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TECHNICAL PAPERS

State Estimation With Finite Signal-to-Noise Models via Linear Matrix Inequalities

[+] Author and Article Information
Weiwei Li1

Mechanical and Aerospace Engineering Department, University of California San Diego, La Jolla, CA 92093-0411wwli@mechanics.ucsd.edu

Robert E. Skelton

Mechanical and Aerospace Engineering Department, University of California San Diego, La Jolla, CA 92093-0411

Emanuel Todorov

Cognitive Science Department, University of California San Diego, La Jolla, CA 92093-0515

1

Corresponding author.

J. Dyn. Sys., Meas., Control 129(2), 136-143 (Jul 15, 2006) (8 pages) doi:10.1115/1.2432358 History: Received November 28, 2005; Revised July 15, 2006

This paper presents estimation design methods for linear systems whose white noise sources have intensities affinely related to the variance of the signal they corrupt. Systems with such noise sources have been called finite signal-to-noise (FSN) models, and the results provided in prior work demonstrate that estimation problem for FSN systems (estimating to within a specified covariance error bound) is nonconvex. We shall show that a mild additional constraint for scaling will make the problem convex. In this paper, sufficient conditions for the existence of the state estimator are provided; these conditions are expressed in terms of linear matrix inequalities (LMIs), and the parametrization of all admissible solutions is provided. Finally, a LMI-based estimator design is formulated, and the performance of the estimator is examined by means of numerical examples.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Estimation error of FSN filter (solid line corresponds to the error of state variable x1, dashed-dotted line corresponds to the estimation error of state variable x2)

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Figure 2

Estimation error of Kalman filter (solid line corresponds to the error of state variable x1, dashed-dotted line corresponds to the estimation error of state variable x2)

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Figure 3

Optimal performance as a function of information quality

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Figure 4

Four mass mechanical system with springs and dampers

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Figure 5

Performance as a function of σw+σv corresponding to the two different noise contributions (Star curve corresponds to the output covariance of the first estimation error, diamond curve corresponds to the output covariance of the second estimation error)

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Figure 6

Estimation error for hand movement system, each curve corresponds to the error of each state variable

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