This paper deals with conditional central estimators in a set membership setting. The role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering, in contexts in which disturbances are described through norm bounds, are reducible to the computation of conditional central algorithms. The conditional Chebishev center problem is solved for the case when energy norm-bounded disturbances are considered, A closed-form solution is obtained by finding the unique real root of a polynomial equation in a semi-infinite interval.