode45 with the options AbsTol=10 −4 , RelTol=10 −4 and MaxStep=0.1 used for solving the arisen MDE (its implementation details and the entire state estimation algorithm are presented in Kulikov and Kulikova (section 3.2.1 of Reference )); ODE45‐EKF(sr) is the acronym of the square‐root variant of the state estimator ODE45‐EKF, which is based on solving the arisen square‐root MDE by the MATLAB code ode45 with the options AbsTol=10 −4 , RelTol=10 −4 and MaxStep=0.1 (see further details and explanation in Kulikov and Kulikova (section 3.2 of Reference )); ODE45‐CKF(m) is the acronym of the square‐root CD‐CKF method grounded in the MATLAB code ode45 with the options AbsTol=10 −4 , RelTol=10 −4 and MaxStep=0.1 used for solving the arisen square‐root MDE (equations (20) of Reference ) (see further details and explanation in Kulikov and Kulikova (section 2 of Reference )); ODE45‐CKF(v) is the acronym of the square‐root CD‐CKF method grounded in the MATLAB code ode45 with the options AbsTol=10 −4 , RelTol=10 −4 and MaxStep=0.1 employed for solving the arisen cubature‐point differential equations (equation (35) of Reference ) (see further details and explanation in Kulikov and Kulikova (section 2 of Reference )). …”
Section: Numerical Examination and Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…[9][10][11] In what follows, we focus on the second-type methods because of their flexibility and self-adaptation facility, as motivated recently by Kulikov and Kulikova. [12][13][14][15] We stress that the mentioned filters are also referred to as discretized-linearization ones by other authors. 7,16,17 In particular, the continuous-discrete Kalman filtering approach benefits from using adaptive variable-stepsize ODE solvers with automatic discretization error control employed for accurate calculations of the predicted means and covariances in every time-update step.…”
Section: Introductionmentioning
confidence: 99%
“…Further particulars and properties of the matrix product (13) are elaborated in full detail in Reference 38, for example. In addition, this product is fulfilled by the built-in command kron in MATLAB.…”
mentioning
confidence: 99%