Exact Finite Dimensional Filters for Cryptodeterministic Systems

It is shown that the only cryptodeterministic estimation problems with exact finite dimensional filters are those in which the input-output model is a "subsystem" of a linear system. This generalizes a result of 0. Hijab [1], which covers the special case of time-invariant plant models. Moreover, the proof is much simpler than Hijab\´s, as it is an elementary calculation using Bayes rule and the generalized Fisher-Darmois-Koopman-Pitman theorem.