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

© The Institution of Engineering and Technology
Received 12/11/2018, Accepted 25/04/2019, Revised 05/04/2019, Published 01/05/2019

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.

Inspec keywords: approximation theory; estimation theory; state estimation; Gaussian processes; mixture models; data communication; probability

Other keywords: approximate optimal estimation; state estimation; Gaussian mixture; lossy networks; estimation problem; Riccati-like equation; Kullback-Leiber divergence; approximate optimal estimator; both-side packet dropouts; KLD estimator

Subjects: Communication system theory; Interpolation and function approximation (numerical analysis); Other topics in statistics

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