Linear recurrent filtering of dynamic discrete time processes with partial information on the perturbing processes

Minimax filtering of phase coordinates is discussed for linear dynamic discrete time processes with partial information available on the perturbing processes whose variance is constrained. Necessary and sufficient conditions are provided for the saddle point with total quadratic and local criteria and recurrent equations of the minimax linear filter with boundary conditions true only of the beginning of the observation interval. An example is provided of solving a minimax linear filtering problem for a second-order dynamic process.