Approximate optimal estimation based on Kullback–Leibler divergence for lossy networks without acknowledgement

• Published in: IET control theory & applications Vol. 13; no. 12; pp. 1804 - 1813
• Main Authors: Liang, Shi, Qiu, Chan, Liu, Zhenyu, Peng, Xiang, Liu, Daxin, Tan, Jianrong
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 13.08.2019
• Subjects: approximate optimal estimation; approximate optimal estimator; approximation theory; both‐side packet dropouts; data communication; estimation problem; estimation theory; Gaussian mixture; Gaussian processes; KLD estimator; Kullback‐Leiber divergence; lossy networks; mixture models; probability; Research Article; Riccati‐like equation; state estimation; approximation theory; KLD estimator; estimation theory; approximate optimal estimation; probability; approximate optimal estimator; estimation problem; Riccati-like equation; Kullback-Leiber divergence; Gaussian processes; lossy networks; state estimation; data communication; Gaussian mixture; both-side packet dropouts; mixture models
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2018.6302

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.