State estimation for a dynamical system described by a linear equation with unknown parameters
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.
English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 2, pp 214-235.
Citation Example: Zhuk S. M. State estimation for a dynamical system described by a linear equation with unknown parameters // Ukr. Mat. Zh. - 2009. - 61, № 2. - pp. 178-194.