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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e-mail: wwli@mechanics.ucsd.edu
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March 2007
Technical Papers
State Estimation With Finite Signal-to-Noise Models via Linear Matrix Inequalities
Weiwei Li,
Weiwei Li
Mechanical and Aerospace Engineering Department,
e-mail: wwli@mechanics.ucsd.edu
University of California San Diego
, La Jolla, CA 92093-0411
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Robert E. Skelton,
Robert E. Skelton
Mechanical and Aerospace Engineering Department,
University of California San Diego
, La Jolla, CA 92093-0411
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Emanuel Todorov
Emanuel Todorov
Cognitive Science Department,
University of California San Diego
, La Jolla, CA 92093-0515
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Weiwei Li
Mechanical and Aerospace Engineering Department,
University of California San Diego
, La Jolla, CA 92093-0411e-mail: wwli@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 92093-0515J. Dyn. Sys., Meas., Control. Mar 2007, 129(2): 136-143 (8 pages)
Published Online: July 15, 2006
Article history
Received:
November 28, 2005
Revised:
July 15, 2006
Citation
Li, W., Skelton, R. E., and Todorov, E. (July 15, 2006). "State Estimation With Finite Signal-to-Noise Models via Linear Matrix Inequalities." ASME. J. Dyn. Sys., Meas., Control. March 2007; 129(2): 136–143. https://doi.org/10.1115/1.2432358
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