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