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Probabilistic performance of state estimation across a lossy network

Epstein, Michael and Shi, Ling and Tiwari, Abhishek and Murray, Richard M. (2008) Probabilistic performance of state estimation across a lossy network. Automatica, 44 (12). pp. 3046-3053. ISSN 0005-1098. doi:10.1016/j.automatica.2008.05.026. https://resolver.caltech.edu/CaltechAUTHORS:EPSa08

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Abstract

We consider a discrete time state estimation problem over a packet-based network. In each discrete time step, a measurement packet is sent across a lossy network to an estimator unit consisting of a modified Kalman filter. Using the designed estimator algorithm, the importance of placing a measurement buffer at the sensor that allows transmission of the current and several previous measurements is shown. Previous pioneering work on Kalman filtering with intermittent observation losses is concerned with the asymptotic behavior of the expected value of the error covariance, i.e. E [P-k] < ∞ as k → ∞. We consider a different performance metric, namely a probabilistic statement of the error covariance Pr[P-k ≤ M] ≥ 1 - ε, meaning that with high probability the error covariance is bounded above at any instant in time. Provided the estimator error covariance has an upper bound whenever a measurement packet arrives, we show that for any finite M this statement will hold so long as the probability of receiving a measurement packet is nonzero. We also give an explicit relationship between M and E and provide examples to illustrate the theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.automatica.2008.05.026DOIUNSPECIFIED
ORCID:
AuthorORCID
Murray, Richard M.0000-0002-5785-7481
Additional Information:Copyright © 2008 Elsevier. Received 30 November 2006; revised 21 December 2007; accepted 18 May 2008. Available online 28 November 2008. This paper was not presented at any IFAC meeting. This paper was recommended for publication in reivsed form by Associate Editor George Yin under the direction of Editor Ian R. Petersen.
Subject Keywords:Kalman filtering; Networked control
Issue or Number:12
DOI:10.1016/j.automatica.2008.05.026
Record Number:CaltechAUTHORS:EPSa08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:EPSa08
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13067
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:16 Jan 2009 19:56
Last Modified:08 Nov 2021 22:35

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