Approximate optimal estimation based on Kullback–Leibler divergence for lossy networks without acknowledgement. Issue 12 (26th June 2019)

• Record Type: Journal Article
• Authors: Liang, Shi; Qiu, Chan; Liu, Zhenyu; Peng, Xiang; Liu, Daxin; Tan, Jianrong
• Is Part Of: IET control theory & applications. Volume 13:Issue 12(2019)
• Page Start: 1804
• Page End: 1813
• Publication Date: 2019-06-26
• Subjects: Gaussian processes -- state estimation -- approximation theory -- probability -- mixture models -- estimation theory -- data communication; approximate optimal estimator -- approximate optimal estimation -- estimation problem -- state estimation -- KLD estimator -- Gaussian mixture -- Kullback‐Leiber divergence -- Riccati‐like equation -- both‐side packet dropouts -- lossy networks; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2018.6302
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : 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.