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Estimation with Information Loss: Asymptotic Analysis and Error Bounds

Shi, Ling and Epstein, Michael and Tiwari, Abhishek and Murray, Richard M. (2005) Estimation with Information Loss: Asymptotic Analysis and Error Bounds. In: 2005 44th IEEE Conference on Decision and Control & European Control Conference. IEEE , Piscataway, NJ, pp. 1215-1221. ISBN 0-7803-9567-0.

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In this paper, we consider a discrete time state estimation problem over a packet-based network. In each discrete time step, the measurement is sent to a Kalman filter with some probability that it is received or dropped. Previous pioneering work on Kalman filtering with intermittent observation losses shows that there exists a certain threshold of the packet dropping rate below which the estimator is stable in the expected sense. That work assumes that packets are dropped independently between all time steps. However we give a completely different point of view. On the one hand, it is not required that the packets are dropped independently but just that the information gain π_g, defined to be the limit of the ratio of the number of received packets n during N time steps as N goes to infinity, exists. On the other hand, we show that for any given πg, as long as π_g> 0, the estimator is stable almost surely, i.e. for any given ε > 0, the error covariance matrix P_k is bounded by a finite matrix M, with probability 1 -ε. We also give explicit formula for the relationship between M and ε. We consider the case where the observation matrix is invertible.

Item Type:Book Section
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Murray, Richard M.0000-0002-5785-7481
Additional Information:© 2005 IEEE. Issue Date: 12-15 Dec. 2005; Date of Current Version: 30 January 2006. The authors are all equally contributed to this work.
Record Number:CaltechAUTHORS:20110825-140024412
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Official Citation:Ling Shi; Epstein, M.; Tiwari, A.; Murray, R.M.; , "Estimation with Information Loss: Asymptotic Analysis and Error Bounds," Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on , vol., no., pp. 1215- 1221, 12-15 Dec. 2005 doi: 10.1109/CDC.2005.1582324
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25102
Deposited On:25 Aug 2011 21:59
Last Modified:09 Nov 2021 16:29

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