In the context of set membership identification the feasible parameter set is defined as the set of plant parameters which are consistent with the model structure, the assumptions on (unknown but bounded) disturbances and all available measurements. It appears more convenient in practice to build an outer-bounding set, typically an ellipsoid, a parallelotope or an orthotope. This paper describes methods for adjusting set membership techniques, which are only applicable to equation error models, to the case of output error models. A method for building the optimal outer-bounding orthotope is also proposed. Equation error and output error methods are evaluated on the example of the estimation of a missile state space model in the presence of measurement noise and neglected dynamics.