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The problem of filtering a signal from a linear time invariant system with white Gaussian observation and unknown driving noise bounded at each instant of time is considered. We review the minimax filter of Johansen and Berkovitz Pollard for the double integrator. While their solution is very elegant, the optimal filter is infinite dimensional. We show that nearly the same performance can be achieved by a two dimensional filter and we generalize this to other linear time invariant systems. This is joint work with Wei Kang.