Park and Rizzoni (1993) obtained closed-form expressions for detection filters; i.e. the structure of all detection filters for a given fault direction was defined. An important consequence of these results is that they permit the formation of the optimal detection filter problem, for optimization with respect to process and measurement noises. The necessary conditions for the existence of the optimal detection filter are obtained, and a numerical solution technique is shown to be feasible by virtue of the uniqueness of the detection filter gains. From an optimization point of view the problem can be regarded as optimal estimation with some structural constraints on the observer gain. This problem is solved for both the continuous-time and the discrete-time cases.