Non-statistical statement and solution of one filtering problem

A filtering problem is solved for a discrete time process which is observed in a mixture with an additive disturbance. The process is formed from the noise at the input of a linear dynamic element. The disturbance and noise are regarded as limited. No assumption is made on the existence of laws of disturbance and noise distribution. A solution is obtained as recurrent relations for parameters of multiple estimates which has the form of multidimensional ellipsoids in the state space of the process being filtered.