We investigate the state estimation problem for a dynamical system described by a linear operator equation with unknown parameters in a Hilbert space. In the case of quadratic restrictions on the unknown parameters, we propose formulas for a priori mean-square minimax estimators and a posteriori linear minimax estimators. A criterion for the finiteness of the minimax error is formulated. As an example, the main results are applied to a system of linear algebraic-differential equations with constant coefficients.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 2, pp. 178-194, February, 2009.
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Zhuk, S.M. State estimation for a dynamical system described by a linear equation with unknown parameters. Ukr Math J 61, 214–235 (2009). https://doi.org/10.1007/s11253-009-0210-4
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DOI: https://doi.org/10.1007/s11253-009-0210-4