Open AccessOptimal linear filtering design for discrete‐time systems with cross‐correlated stochastic parameter matrices and noises
Author(s) -
Wang Wei,
Zhou Jie
Publication year - 2017
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.2017.0425
Subject(s) - decorrelation , control theory (sociology) , kalman filter , estimator , linear system , discrete time and continuous time , mathematics , filter (signal processing) , transformation (genetics) , stochastic process , computer science , algorithm , statistics , mathematical analysis , control (management) , artificial intelligence , biochemistry , chemistry , computer vision , gene
This study investigates the design of an optimal linear estimator for a class of discrete‐time linear systems with correlated stochastic parameter matrices and noises. The considered systems are endowed with the following two main features: (i) cross‐correlated stochastic matrices involved in the state and observation equations are assumed and (ii) the process and observation noises have cross‐correlation at the same time instant. A decorrelation framework is established to reconstruct such systems. With the equivalent transformation of original dynamic systems resulting from decorrelating operations, the optimal linear recursive filter in the minimum mean square error sense is developed by employing the results of Kalman filtering. The discrete‐time linear systems with multiple packet dropouts are modelled as a particular case, and then the proposed filter is applied directly to estimate the system state, while a comparative analysis between the new method and the existing approaches is provided. Simulations demonstrate the effectiveness of the presented algorithm.