On minmax filtering over observations with a vector discontinuous measure

The minmax filtering equations over observations with a vector discontinuous measure follow from the minmax filtering equations over continuous observations given in Bertsekas and Rhodes (1971) by virtue of replacing an absolutely continuous function u(t) by a bounded variation one in accordance with an observation equation. No additional computation is needed. The minmax filtering equations over vector discrete observations follow from the minmax filtering equations over continuous ones by virtue of transferring to observations with a vector discontinuous measure and assuming a bounded variation function u(t) to be piecewise constant. The definition of a solution to the system of filtering equations ensures the stability of the optimal estimate with respect to small variations of a vector bounded variation function u(t) and, therefore, observations