Open AccessEquivalence of recursive three‐step filter and infinity augmented Kalman filter for linear discrete‐time stochastic systems with direct feedthrough
Author(s) -
Ding Bo,
Zhang Tianping
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.1387
Subject(s) - control theory (sociology) , kalman filter , mathematics , feedthrough , equivalence (formal languages) , filter (signal processing) , alpha beta filter , extended kalman filter , discrete time and continuous time , covariance , recursive filter , noise (video) , computer science , filter design , engineering , root raised cosine filter , moving horizon estimation , statistics , artificial intelligence , control (management) , discrete mathematics , electrical engineering , computer vision , image (mathematics)
In this study, the recursive three‐step filter method introduced by Gillijns and Moor (2007) is proved strictly to be equivalent to the augment Kalman filter (AKF) when the covariance of process noise about the input approaches infinity. This result indicates that if the information about the exogenous input is unknown, the AKF can also be used to simultaneously obtain the state and exogenous input estimation. Numerical examples illustrate the authors' main results.