Chung et al. have proposed the conservative and the optimistic limited lookahead policy (LLP) supervisors in the limited lookahead setting. Recently, Kumar et al. have proposed the extension based Limited lookahead (ELL) supervisor and the modified ELL supervisor which use estimates of the system behavior. We consider the estimate based limited lookahead supervision in the case that a specification is described as a closed language. First, we consider the case that the ELL supervisor is used for a closed language specification although it is less permissive than the modified ELL supervisor. Then the ELL supervisor is equivalent to the LLP supervisors as shown in this note. We next show that the N + 1-tree representing the future behavior of the system suffices for the estimate based supervisor to compute a control action. Moreover, a closed-form expression for the language generated under the estimate based supervision is obtained.