Optimal state estimation in the presence of communication costs and packet drops
Consider a first order, linear and time-invariant discrete time system driven by Gaussian, zero mean white process noise, a pre-processor that accepts noisy measurements of the state of the system, and an estimator. The pre-processor and the estimator are not co-located, and, at every time-step, the...
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Published in | 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton) pp. 160 - 169 |
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Main Authors | , |
Format | Conference Proceeding |
Language | English |
Published |
IEEE
01.09.2009
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Subjects | |
Online Access | Get full text |
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Summary: | Consider a first order, linear and time-invariant discrete time system driven by Gaussian, zero mean white process noise, a pre-processor that accepts noisy measurements of the state of the system, and an estimator. The pre-processor and the estimator are not co-located, and, at every time-step, the pre-processor sends either a real number or an erasure symbol to the estimator. We seek the pre-processor and the estimator that jointly minimize a cost that combines three terms; the expected estimation error and a communication cost. The communication cost is zero for erasure symbols and a pre-selected constant otherwise. We show that the optimal pre-processor follows a symmetric threshold policy, and that the optimal estimator is a Kalman-like filter that updates its estimate linearly in the presence of erasures. Other existing work has adopted such a Kalman-like structure, but this paper is the first to prove its optimality. |
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ISBN: | 9781424458707 1424458706 |
DOI: | 10.1109/ALLERTON.2009.5394899 |