This paper addresses the problem of blind identification in a set membership framework. Given a finite collection of noisy data and some a priori information about the sets of admissible plants and inputs, the objective is to (i) identify a suitable (model, input) pair that can explain the available experimental information, and (ii) provide a worst-case bound on the identification error. The main results of the paper consist in an analysis of the convergence properties of any interpolatory algorithm in the presence of unknown but bounded inputs and noise. In order to overcome the non convexity of the problem, additional results include an identification procedure to approximately check consistency between the a priori assumptions and the a posteriori experimental information, by sampling the set of admissible inputs. The proposed algorithm is illustrated with a practical application that involves tracking a human being in a sequence of video images.