Open AccessApproximate optimal estimation based on Kullback–Leibler divergence for lossy networks without acknowledgement
Author(s) -
Liang Shi,
Qiu Chan,
Liu Zhenyu,
Peng Xiang,
Liu Daxin,
Tan Jianrong
Publication year - 2019
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.2018.6302
Subject(s) - estimator , mathematics , divergence (linguistics) , stability (learning theory) , mathematical optimization , optimal estimation , lossy compression , control theory (sociology) , efficient estimator , acknowledgement , kullback–leibler divergence , computer science , statistics , minimum variance unbiased estimator , artificial intelligence , linguistics , philosophy , control (management) , computer security , machine learning
This study is concerned with the estimation problem for systems with both missing inputs and measurements but without any acknowledgement mechanism. The acknowledgement mechanism is used to provide the estimator with the status information that whether the input is lost or not during the transmission. Affected by the missing input with unknown status information, the probability density function of system state is a Gaussian mixture, of which the number of terms is growing exponentially with time. Two major limitations of state estimation for these systems are (i) the computational inefficiency of the optimal estimation and (ii) the undetermined stability of the approximate optimal estimation. Thus, the aim of this study is to design an estimator such that it can enhance computational efficiency greatly while its stability can be guaranteed simultaneously. Using Kullback–Leiber divergence, an approximate optimal estimator, which is named as the KLD estimator, is developed as an efficient alternative to the optimal one. By establishing a Riccati‐like equation subject to both‐side packet dropouts, a sufficient and necessary condition is given for the stability of the KLD estimator. It reveals an interesting fact that the proposed approximate optimal estimator has the same stability as the optimal estimator.